EDHEC Survey of the Asset and Liability …...An EDHEC-Risk Institute Publication 3 EDHEC Survey of...

EDHEC Survey of the Asset and Liability Management Practices

of European Pension Funds June 2010

An EDHEC-Risk Institute Publication

Institute

Sponsored by:

2

We thank AXA Investment Managers for its support for our research.

We express our warm thanks to Lin Tang for research assistance and to Noël Amenc, Lionel Martellini, and Vincent Milhau for very useful comments.

Printed in France, June 2010. Copyright© EDHEC 2010.The opinions expressed in this study are those of the authors and do not necessarily reflect those of EDHEC Business School.The authors can be contacted at [email protected].

Abstract ....................................................................................................................5

Executive Summary ...............................................................................................7

Introduction ..........................................................................................................21

1. Design of Asset/Liability Management Strategies .....................................25

2. Risk and Performance Measurement ............................................................59

3. Does Being Knowledgeable Help? .................................................................69

4. Bibliography ......................................................................................................75

5. Appendices ........................................................................................................79

About EDHEC-Risk Institute ...............................................................................85

About AXA Investment Managers .....................................................................89

EDHEC-Risk Institute Publications and Position Papers (2007-2010) .........91

Table of Contents

3An EDHEC-Risk Institute Publication

EDHEC Survey of the Asset and Liability Management Practices of European Pension Funds — June 2010

This survey has been taken as part of the second year of the AXA Investment Managers "Regulation and Institutional Investment" research chair at EDHEC-Risk Institute. The objective of this research chair is to increase institutional investors' awareness not only of the challenges posed to financial management by regulatory developments but also of research advances in asset management and asset/liability management (ALM) that enable them to meet these new regulatory challenges.

The results of our pan-European survey suggest that, despite the professionalisation of ALM in pension funds and their service providers, risk-controlled strategies may not have been taken up widely enough. That these strategies are understood by only half of respondents may account, in part, for the lack of widespread adoption.

The recent underfunding of sophisticated pension funds suggests that there are biases that prevent many pension funds from managing their assets optimally. In theory, rule-based risk-controlled investing and discretionary economic capital should lead to the same insurance of risks. One of the theoretical drawbacks of economic capital is that it is a myopic strategy. A practical drawback is that the reliance on discretionary investment policies involves the risk of delays and of behavioural biases that distort the theoretical strategy (pension funds may be reluctant to sell at a loss, even though they rely essentially on market values and should, in theory, pay no attention to book values).

In general, because rule-based strategies are compatible with economic capital and prudential risk-based regulations, we recommend more reliance on these strategies. Very simple and intuitive methods that require little or no mathematical background can prove to be efficient means of insuring risks.

The survey also suggests that pension funds have a blinkered vision of risks; only a minority, for instance, manage accounting risk and sponsor risk. The reluctance to manage their risks exhaustively can be seen as increasing risk to no purpose and may also lead to inappropriate volatility in the sponsor’s books.

The survey suggests, finally, that pension funds make insufficient efforts to measure the performance of their portfolios and to assess the suitability of the design of their strategies.

We would particularly like to thank our partners at AXA Investment Managers for their support of our research and the publishing team ably led by Laurent Ringelstein. We wish you an agreeable and informative read.

Noël AmencProfessor of FinanceDirector of EDHEC-Risk Institute

Foreword

4 An EDHEC-Risk Institute Publication


About the Author

Samuel Sender has participated in the activities of EDHEC-Risk Institute since 2006, first as a research associate—at the same time he was a consultant to financial institutions on ALM, capital and solvency management, hedging strategies, and the design of associated tools and methods. He is now a full-time applied research manager at EDHEC Risk Institute. He has a degree in statistics and economics from ENSAE (Ecole Nationale de la Statistique et de l'Administration Economique) in Paris.


Abstract



EDHEC recently took a survey of pension funds, their advisers, regulators, and fund managers. One hundred twenty-nine of these asset/liability management (ALM) specialists, representing assets under management (AUM) of around €3 trillion, responded to the survey. Pension funds and their sponsors account for approximately €0.9 trillion.

The first challenge for a pension fund involves meeting its liability by fully or partially hedging it away. The survey suggests that the liability-hedging portfolio (LHP) is modelled imprecisely at 45% of pension funds.

The second challenge for pension funds is to gain access to performance through optimal diversification within and between asset classes. Most respondents use market indices to define the investment benchmarks of investment funds, even though market indices are weighted by capitalisation and are known to be highly inefficient. In addition, although they are the longest-term investors and are not subject to liquidity risk, pension funds invest relatively little in potentially illiquid assets.

The last challenge for pension funds is to respect their minimum funding ratios by insuring risks away. To manage prudential constraints, 28% of respondents use risk-controlled investing (RCI) strategies, whereas 56% use economic/regulatory capital. Like RCI, economic capital relies on the measure of a risk budget and of a surplus. Economic capital, however, involves a discretionary, rather than rule-based, investment strategy, and possible delays. We thus recommend that pension funds rely more heavily on rule-based strategies

in their economic capital models.

The majority of respondents have a blinkered view of their risks: accounting risk (the volatility from the pension fund in sponsor’s books) is managed by only 33% of respondents, and more than 50% ignore sponsor risk (the risk of a bankrupt sponsor’s leaving a pension fund with deficits).

Last, pension funds generally do not assess the adequacy of their ALM, a failing that may lead to sub-optimal decisions’ being taken again and again.

Abstract


2. xxxxxxxxxxxxxxxxxxExecutive Summary




MotivationBrinson, Hood, and Beebower’s (1986) conclusion that more than 90% of the average time-variation in returns is explained by strategic asset allocation has led to widespread recognition of the importance of asset allocation to investment returns and thus to pension fund performance.

Since their study, asset management (AM) and asset/liability management (ALM) practices have undergone marked changes, as many institutions now allocate significant shares of their portfolios to alternative assets such as listed and unlisted real estate, commodities, infrastructure, hedge funds.

The recognition that pension funds seek first to cover their liabilities and then to generate performance has led to formalisation of financial techniques for the asset and liability management of pension funds; portfolios are constructed with a liability-hedging portfolio to cover liabilities and a performance-seeking portfolio to generate performance. In addition to financial risk, pension funds are subject to non-hedgeable risks, usually biometric risks (mainly longevity risk). Tentative steps to create a market for the transfer of these risks, in the form of CAT bonds, longevity swaps, or securitisation, have also been taken. Since the 1990’s, pension fund regulation has grown considerably stricter. The 2003 European directive for pension funds, the IORP directive, allows underfunding for an undefined “limited period of time” and in the main requires a realisable recovery plan. Some countries, such as the Netherlands, adopted a risk-based prudential framework inspired by Solvency II, the prudential

regulation of insurance companies. The Dutch FTK requires a minimum funding ratio of 105% plus buffers against market risks. Although regulation was temporarily relaxed after the 2008 crisis, the overall trend has been towards tightening prudential regulations; at the same time, stricter accounting standards have made an impact on the accounts of sponsors of corporate pension funds.

Stricter regulations have led to the development of risk-insurance techniques that focus on risk control through state-dependent asset allocation to ensure that minimum funding constraints are respected.

However, no representative overview of the ALM practices of pension funds is currently available, since most surveys merely review the asset holdings of pension funds. This survey examines the ways ALM at pension funds makes use of modern investment management techniques. In short, we assess the ways European pension funds define investment policy, how they implement it, and how the performance of the investment policy is analysed.

We will thus shed light not only on the conception of the ALM strategy but also on the way it is implemented. This survey allows pension fund managers to compare their strategies, techniques, and organisation with those of their peers, and, above all, to take stock of any gaps between their practices and best practices. It is our hope that it will also spark dialogue between research and industry.

EDHEC's recent survey of pension funds, their advisers, regulators, and fund managers

Executive Summary



elicited responses from one hundred twenty-nine of these asset/liability management (ALM) specialists, representing assets under management (AUM) of around €3 trillion, responded to the survey. Pension funds and their sponsors account for approximately €0.9 trillion. Pension fund stakeholders (trustees, pension funds, their sponsors, and fiduciary managers) work, in the main, in ALM, risk management, or investing.

What is your field of expertise (pension fund stakeholders)?

Non-responseLiabilitiesInvestmentsRisk managementALMReportingFund managementDerivatives, structured products, or dynamic strategies

1.4%

38.4%

17.8%

12.3%

21.9%

1.4%

5.5%1.4%

ALM is a dual challenge: liabilities must be covered and performance must be generated. In addition, pension funds must respect their minimum funding ratios, or, more broadly, achieve their goals. Covering liabilities requires hedging risks away by defining a liability-hedging portfolio; generating performance in efficient portfolios requires diversification in a performance-seeking portfolio; ensuring that minimum funding ratios and other constraints are respected at all times requires insuring risk away.

After a brief description of the profile of respondents, in the first section, we provide a brief overview of existing ALM techniques and for each of the relevant fields—hedging, generating performance, and insuring risks—we show the extent to which respondents understand and use the relevant techniques by summarising their answers to the online questionnaire used for this research; we also comment on their portfolio holdings. In the second section we analyse risk and performance measurement techniques and practices, following the same methodology. Finally, we conclude.

Analysis of ALM practices in the European pension fund industryThe table below provides a summary of the main answers to the survey for all respondents as well as for the three main geographies:1. The United Kingdom, with its mix of traditional defined-benefit (DB) and full defined-contribution (DC) schemes.2. Northern European countries, including the Netherlands, characterised by hybrid pension schemes and regulations inspired by Solvency II and economic capital models—often referred to as traffic-light systems in these countries.3. Core European countries, such as Germany and Switzerland, with somewhat more traditional pension regulation.

“Total” includes all respondents, those previously mentioned and a few outside Europe.

Executive Summary



Summary of characteristics of main geographies

Hedging risk away and the liability-hedging portfolio Respondents in continental Europe generally have hybrid liabilities (28% in core Europe and 71% in Northern Europe), a reflection of the shift from traditional defined benefits to more hybrid forms such as funds with conditional indexation liability (some form of guarantee is almost always required). Hybrid schemes do not exist in the UK and DB pension funds have been closed (Amenc, Martellini, and Sender 2009).

The first challenge for pension funds involves covering their liability by hedging it away. Hedging liabilities away requires that a liability-hedging portfolio, a liability benchmark whose focus is on replication and which takes the definition and the characteristics of the liability as the main input, be defined. Deterministic cash flows or cash flows indexed to inflation can be hedged perfectly, but hedging more generally involves matching the

Executive Summary

Question UK Core Europe

Northern Europe

(incl. the Netherlands)

Total sample

Liabilities and LHP % of hybrid schemes 0% 23% 71% 35%

% having defined an LHP 75% 63% 53% 62%

% allocating more than 20% to inflation derivatives 40% 12% 13% 24%

% allocating more than 20% to inflation-linked assets 64% 30% 39% 32%

% using more than 20% swap contracts 60% 33% 54% 40%

LDI - static risk budgets

% that use LDI 71% 46% 52% 46%

% that use surplus optimisation 14% 25% 29% 21%

% that use economic capital 57% 21% 33% 30%

Performance-seeking portfolio

Average share of equities in PSP 34% 27% 40% 32%

Average cumulative share of private equity, hedge funds, and infrastructure in PSP “illiquid assets”

19% 15% 15% 16%

Risk insurance Master RCI techniques 77% 61% 61% 56%

Currently use RCI techniques 54% 44% 40% 41%

Use RCI to manage prudential risks 17% 18% 24% 28%

Use economic capital to manage prudential risks 25% 56% 52% 56%

Holistic view? Model sponsor risk 62% 42% 52% 48%

Manage prudential risk 33% 55% 50% 49%

Manage accounting risk 17% 38% 33% 33%

Risk aggregation Use explicit risk factors to aggregate risk 0% 26% 33% 24%

Performance measurement, implementation

PSP evaluation frequency once per year or less 38% 44% 31% 39%

% of respondents having outperformance of a market index as a sole performance measure for the PSP

67% 33% 57% 48%

% having risk-return efficiency as a performance measure for the PSP

22% 12% 11% 12%



sensitivity exposure of liabilities to traded risk factors such as interest rates and inflation.

As it happens, the liability-hedging portfolio (LHP) is poorly defined at 45% of pension funds, 25% of pension funds have not defined their liabilities precisely (they assert that their liabilities are not defined even though they are not full DC plans), and more than 30% do not define an LHP at all. In addition, 60% of pension funds include hedge funds, which seem inconsistent with the very notion of an LHP, in their LHPs—even if usually at between 0% and 10%.

A reason for the failure to define an LHP (45% of respondents do not fully identify one) formally and for the incorporation of hedge funds in LHPs lies in the use of portfolio optimisation techniques such as economic capital (used by 30% of respondents) and surplus optimisation (used by 21% of respondents). These techniques, defined below, do not require the identification of a liability-hedging portfolio and of a performance-seeking portfolio. EDHEC argues that optimisation techniques that do not identify a liability-hedging portfolio run the risk of unintentional imperfect liability hedging.

When pension funds do define a liability-hedging portfolio, the instruments it contains vary from one country to another. In the UK, formal indexation to inflation is the standard, and inflation-linked assets account for more than 20% of the portfolios of 64% of UK respondents; because there are caps and floors in the indexation formula—indexation to inflation in the UK, capped

to between 2.5% and 5%, depending on the year of service of liabilities—inflation derivatives are the easiest way to replicate this non-linear indexation, and inflation derivatives account for 20% of the liability-hedging portfolios of 40% of respondents from the UK but for only 12% of those from continental Europe. Non-linear indexation to inflation is far less frequent in the rest of Europe than in the UK.

Respondents from Northern European countries and from the UK rely heavily on swaps to manage their interest rate duration exposure: 54% of respondents from Northern European countries invest more than 20% of their liability-hedging portfolios in swaps, and 60% do so in the UK. The flexibility of swaps accounts for their popularity: in the UK they make possible accurate replication of a fully defined liability and in Northern Europe the matching of very long-term cash flows. In core European countries, Germany and Switzerland, in particular, regulatory provisions bias pension funds towards lower interest rate duration on the asset side than on the liability side, a bias that may account for the lower popularity of swaps (33% of respondents from core European countries invest more than 20% of their liability-hedging portfolios in swaps).

Asset-management and risk-diversification practicesIn addition to hedging liabilities, the second challenge for pension funds is to gain access to performance, by optimally diversifying market risk, for the benefit of plan sponsors (through diminished contributions) and of plan members (through increased value of pension payments,

Executive Summary



particularly in hybrid funds). Pension funds with a structured approach to investing define their market exposure in a performance-seeking portfolio (PSP), a portfolio dedicated to the pursuit of optimal (risk-adjusted) performance.

The techniques most needed to build efficient portfolios are robust estimation techniques. As it happens, 69% of respondents report that they understand robust estimation and simulation techniques, and 62% that they use them. Bayesian and resampling techniques, useful means of accounting for estimation risk, are, by contrast, understood “very much” or “fully” by only 35% of respondents; they are used by only 22% of respondents. Fifty percent of all respondents and 51% of pension stakeholders prefer to deal with estimation risks in portfolio construction by putting limits on portfolio weights, a much more popular means of dealing with these risks than statistical robustness techniques, used by 19% of respondents. Limits on portfolio weights, especially within an asset class, despite the relative disfavour with which academe views them, are not useless, as they are formally equivalent to a form of shrinkage, useful when large or small covariances are the result of sampling error (Jagannathan and Ma 2003).

From a practical standpoint, the first step in the construction of a performance-seeking portfolio is to choose benchmarks for each asset class. We find that 66% of respondents and 81% of pension stakeholders use market indices as the benchmarks for investment funds. EDHEC argues that, within an asset class, benchmarks should not be market indices or other cap-weighted mechanisms, because they have proven grossly inefficient

(cap-weighting involves trend-following and concentrated portfolios with unstable exposures). Within an asset class, one should instead resort to simple heuristics such as the equally weighted portfolio, to fundamental indices (Arnott, Hsu, and Moore 2005), or to optimisation methods to try to build efficient portfolios (Amenc et al. 2010) or by default minimum-variance portfolios (DeMiguel, Garlappi, and Uppal 2007). How do you (all respondents, excluding non-responses; multiple choice question) define the reference portfolios?Sixty percent of respondents use market indices to define the PSP. More—66%—use market indices as benchmarks for individual funds.

PSPIndividual funds

In terms of liability profile

As market indices

As a bond/cash index

Throughoptimisation

0

10

20

30

40

50

60

70

80

Between asset classes, one must resort to portfolio optimisation, a practice that requires robust portfolio construction methods that also rely on statistical robustness or noise-filtering (or both) and to methods that incorporate the investment horizon of the pension fund. Multi-period models, for instance, are useful because pension funds invest on long horizons (Hoevenaars et al. 2008). In addition, because of the possible unstable relationship between the asset classes (think of stocks and bonds), models that capture

Executive Summary



the time-variation in coefficients (Engle 2002; Engle and Kelly 2009) can improve parameter estimates.

These techniques must be applied on a set of asset classes. As to which asset classes are available, the traditional list of stocks and bonds with various geographies and ratings has expanded to include so-called alternatives: private equity, real estate, commodities, hedge funds, as well as mortality derivatives and reinsurance. Performance-seeking portfolios (PSPs) are often heavy on equities (this asset class alone accounts, on average, for 32% of the PSPs). In addition, they invest relatively little in the most (potentially) illiquid strategies: the average cumulative weight of their investments in hedge funds, private equity, and infrastructure comes to 15%, and combined with real estate, investment in these asset classes is less than 25%. As the exposure of institutional investors to liquidity risk should be driven primarily by the maturity of their liabilities and by the risk of liquidity runs, one would expect pension funds, the longest-term institutional investors, to have the largest holdings in illiquid alternatives (such as hedge funds and private equity) of all (institutional) investors.

Last, pension funds must act on their asset allocation by allocating to the main building blocks as defined in liability-driven investing: the liability-hedging portfolio, the performance-seeking portfolio, and the residual cash account. Popular industry methods such as economic/regulatory capital and surplus optimisation allocate assets directly without necessarily having a clear view of whether they contribute to hedging or diversification.

Surplus optimisation is a technique that attempts to maximise the expected surplus for a given degree of risk, and that usually assumes a fixed-mix or buy-and-hold investment strategy. The aim of surplus optimisation is not to avoid shortfalls, even though one may control for the probability of shortfalls. Economic/regulatory capital management is a technique that attempts to ensure that funding ratios remain always higher than a minimum by requiring that the Value at Risk (usually defined at the 97.5% confidence interval at pension funds) be less than the surplus. These two quantities are monitored on a quarterly basis, and the planned repetition of economic/regulatory capital optimisation is supposed to make the probability of shortfall less than the 2.5% assumed in the Value-at-Risk measure.

To determine their allocation, at least 45% of respondents resort to methods other than LDI, methods that do not explicitly require that a liability-hedging portfolio and a performance-seeking portfolio be defined. For instance, 21% of respondents use surplus optimisation methods and 30% economic capital (multiple choice answers). EDHEC argues first that these static risk-budgeting techniques are essentially useful in the absence of minimum/maximum funding ratio constraints. Because economic capital and surplus optimisation do not require defining the liability-hedging portfolio, the risk-free portfolio in an ALM setting, pension funds may find themselves unable to switch their investments quickly to this risk-free portfolio; the lack of clarity of these techniques is a limitation. Liability-driven investing (LDI) makes it easier to switch to a risk-free ALM strategy

Executive Summary



and to rationalise this switch by defining rule-based strategies for risk insurance.

Dynamic risk-budget management and the management of minimum funding ratiosAfter hedging and diversification, the third challenge for pension funds is to ensure that minimum funding ratios are not breached by insuring risk away. Prudential regulations generally require recovery plans involving additional contributions from the sponsors when funding requirements are not met. IAS 19 also penalises sponsors whose pension funds have funding ratios that lie outside the 90%-110% range. Even without considering regulatory restrictions, traditional defined-benefit pension funds also generally look to ward off deficits, as deficits involve sponsor risk—the risk of a sponsor’s inability to compensate for pension deficits.

The survey suggests that pension funds generally understand risk insurance strategies more than they use them: these strategies are understood by 67% of respondents but used by only 41%. Likewise, they are understood by 50% of pension funds but used by 30%. Static approaches to investing are thus generally preferred to dynamic approaches.

EDHEC argues, however, that static approaches to investing, even when parameters are fixed and the opportunity set is constant, generally do not guarantee that minimum funding ratios are not breached, unless they are implemented in an overwhelmingly conservative way, with a unitary allocation to the liability-hedging portfolio and long-only

investments in risky assets with total weights lower than the surplus (a pension fund with a 120% funding ratio must then invest no more than 20% in risky assets). In the end, fixed-mix strategies will always involve an overly low allocation to performance-seeking assets in normal times, with an associated high opportunity cost, and too high an allocation to performance-seeking assets in difficult market conditions.

When incorporating terminal funding constraints in the utility function, pension funds can rely on the martingale or convex duality approach to dynamic asset allocation problems (Karatzas, Lehozcky, and Shreve 1987; Cox and Huang 1989), first to find the optimal terminal payoff—an option—then to replicate this terminal payoff. This replication requires a form of dynamic asset allocation that may be called dynamic risk-budget management or risk-controlled investing (RCI). RCI involves a strategic allocation to the performance-seeking portfolio and liability-hedging portfolio that changes as a direct function of the funding ratio.

Rule-based risk-controlled strategies vs. discretionary economic/regulatory capital managementPractitioners may want to know whether preferred industry methods can result in portfolio insurance strategies that approximate the desired theoretical payoffs. After all, static risk-budgeting that embeds the possibility of breaching funding constraints, such as economic capital, but repeated at a sufficient frequency also results—after the fact—in a portfolio insurance strategy. When they state that regulatory VaR constraints decrease the

Executive Summary



gains from risk insurance, Binsbergen and Brandt (2007) implicitly suggest that economic/regulatory capital management, plus maximum weight constraints, results in a strategy similar to the optimal portfolio insurance programme.

Economic/regulatory capital management, unlike surplus optimisation,1 is a static risk-budgeting tool built in the spirit of risk insurance. After all, economic/regulatory capital is imposed by regulators to ensure that minimum funding ratios are met—they were formalised in Solvency II and applied to both the insurance and pension sectors in some Northern European countries. In pension funds, economic/regulatory capital usually requires that the 97.5% Value at Risk be less than the surplus and that it be checked every quarter.

The survey reveals that the industry standard for managing risk seems to be economic/regulatory capital rather than risk-controlled investing: 28% of pension fund stakeholders use risk-controlled investing to manage prudential constraints, whereas 56% use risk management tools that can be classified as economic/regulatory capital. Likewise, 40% of all respondents use risk-controlled investing, whereas 81% use economic/regulatory capital tools.

Which underlying strategies do you (all respondents) prefer to use to manage prudential, accounting, and economic risk? That the orange bars are higher than the yellow bars shows that economic capital is far more popular than risk-controlled investing. Fewer than half the respondents re-evaluate their strategies frequently (red bars), though frequent re-evaluation is much needed when RCI strategies are not used.

Risk-controlled investingEconomic capital (economic regulatory capital)Frequent re-evaluation

Prudential Accounting Economic0

10

20

30

40

50

60

The management of economic capital is discretionary: the means of adjusting the investment strategy to the risk budget are usually discussed first in ALM committees, then in investment committees. These practitioners’ methods are better suited to the traditional organisation of pension funds and the role of the trustees in asset allocation. EDHEC argues that such strategies present implementation risks: the lack of formally defined liability-hedging and performance-seeking portfolios and of pre-defined investment rules means that pension funds may lose responsiveness and make investment changes too late.

EDHEC thus recommends that pension funds rely more heavily on rule-based strategies, such as risk-controlled investing, in their economic capital models. With rule-based economic capital, investment decisions are implemented by following appropriate rules.

Executive Summary

1 - Surplus optimisation generally involves the volatility of the funding ratio rather than the shortfalls and their probability; in addition, it simulates a fixed-mix or buy-and-hold investment strategy, inconsistent with the strategy used ex post when the optimisation programme is run again. Unlike economic capital, which generally implies a quarterly revision of the asset allocation, surplus optimisation gives no clear indication of when a strategy should be modified.



Introduction of maximum funding constraintsNaturally, risk insurance has a cost. First, as with options, downside protection means forgoing upside potential. This opportunity cost can be lowered by forgoing performance beyond a threshold at which higher wealth provides relatively lower utility, which is tantamount to “selling” out-of-the-money participation in the upside. A call-spread option involves the sale of an out-of-the money call option that can then finance greater participation in the stock market between the two strike prices.

Fifty-four percent of pension fund stakeholders report that they introduce maximum funding constraints (relatively few respondents answer this question, so, when one accounts for non-respondents, only 29% introduce maximum funding constraints in the definition of their strategy). This percentage is marginally higher for all categories of respondents.

Risk-controlled strategies require a decrease in allocation to the performance-seeking portfolio after substantial falls in prices, when performance-seeking portfolio assets (stocks) are cheap, decreases that come with a high cost in mean-reverting markets. Risk insurance can also be applied to unconstrained dynamic strategies that account for mean reversion. In other words, life-cycle investing and risk-controlled investing are not mutually exclusive and can be combined to generate greater benefits for pension funds. Ultimately, when funding ratios approach their floors, holdings of risky assets fall.

Measuring risk and allocating risk budgetsWhen there are funding constraints, asset allocation, in the form of risk-controlled investing or the economic/regulatory capital management form, relies on risk budgeting. Prudential regulations are becoming more risk-based and generally require an understanding of the risks run by pension funds.

Thirty-five percent of respondents—answers are similar for pension funds—neither aggregate risk from individual funds to building blocks such as the performance-seeking portfolio and liability-hedging portfolio nor measure total investment risk. Twenty-eight percent do not measure aggregate balance sheet risk.

In addition, for those who use economic capital and need to allocate a risk budget at regular intervals, risk aggregation measures must also enable the allocation of risk. Aggregation of VaR figures does not make possible proper allocation of risk, as disaggregation is not possible. After all, VaR figures are indicative only of an amount of risk, not of the exposure to risk factors, and without this information aggregate VaR figures are blind: they fail to show which risk factor has become riskier.

We find that 40% of respondents aggregate VaR measures directly. Only 25% aggregate exposure to explicit risk factors—such factors, identical for all investment funds, make it possible to aggregate risk.

Except in the rare instances in which asset allocation is entirely rule-based, the lack of appropriate risk measurement and risk

Executive Summary



allocation methods greatly diminishes the ability to manage the balance sheet efficiently.

An insufficiently comprehensive view of risksFor risk-controlled investing or economic capital effectively to insure the pension fund against the risk of losses for pensioners, pension funds must have a comprehensive view of risks. If a major risk such as interest rate risk or sponsor risk is not adequately taken into account, then, for all its sophistication, the pension fund may be ill managed.

Our survey reveals that respondents have a blinkered view of risks. More than half do not model or measure sponsor risk at all. In addition, pension stakeholders are much more likely to measure risk than to manage it effectively. For instance, 62% of pension stakeholders measure prudential risk, but only 42% manage it. Accounting risk is likewise measured by 45% of pension stakeholders but managed by only 30%.

Are pension funds managing risks or simply measuring them? British pension funds and sponsors take sponsor risk into account more frequently than their European counterparts (62% of British respondents do so, vs. 48% in core European countries and 52% in Northern Europe). After all, there are more hybrid funds with multiple sponsors and limited sponsor commitment in Northern Europe.

The red bars show the proportion of pension stakeholders who manage regulatory risks, whereas the orange bars show the proportion that simply measure risks. Prudential risks are managed by only 42% of pension stakeholders, and accounting risk by 30%.

Non-responseDo you measure it?Do you manage it?

Prudential risk(minimum funding constraints and the risk of breaching them)

Accounting risk(risk of large losses in

the P&L of the sponsor)

Economic/financial risk(surplus and risk of a shortfall)

0

10

20

30

40

50

60

70

80

Surprisingly, however, only 17% of UK respondents manage accounting risks—the risk of volatility of the defined-benefit obligation in the accounts of the sponsor. This is the lowest percentage of the three geographies analysed; it compares with 33% in Northern Europe and 38% in core European countries; 36% of all traditional DB schemes manage this risk. The failure to manage this risk is striking, as the UK has the most stringent accounting standards, and as UK sponsors have no obligation to provide their employees DB schemes. In general, our survey suggests that the failure to manage accounting risk in the UK may account, in part, for the wave of closures of DB schemes.

In addition, our survey suggests that respondents from the UK have less sophisticated practical risk measurement and allocation tools. Again, a more highly fragmented industry, with less access

Executive Summary



to qualified resources, as well as fewer regulatory guidelines than in Northern Europe, may account for this situation.

EDHEC recommends that, in addition to minimum funding ratios, pension funds take into account the regulatory discount rate in the definition of their dynamic risk-budget management and that they manage sponsor risk. Sponsors offer a guarantee for defined-benefit funds, a guarantee that disappears if the sponsor goes bankrupt. Pension trustees must act in the interest of participants and should thus manage sponsor risk. Managing sponsor risk may also require dynamic allocation to the sponsor company stock or, when they are available, to credit default swaps or hybrid options.

Performance measurementBecause the largest source of value added in a pension fund lies not in the selection of the manager but in the choice of appropriate investment benchmark and of the appropriate allocation to these investment benchmarks, performance measurement is essential to measuring the quality of the design and of the implementation of the strategy.

We find that 25% of respondents and 20% of pension stakeholders do not assess the suitability of the design of ALM strategy.

In the wake of Brinson, Hood, and Beebower (1986, 1995), numerous academic methods have analysed the drivers of performance in asset management, but they do not yet evaluate portfolio performance in the presence of risk insurance. The lack of recognised academic methods to

attribute performance for convex strategies should lead pension funds to benchmark the design of the strategy to its stated goals and to assess the quality of the liability-hedging portfolio (LHP) and the risk-adjusted performance of the performance-seeking portfolio (PSP) independently. After all, classic attribution methods usually suffice for these building blocks.

Forty-six percent of pension fund stakeholders, however, do not assess the performance of the LHP, and crude outperformance is used by 39% of pension stakeholders. Likewise, 52% of pension stakeholders do not assess the quality of the implementation of the LHP, and when they do so outperformance is again by far their preferred measure. The LHP attempts to replicate the liability; the objective is to minimise risk and outperformance measures seem largely unsuitable.

Evaluation of the implementation of the PSP (all respondents who answered a question on performance measurement)

Outperformance is the preferred measure for the PSP. Again, pension stakeholders respond in much the same way as all respondents and their specific answers are not shown.

%

Non-response 30%

Outperformance of a liability index 11%

Outperformance of a market index 51%

Outperformance of a style benchmark 7%

Sharpe/Treynor ratio 11%

Sortino/Jensen/ measures based on VaR/M square/Graham Harvey

5%

We access its risk-return efficiency with respect to other benchmarks

11%

Twenty-seven percent of respondents and 32% of pension fund stakeholders

Executive Summary



likewise do not assess the adequacy of the design of the PSP, and 34% of pension fund stakeholders do not measure the performance of the performance-seeking portfolio. The preferred performance measure is the outperformance of a market index, without any reference to risk, a measure used by 50% of pension stakeholders. Risk-adjusted measures of performance are little used (Sharpe or Treynor ratios by 7% of respondents, Sortino or Jensen ratios, measures based on VaR, Modigliani and Modigliani or Graham-Harvey measures by 3%), and only 5% of pension fund stakeholders explicitly assess the risk-return efficiency of the performance-seeking portfolio. EDHEC argues that the PSP attempts to generate performance efficiently, so risk-adjusted performance measures such as the Sharpe ratio should be used to determine if it is in fact generating performance efficiently; relative risk measures such as Jensen’s alpha or Graham/Harvey measures should be used to assess the performance of managers relative to a given benchmark.

For individual funds, more traditional measures are used more often, as only 20% fail to assess the performance of individual funds and usual absolute and relative risk-adjusted performance measures are used twice as often as for the PSP as a whole. As surprising as it may seem, the lessons from Brinson, Hood, and Beebower (1986) have not been learnt. Twenty-five years on, closer attention is still paid to less important aspects of performance such as the monitoring of countless individual investment funds and the attribution of performance to these funds than to crucial matters such as the design and implementation of the investment strategy.

The failure of pension funds and related service providers to assess the suitability—to measure the performance—of the design and implementation of investment strategies is a shortcoming that may lead to sub-optimal decisions’ being taken again and again.

ConclusionPension funds have been described as the new financial giants, and they have a reputation for superior approaches to investing that allow them to perform better than other investors. At the same time, abysmal pension deficits, the closure of DB funds, and the losses in pension benefits when sponsors go bankrupt are making the news. The pension fund industry as a whole experienced sharp drops in funding ratios in late 2008, even at highly sophisticated institutions: the average funding ratio of Dutch industry-wide pension funds fell from 150% in mid-2007 to 89% in Q1-2009. The combination of a sophisticated pension fund industry, of the prudential regulation that requires funding ratios always higher than 105%—on average close to 125%—and of the risk-based regulation that requires the use of economic capital has not altogether managed to prevent underfunding.

Our first conclusion is that, despite the professionalisation of ALM in pension funds and their service providers, risk-controlled strategies, used by 30% of European pension funds, may not have been taken up widely enough. That these strategies are understood by only half of respondents may account, in part, for the failure to take them up more widely.

Executive Summary



The underfunding of sophisticated pension funds in late 2008 suggests that there are biases that prevent many pension funds from managing their assets optimally. In theory, rule-based risk-controlled investing and discretionary economic capital should lead to the same insurance of risks. One of the theoretical drawbacks of economic capital is that it is a myopic strategy. A practical drawback is that the reliance on discretionary investment policies involves the risk of delays and of behavioural biases that distort the theoretical strategy (pension funds may be reluctant to sell at a loss, even though they rely essentially on market values and should, in theory, pay no attention to book values). As it happens, respondents do not always adopt the strategy implied by their risk-management tools or models. Many Dutch pension funds have often failed to reduce risk as significantly as the FTK regulation theoretically commands (they kept a larger share of risky assets than their funding ratio allows).

In general, because rule-based strategies are compatible with economic capital and prudential risk-based regulations, we recommend more reliance on these strategies. Very simple and intuitive methods that require little or no mathematical background can prove to be efficient means of insuring risks. For all their sophistication, pension funds seem to make insufficient use of these basic but robust methods.

The survey also suggests that pension funds have a blinkered vision of risks; only a minority, for instance, manage accounting risk and sponsor risk. The reluctance to manage their risks exhaustively may have severe consequences for pension funds.

First, this reluctance increases risk to no purpose. And the reluctance to manage accounting risks may also lead to inappropriate volatility in the sponsor’s books, volatility that may trigger closure of pension funds in countries such as the UK, where there is no obligation to provide DB plans, or to limiting the support of sponsors in countries such as the Netherlands, where some guarantees are mandatory.

The survey suggests, finally, that pension funds make insufficient efforts to measure the performance of their portfolios and to assess the suitability of the design of their strategies. Standard industry methods are appropriate means of measuring the performance of the building blocks—the liability-hedging portfolio and the performance seeking portfolio—yet the survey shows that 30% of respondents do not assess design of the performance-seeking portfolio, and that more than 50% of respondents use crude outperformance measures. The failure to measure performance may lead to sub-optimal decisions’ being taken again and again.

Executive Summary


2. xxxxxxxxxxxxxxxxxxIntroduction




MotivationBrinson, Hood, and Beebower’s (1986) conclusion that more than 90% of the average time-variation in returns is explained by strategic asset allocation has led to widespread recognition of the importance of asset allocation to investment returns and thus to pension fund performance.

Since their study, asset management (AM) and asset/liability management (ALM) practices have undergone marked changes, as many institutions now allocate significant shares of their portfolios to alternative assets such as listed and unlisted real estate, commodities, infrastructure, hedge funds.

The recognition that pension funds seek first to cover their liabilities and then to generate performance has led to formalisation of financial techniques for the asset and liability management of pension funds; portfolios are constructed with a liability-hedging portfolio to cover liabilities and a performance-seeking portfolio to generate performance. In addition to financial risk, pension funds are subject to non-hedgeable risks, usually biometric risks (mainly longevity risk). Tentative steps to create a market for the transfer of these risks, in the form of CAT bonds, longevity swaps, or securitisation, have also been taken. Since the 1990’s, pension fund regulation has grown considerably stricter. The 2003 European directive for pension funds, the IORP directive, allows underfunding for an undefined “limited period of time” and in the main requires a realisable recovery plan. Some countries, such as the Netherlands, adopted a risk-based prudential framework inspired by Solvency II, the prudential

regulation of insurance companies. The Dutch FTK requires a minimum funding ratio of 105% plus buffers against market risks. Although regulation was temporarily relaxed after the 2008 crisis, the overall trend has been towards tightening prudential regulations; at the same time, stricter accounting standards have made an impact on the accounts of sponsors of corporate pension funds.

Stricter regulations have led to the development of risk-insurance techniques that focus on risk control through state-dependent asset allocation to ensure that minimum funding constraints are respected.

However, no representative overview of the ALM practices of pension funds is currently available, since most surveys merely review the asset holdings of pension funds. This survey examines the ways ALM at pension funds makes use of modern investment management techniques. In short, we assess the ways European pension funds define investment policy, how they implement it, and how the performance of the investment policy is analysed.

We will thus shed light not only on the conception of the ALM strategy but also on the way it is implemented. This survey allows pension fund managers to compare their strategies, techniques, and organisation with those of their peers, and, above all, to take stock of any gaps between their practices and best practices. It is our hope that it will also spark dialogue between research and industry.

Introduction



Contents of the surveyThe survey first attempts to assess whether pension funds master the hedging, diversification, and risk-insurance techniques required for the management of a pension fund when there are regulatory funding constraints. Qualitative questions attempt to determine whether survey respondents are familiar with and use these techniques and, in particular, how they manage their prudential and accounting constraints. We analyse the instruments and asset classes in their portfolios.

The second section reviews risk and performance measurement. We first review the means of identifying and measuring risks and allocating a risk budget. We attempt to determine whether pension funds use state-of-the-art methods to measure their risks and aggregate them on the balance sheet. We then review performance measurement practices. Reviewing the performance of fund managers is now standard practice in the pension fund and consulting industries. Here, we ask respondents to identify the methods they use to evaluate the performance of the investment policies defined by ALM departments.

Last, to synthesise, we search for a link between the sophistication of respondents to the survey and their effective control of their funding ratios.

Profile of respondentsThere are 129 respondents to the survey.

We have defined three geographies that, in our view, represent three distinct groups of pension funds: • The UK, with its mix of traditional DB and full DC schemes, accounts for 11% of respondents.• Northern Europe, including the Netherlands, characterised by hybrid pension schemes and regulations inspired by Solvency II and economic capital models—often referred to as traffic-light systems in these countries—accounts for 28% of respondents.• Core European countries such as Germany and Switzerland, with somewhat more traditional pension regulation, account for 37% of respondents.

Respondents have approximately €2.7 trillion of assets under management (AUM). Pension funds surveyed have AUM of approximately €0.9 trillion.

Figure 1-a: Employers of participantsPension funds account for 42% of respondents, their sponsors for 13%; advisors, fiduciary managers, and asset managers for 41% of respondents.

Pension fundParticipantSponsor

Fiduciary managerAsset managementInvestment bank

Regulator/supervisorAdvisor/actuary

2%6%

42%

13%

22%

1%

13%

1%

Introduction



Figure 1-b: Countries of respondentsThe Netherlands and Germany are the two most heavily represented countries; Switzerland and the UK each account for 11% of respondents

BelgiumFranceGermanySwitzerlandNetherlandsOther Northern EuropeUnited KingdomUnited StatesOther

11%

9%

4%

16%

5%

19%

22%

3%

11%

Figure 1-c: Geographies of respondentsCore European countries account for 37% of respondents; Northern European countries account for 28% of respondents and the UK for 11%.

Core European countriesNorthern European contriesUnited KingdomOther

37%

28%

24%

11%

Figure 1-d: Assets under managementThe assets under management of survey respondents are approximately €2.7Trn. Pension funds surveyed have AUM of approximately €0.9Trn. Twenty-one percent of respondents have less than €1Bn of AUM, and 4% have more than €100Bn.

Less than 1bn1bn to less than 5bn5bn to less than 10bn10bn to less than 50bn50bn to less than 100bnMore than 100bnNon-response

21%

23%

13%

14%

4%

3%

22%

Introduction


1. Design of Asset/Liability Management Strategies



1.1. BackgroundWhen it designs investment strategies, the ALM department designs a policy for capital adequacy—it is expected to design a dynamic investment strategy or to rely on methods such as economic capital. ALM departments also determine the allocation of assets to specific categories—liability replication and risk taking—categories for which specific benchmarks, along with the risk budget, are usually communicated to the asset management departments.

The two main portfolios can be defined as the LHP (the hedging portfolio that mimics liabilities) and the performance-seeking portfolio or PSP (the portfolio whose purpose is to enhance returns). In practice, when portfolios are defined according to their targets, tactical bets (meant to contribute to enhanced returns) are separated from the longer-horizon PSPs. Tactical bets, or tactical asset allocation (TAA) are defined either as a free risk budget to be used at the discretion of the asset manager or as an additional benchmark.

1.1.1 The Liability-Hedging PortfolioIn the formal ALM model illustrated below for the dynamic asset allocation framework, the LHP, defined as

σ '( ) −1

σL ,is the projection of available assets on the liability (see mathematical derivation in section 1.1.4).

When the liability benchmark is designed, the focus is on replication; the characteristics of the liability are the main inputs.

Although cash instruments such as bonds can be used to design LHPs, derivatives such as futures and swaps allow more efficient replication of the interest rate and inflation risks present in liability structures.

Derivatives allow better replication when claim patterns are irregular. Replicating a distant, important claim with couponed bonds involves receiving intermediate coupon payments that must be offset by negative exposure to bonds. Interest rate swaps may also modify the cash-flow profile of the assets. In Northern Europe, for instance, after regulation of pension funds stiffened, many funds used swaps to lengthen the duration of their asset portfolios, mainly because the swap market for very long maturities is much deeper than that for government (and corporate) bonds. Inflation swaps, for example, can be used to manage inflation risk.

Derivatives are the simplest way to hedge option-like exposures, such as the mandatory indexation to inflation in the UK, which is capped annually at 2.5%, 3%, or 5%, depending on time of service (when pension rights were earned). Non-linear exposure may require either derivatives or specific over-hedging strategies, as illustrated in Amenc, Martellini, and Sender (2009).

Several instruments can be used to implement the LHP (just as for the PSP). After all, both portfolios should be defined primarily as exposures to risk factors, a definition that leaves a choice of replicating instruments to the ALM and asset management teams. The exact




mix of cash instruments and derivatives for replication and risk taking depends on the organisation of the pension fund and on its management of available liquidity (including liquidity risk).

1.1.2. The Performance-Seeking PortfolioCharacteristics of the PSPWhen the PSP is designed, the focus is on generating performance. In theory, it is the portfolio with the highest Sharpe ratio. When the distribution is non-Gaussian and exhibits higher moments, the Sharpe ratio is not a consistent measure, and one can resort to utility optimisation, or use Value at Risk instead of volatility to account for these higher moments—the efficient portfolio is then that with the highest ratio of return to Value at Risk. In addition, participants are generally required to reveal their aversion to risks other than market risks, such as liquidity, uncertainty, and operational risks.

In sum, in the case of normal returns, with r the risk-free rate, μ the vector expected return of traded assets, and σ the matrix of volatilities, the optimal portfolio ωM reads:

ωM =σσ '( ) −1

μ − r1( )1' σσ '( ) −1

μ − r1( )

When expected returns are normal it is simply the portfolio that minimises variance (the global minimum-variance portfolio or GMV).

When returns are not normal, not all risk measures are equivalent, and investors need to construct their portfolios using their own utility function or a ratio of

expected returns to the (conditional) Value at Risk rather than the Sharpe ratio. Supposing one can measure up to the fourth moment of (portfolio) returns, an investor would usually solve the following maximisation problem, which results from the Taylor development with order 4 of the utility function, around mean expected portfolio returns:

MaxU (k )(E (R ))

k!k=0

4

∑ E (R − E (R )) k

= MaxU (k )(E (R ))

k!k=0

4

∑ μ (k )(R )

(and where μ(k )(R ) are the centralised k

first moments).

As illustrated by methods derived from economic/regulatory capital constraints, institutional investors usually consider their risk consumption equal to their Value at Risk, usually at a 97.5% confidence interval (for pension funds).

The typical institutional PSP can be derived as follows (here, higher moments are taken into account in the Cornish-Fisher VaR expansion):

Max(E (R ) − λa Q1−α (R )) ,

or Max(E (R ) + λb z2.5% ⋅σ )

with

z2.5% = z2.5% + 1

6( z

2.5%

2 −1)S +1

24( z

2.5%

3 − 3z2.5% )

K −1

36( 2z2.5%

3 − 5z2.5% )S 2

where S is the sample skewness, K the excess kurtosis of the sample, the second and a half percentile of the normal distribution, and the modified




percentile (usually a lower value when S is negative and a higher value when it is positive, thus indicating less risk in the left tail).

Liquidity, uncertainty and operational risks can be taken into account in the same framework.

Benchmarks for individual asset classesThe design of the PSP involves two steps: the construction of appropriate benchmarks for individual asset classes and then of a portfolio from the appropriate weighting of the asset classes.

Within an asset class, one should seek exposure to the market through benchmarks that should not be market indices or other cap-weighted mechanisms that have proven grossly inefficient, as research has shown that market indices have unstable exposures to implicit factors as well as to sectors; they result in trend-following strategies that lead to a loss of performance when markets are noisy (trend following also subjects the investor to excessive noise, as it leads to overweighting the assets most subject to noise); under no realistic condition can an investor thus desire to be exposed to market indices.2

One should thus resort to simple heuristics such as the equally weighted portfolio, to fundamental indices (Arnott, Hsu, and Moore 2005), to risk-based indices (DeMiguel, Garlappi, and Uppal 2007), or to efficient indices (Amenc et al. 2010); one might also use optimisation methods to build efficient portfolios within an asset class. Whereas risk-based indices as presented in DeMiguel, Garlappi, and

Uppal (2007) minimise portfolio volatility, efficient indices attempt to introduce return predictability to maximise the Sharpe ratio directly.

Fundamental indicesFundamental indices (Arnott, Hsu, and Moore 2005) attempt to proxy expected returns. They rely on book values to proxy undervalued firms; by design, therefore, these indices have a value bias. Amenc, Goltz, and Le Sourd (2009) and Blitz and Swinkels (2008) formally test for the value bias of these strategies.

Risk-based indicesRisk-based indices often attempt to minimise risk in portfolios (see examples in DeMiguel, Garlappi, and Uppal 2007); attempts have been made, however, to maximise the Sharpe ratio (Amenc et al. 2010) directly.

The main challenge, when portfolios from homogeneous asset classes are constructed, is to deal with the noise in financial markets, which leads to noise in the measurement of the covariance matrix. In addition, it is hard to estimate expected returns, as they are not stable.

Measurement noise makes naive methods yield inefficient results. Uninformed investors (investors who are able to measure neither expected returns nor their variance-covariance matrix) build portfolios that are more efficient on an out-of-sample basis than informed investors with naive measurement tools.

As it turns out, the equally weighted portfolio is the optimal portfolio for the investor who has information neither


2 - For one to invest in market indices one must first assume that a representative investor exists in the economy; then assume that one is that very investor; third, that one can invest in the average wealth in the economy, including real estate and human capital. Then one will invest in cap-weighted indices.



on expected returns nor on the variance covariance matrix, and hence makes the assumption that all expected returns are equal, that all variances are equal, and that the correlation of all assets is equal.3

Using sector returns as a proxy for individual assets in an asset class, DeMiguel, Garlappi, and Uppal (2007) show that when the covariance matrix is estimated from monthly returns, none of the optimisation methods commonly used in the industry consistently has statistically significant higher Sharpe ratios than the equally weighted portfolio on an out-of-sample basis (the significance in the difference in the Sharpe ratios taken as in Jobson and Korkie 1981).

There is no reason to think that a single construction method should be efficient in all situations. The equally weighted portfolio would be efficient when securities are homogeneous, but for heterogeneous assets such as individual stocks, where quite different variances are found, structured sample estimates of the variance-covariance matrix capture meaningful information, and using it results in superior portfolios.

Heterogeneity justifies the use of robust portfolio construction techniques.

Robust portfolio constructionTwo classes of techniques have been compared in the literature: to avoid excess random weights in portfolio construction, one may impose restrictions—short-sale constraints and limits on securities holdings. The other technique involves robust parameter estimates; it focuses on estimates of the covariance matrix.

Jagannathan and Ma (2003), point out that imposing weight constraints, traditionally seen as imposing “wrong constraints” on the portfolio optimisation problem, is equivalent to a specific form of shrinkage, useful when large or small covariance figures are the result of sampling error. Portfolio constraints and robust estimates are thus not contradictions in terms.

For robust estimates of the covariance matrix, one may resort to principal component analysis (PCA), to implicit factor exposures, in other words.4

Marchenko and Pastur (1967) give explicit results from the random matrix theory to select the factors that are statistically most relevant, and show the asymptotic density of the largest and smallest eigenvalues, as follows:

f (λ) =

T2π N

(λ − λmax )(λ − λmin )

λ,

λmax = 1+

NT

+ 2N

T, and

λmax = 1+

NT

− 2N

T

Practitioners also use rules of thumb such as selecting a fixed number of factors, usually from three to five.

An alternative to PCA is to rely on shrinkage techniques. These techniques rely on the optimal shrinkage of the sample covariance matrix S towards a highly structured estimator, F, either a one-factor model (Ledoit and Wolf 2004) or a constant correlation covariance matrix (Ledoit and Wolf 2003). The shrinkage is optimal in the model as it minimises an expected quadratic loss function, the distance between the true covariance matrix and


3 - In this framework, any optimisation method yields equally weighted portfolios, as demonstrated below. Since expected returns are equal, the optimal portfolio minimises risk, as follows,

with a constraint that,, where e and Σ

represent the variance-covariance matrix. For the optimal allocation to be an equally weighted portfolio, it is sufficient that the variances and covariances across all asset classes be a constant.4 - The industry standard is to rely on explicit multi-factor models. They are useful for risk aggregation, but not so much for the construction of optimal portfolios within relatively homogeneous assets.



the estimator; it usually depends on sample variance and covariance and is linear in the inverse of T (in the constant parameter case, of course, no shrinkage is necessary when the sample is infinite). In practice, though the shrinkage is optimal, the structured covariance matrix is not unique and it is subject to arbitrary choices, so this estimator is subject to the risk of misspecification.

Because variance and covariance are not constant, structured estimators of the variance-covariance matrix have been proposed in a setting with stochastic parameters. Engle (2002) models time-varying correlations with a new class of multivariate models called dynamic conditional correlation (DCC) models. Engle and Kelly (2009) propose a more structured version, the dynamic equicorrelation (DECO) that relies on the constant correlation assumption on top of the DCC model. This assumption reduces the dimensionality of the problem and makes it possible to estimate the model parameters for arbitrarily large covariance matrices with ease. The model involves adjusting for individual volatilities and using quasi-maximum likelihood estimates to come up with measures of correlation.

Appropriate mix of asset classesThe appropriate mix of asset classes depends obviously on the expected risk-and-return characteristics of the asset classes. It also depends on the investment horizon, as illustrated by Hoevenaars et al. (2005), who take a pension fund that has a constant maturity liability (they make the assumption of a constant asset allocation because there are no

minimum funding ratio constraints or horizon effects). Hoevenaars et al. (2005) evaluate the benefits of defining a long-term investment strategy in the presence of liability constraints, where the liability is indexed to inflation and there are no inflation-linked securities.5 Following the notion of a term structure of risk as introduced by Campbell and Viceira (2005), they derive the covariance structure of assets and liabilities from a vector autoregressive model for returns and other state characteristics. In vector autoregressive models, correlations compound over time.

In a vector autoregressive framework, future returns are read as a combination of past returns.

dzt +1 = Φ0 + Φ1 ⋅dzt + ut +1 , which in turn makes it possible to compute future returns as compounded from past returns:

dzt + j = ( Φ1

i

i =0

j −1

∑ ) ⋅ Φ0 + Φ1j ⋅dzt + Φ1

i

i =0

j −1

∑ ut + j −i ,

which has a forecast error of

dzt + j − dzt + j = Φ1

i

i =0

j −1

∑ ut + j −i

When the notation in Hoevenaars et al.(2005),

Z (k )

t +k = dzt + j

j =1

k

∑ , is taken as the cumulative holding return, the forecast error reads

Z (k )

t − Z (k )t = Φ1

i

i =0

j −1

∑ ⋅ut + j −ij =1

k

∑ and the covariance matrix of the k-period errors follows:

Σ(k ) = (( Φ1

i

i =0

j −1

∑j =1

k

∑ )Σ( Φ1i

i =0

j −1

∑ )')

Hoevenaars et al. show that building the portfolio strategy with a long-term view on returns has significant benefits, that these benefits naturally increase


5 - This approach is often considered equivalent to the approach that assumes that there are inflation-linked securities, but where the risk premium on inflation-linked bonds is such that it prevents investors from buying these securities. In that case, however, the LHP would consist entirely of inflation-linked bonds (ILBs), and the PSP would go short the same amount of ILBs. Given the overall low issuance of ILBs worldwide, which is insufficient for pension funds to hedge inflation risk, their assumption thus allows for a clear understanding of one of the means by which pension funds can hedge their long-term inflation risks.



with the investment horizon, and that these benefits are higher when there are liabilities.

Figure 2: Benefits of long-term portfolio choice The figure shows the benefits from long-term investing for an Asset/Liability (solid line) and an asset-only (dashed line) investor. Benefits from being strategic (α(T)) instead of choosing the asset allocation in a single-period context (α(1)) are expressed as a certainty equivalent in percentages (on y-axis) for different investment horizons (in quarters on x-axis). The risk-aversion parameter γ = 20.

Source: Hoevenaars et al. (2005).

State-dependent parametersIn addition, because of the possibly unstable relationships between asset classes (think of stocks and bonds), models that capture the time-variation in coefficients (Engle 2002; Engle and Kelly 2009) can improve parameter estimates.

The correlations of asset classes also vary over time and are state dependent; they are high during crises. In such times, when risky assets fall sharply, increased correlation means a loss of diversification. In addition, diversification also leaves investors with systematic risk, which is likely to increase during crises as well.

Risk appetite of long-term investors and investments in illiquid assetsAlternative asset classes have diversification benefits; they also introduce risks such

as uncertainty, valuation risk, liquidity risk, and possibly more significant non-financial risks. A popular means of dealing with ambiguity risk is to use so-called maxmin preferences, as in Gilboa and Schmeidler (1989), where investors maximise their expected utility defined in a standard way (with risk aversion as its main characterisation), but where there is a set of possible probability distributions instead of only one. Maxmin preferences involve maximising expected utility over the worst possible distribution.An intuitive alternative, suggested by Barberis (2000), simply takes into account the higher risk of uncertainty about expected returns—a greater dispersion of possible outcomes at terminal date.

The average (individual) investor’s preferences for liquidity mean that investors must pay a premium for it; assets that can be sold with low frictional costs (low transaction costs, i.e., low bid/ask spreads) are required. For this reason, the first measures of the cost of liquidity were based on bid/ask spreads (Amihud and Mendelson 1986). These authors introduce the notion that the liquidity cost is higher for short-term investors because the annualised impact of the trading cost, seen as a one-off cost, falls as the holding horizon lengthens. By the same token, long-term investors may benefit from the liquidity risk premium by investing in assets with very high bid/ask spreads and holding them for a very long period.

Institutional investors have longer investment horizons than do individual investors. Unlike retail investors, institutional investors have huge amounts





of wealth to invest and the resources to analyse strategies. Because of the nature of their liabilities, they also have more distant investment horizons; in addition, by pooling savings they diversify away the specific risk of the individual’s requiring liquidity in times of financial stress (each individual is subject to the risk of unemployment after a crisis, but in all likelihood only a fraction of investors will lose their jobs at any one time, so the institutional investor can invest in less liquid securities).

Pension funds have the longest investment horizons of any institutional investors, not only because of the long-term nature of their liabilities but also because the restrictions they face in the short term are generally laxer than those of other investors (as pension funds are not commercial entities, they cannot go bankrupt).

As academic studies point out that assets with higher bid/ask spreads have higher expected returns, long-term investors may be advised to invest in assets that have large bid/ask spreads and, in general, in those that have the highest premium. That more than 60% of Yale University’s endowment is allocated to alternative strategies is illustrative of this pursuit of liquidity risk. Indeed, the endowment’s chief investment officer notes: “Accepting illiquidity pays outsize dividends to the patient long-term investor” (Arnsdorf 2009, p. 1).

Amihud (2009) provides the rule of thumb that the liquidity risk premium should be at least equal to the (round-trip) trading costs times the average

number of trades per year on a given security. To confirm these calculations, Amihud and Mendelson (1986) estimate that a 1% increase in bid/ask spread yields a 2.5% increase in returns. These calculations were made on pre-1986 data, when annual stock turnover was around 50%—much less than it is today—so they expect this excess return to have risen.

More recent estimates show that the liquidity premium can be considerable: Loderer and Roth (2003) show that median-spread stocks trade at a 30% discount to zero-spread stocks (Nasdaq 1995-2001). Aragon’s (2004) analysis, more specific to hedge fund returns, shows that liquidity restrictions on hedge funds, summarised as lockup provisions and redemption periods, account for a significant share of their returns and that funds with lockup provisions have equally weighted annual returns 7%–8% higher than funds without such provisions, and value-weighted returns 4%–5% higher.

1.1.3. Liability-Driven and Life-Cycle InvestingPension funds must allocate their assets to the liability-hedging portfolio (LHP), the performance-seeking portfolio (PSP), and the residual cash account. In the pension fund industry, disentangling the LHP and the PSP in the definition of the asset allocation is known as liability-driven investing (LDI).

This approach, summarised in Amenc, Martellini, and Sender (2009), is also implicit in studies such as Hoevenaars et al. (2005).



We consider n risky assets, with price dynamics:

dPti = Pt

i μidt + σijdWtj

j =1

n

∑⎛

⎝⎜

⎞

⎠⎟ , i = 1,...,n

The risk premium process is

θt = σt−1 μt − rt 1( )

The liability process is:

dLt = Lt μLdt + σL, jj =1

n

∑ dWtj + σL,εdWt

ε⎛

⎝⎜

⎞

⎠⎟

The optimal terminal funding ratio obtained as a solution to the programme:

Maxws ,t ≤s ≤T

Et

ATLT

( ) 1−γ

1− γ

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥

, such that :

Et

QLAT

LT

⎡⎣⎢

⎤⎦⎥

=At

Lt , where At( ) is financed by a feasible trading strategy with initial investment A0( ) , is given by:

while the optimal portfolio strategy is: .

w * =

1γ

σσ '( )−1 μ − r1( ) + 1−1

γ⎛⎝⎜

⎞⎠⎟

σ '( )−1σL

We thus obtain a three-fund separation theorem, where the optimal portfolio strategy is to hold two funds, one with weights

ωM =σσ '( ) −1

μ − r1( )1' σσ '( ) −1

μ − r1( )

and another with weights ωL = σ '( ) −1

σL ,the remainder invested in the risk-free asset.

The first portfolio is the standard mean-variance efficient portfolio, the performance-seeking portfolio (PSP). The amount invested in that portfolio is directly proportional to the investor’s Arrow-Pratt coefficient of risk-tolerance

−

JF

FJFF=

1γ

(the inverse of relative risk aversion). The greater the investor’s (funding) risk tolerance, the greater the allocation to that portfolio.

The second portfolio is the liability-hedging portfolio (LHP), which minimises correlation with the liabilities. The LHP, defined as

ωL = σ '( ) −1

σL , is the projection of available assets on the liability. In other words, it is the portfolio that minimises the local volatility σF

w of the funding ratio. As such, it is the equivalent of the minimum variance portfolio for a pension fund—it is the equivalent of the risk-free asset in complete markets in which liability risk is entirely spanned by existing securities ( σL,ε

2 = 0 ). In our notations, the PSP weights sum to one, the LHP weights do not.

The optimal portfolio strategy can be written:

w* =

1γ

σσ '( ) −1μ − r1( ) + 1−

1γ

⎛

⎝⎜⎞

⎠⎟ωL

In a constant opportunity set, without funding constraints, the asset allocation of investors with power utility will be a fixed-mix of these three funds (and the log-investor will not invest in the liability hedging portfolio, which can be understood because the LHP also provides a form of intertemporal hedge to which the log investor gives no importance).


FT

* =AT

*

LT= ηL t ,T( )( )−1 At

Ltξ t ,T( )( )−

1γ Et

ξL t ,T( )ηL t ,T( )

⎡⎣⎢

⎤⎦⎥

⎛⎝⎜

⎞⎠⎟

−1

Et ξ t ,T( )1−1

γ⎡

⎣⎢⎤

⎦⎥⎛⎝⎜

⎞⎠⎟

−1



A stochastic opportunity set gives rise to additional hedging demands that professionals often fail to take into account. Of particular importance are these hedging demands when returns are predictable (Barberis 2000). Innovations in predictors (such as the dividend yield) are often negatively correlated with returns (a fall in prices leads to a rise in dividend yield and better subsequent returns), which introduces a strategy that aims to buy low and sell high (or buy when the predictor—dividend yield—is high and sell when it is low) to benefit from reversion to the mean. Hedging thus involves a dynamic strategy that depends on the state variables (but not directly on wealth or on the funding ratio).

1.1.4. Risk Insurance: Risk-Controlled Investing and Economic CapitalRisk-controlled investing as a rule-based strategyStatic risk budgeting, even when parameters are fixed and the opportunity set is constant, do not guarantee that minimum funding ratios will not be breached unless pension funds invest less than their surpluses in risky assets, an investment policy that will always be judged insufficiently risky. By contrast, when its funding ratio is falling, a pension fund will be criticised, ex post, for having allocated too heavily to risky assets.

Pension funds need non-linear payoffs. This need is made explicit when one incorporates regulatory constraints in the definition of target strategy. After all, prudential regulations create minimum funding constraints: they require actuarial valuations at

frequencies of one to three years; when funding requirements are not met these regulations may also require recovery plans involving additional contributions from the sponsors. IAS 19 also penalises sponsors of pension funds whose funding ratios fall outside the 90%-110% range. Even without considering regulatory restrictions, traditional DB pension funds also generally look to ward off deficits, as deficits involve sponsor risk—the risk of a sponsor’s inability to compensate for pension deficits.

When incorporating terminal funding constraints in the utility function, pension funds can rely on the martingale or convex duality approach to dynamic asset allocation problems (Karatzas, Lehozcky, and Shreve 1987; Cox and Huang 1989), first to find the optimal terminal payoff—an option—then replicating this terminal payoff. The replication of a terminal payoff with minimum funding constraints requires a form of dynamic asset allocation that may be called dynamic risk-budget management or risk-controlled investing (RCI). RCI involves a strategic allocation to the performance-seeking portfolio and liability-hedging portfolio that changes as a direct function of the (inverse of the) funding ratio.

In the formal ALM model presented in Amenc, Martellini, and Sender (2009), dynamic asset allocation is necessary to protect against the risk of shortfalls, as illustrated below.

When we make minimum funding constraints part of the formal ALM model described in section I.1.3, using the same notations, the maximisation program is:




Maxws ,t ≤s ≤T

Et

ATLT

− k( ) 1−γ

1− γ

⎡

⎣

⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥

it can be shown that the asset allocation to these three funds is not only dynamic but also directly linked to the funding ratio. The optimal risk insurance strategy is then:

And the weights allocated to the PSP and to the LHP are:

wm* =

1γ

1−k

Fs

⎛

⎝⎜⎞

⎠⎟1' σσ '( ) −1

μ − r1( )⎡⎣⎢

⎤⎦⎥

wl* = 1−

1γ

1−k

Fs

⎛

⎝⎜⎞

⎠⎟⎛

⎝⎜

⎞

⎠⎟

One can thus see that risk-controlled investing is a direct extension of liability-driven investing. For this reason, it has been called dynamic liability-driven investing, a term sometimes used in the questionnaire but systematically replaced by risk-controlled investing in this publication.

Section 1.1.3 showed that without minimum funding constraints, the power utility investor has a constant exposure to the PSP and to the LHP: its asset allocation is a fixed-mix. Here, still with a constant opportunity set and with minimum funding constraints, investors with power or even log utility have a dynamic exposure to

the LHP—they also need to hedge against the risk of a shortfall by increasing their allocation to the LHP when their surpluses shrink.

As in the unconstrained case, weights (and amounts) allocated to the PSP are a direct function of the risk premium (even though in the current constant opportunity case the hedging of changes in the opportunity set is ignored).

In an attempt to quantify the value added by risk management, Martellini and Milhau (2009) estimate the cost of a given strategy by the average volatility of the contributions from the sponsor that take place when the minimum funding ratio is breached. In their paper, the utility function is the power utility of the funding ratio,6 but the sponsor is required to implement a recovery plan when the pension fund is underfunded at reporting date. The recovery plan restores the minimum funding ratio in one to five years. For a given utility, dynamic asset allocation allows lower average contributions from the sponsor of the pension fund.

Minimum or maximum funding constraints require RCI to replicate a constrained optimal payoff. From a theoretical standpoint, RCI should thus be preferred to other forms of investing. Static investments in derivatives, for instance, have theoretical drawbacks. First, most traded derivatives have a single underlying asset, usually a broad equity market index, a swap rate, or the German bond market. Although combinations of these traded derivatives can ward off deficits, they do not make it possible to replicate


6 - Embedding the minimum funding ratio constraint in the utility function is usually done by using a translated power utility: (A(T)/L(T)-kmin)1-γ/(1-γ) instead of (A(T)/L(T))1-γ/(1-γ), for instance.

w* =1

γ1−

kFs

⎛

⎝⎜⎞

⎠⎟σσ '( ) −1

μ − r1( ) + 1−1

γ1−

kFs

⎛

⎝⎜⎞

⎠⎟⎛

⎝⎜

⎞

⎠⎟ σ '( ) −1

σL

or

w* =1

γ1−

kFs

⎛

⎝⎜⎞

⎠⎟σσ '( ) −1

μ − r1( ) + 1−1

γ1−

kFs

⎛

⎝⎜⎞

⎠⎟⎛

⎝⎜

⎞

⎠⎟ ωL



the optimal payoff RCI would have provided. For instance, when indexation is conditional, as it often is in continental Europe (in the Netherlands, indexation is conditional on the funding ratio of the pension funds; in Germany, or in with-profit insurance-like arrangements, it is conditional on financial returns), liabilities depend on the investment strategy of pension funds, so liabilities alone cannot be replicated (it is not easy to separate the LHP from the PSP). So, if liabilities cannot be replicated statically with derivatives, the optimal payoff cannot always be replicated, either (for instance, when the funding ratio is close to the minimum). On the whole, from an economic standpoint (without accounting for liquidity risk and prudential constraints), derivatives may be farther from optimal than dynamic strategies.

Economic capital as a as a discretionary insurance strategyFrom a practical standpoint, a static risk-budgeting exercise that embeds funding constraints, such as economic capital, but repeated at a sufficient frequency also results—ex post—in a portfolio insurance strategy. When they state that regulatory VaR constraints decrease the gains from risk insurance, Binsbergen and Brandt (2007) implicitly suggest that economic/

regulatory capital management, plus maximum weight constraints, results in a strategy similar to the optimal portfolio insurance programme.

Economic/regulatory capital models treat the surplus as a risk budget and require that the total balance sheet risk, measured at the Value at Risk at a one-year horizon, be less than the surplus (in the Dutch FTK, for instance, assets must be high enough to cover the liabilities over a one-year horizon with a probability set at 97.5%, whereas the confidence interval for insurance companies is 99%).

Economic capital (VaR constraints) involves dynamic exposure to the PSP and the LHP that is similar to that in risk-controlled investment. If this constraint is managed at sufficiently regular intervals, it should also result de facto in a strategy that ensures that minimum constraints are not breached, as illustrated below in a complete market setting (results for the incomplete market case can be found in appendix 5.3).

For an illustration of the relative properties of economic capital and RCI, let us assume that economic capital is applied to the funding ratio; the regulatory constraint is a multiplier of the volatility of the funding


Source: Martellini and Milhau (2009)

Frequency (years) 1 3

Recovery time% of contribution saved

1 3 5 1 3 5

(γ=2) −4.607 −1.623 −0.866 −3.909 −1.374 −0.726

(γ=5) −1.092 −0.415 −0.254 −0.916 −0.384 −0.241

(γ=10) −0.24 −0.092 −0.58 −0.194 −0.083 −0.053

Figure 3: Benefits of dynamic asset allocation are still greater in the presence of minimum funding constraintsThe reporting date is either yearly or every three years (first line). The recovery plan restores the minimum funding ratio in one to five years (second line). A risk-controlled investing strategy achieves the same utility as an unconstrained strategy with lower contributions (the last three lines for degrees of risk aversion).




ratio (not the volatility of the surplus as is usual in regulation). The volatility of the funding ratio reads

(ω − ωL ) ' ⋅σσ ' ⋅(ω − ωL ) + σL ,ε

2

Letting m be the multiplier (which transforms the volatility of an asset class into the one-year-ahead 97.5% confidence interval), the regulatory constraint reads: m⋅ A2(ω − ωL ) ' ⋅σσ ' ⋅(ω − ωL ) = A − kLs

or

m2(ω − ωL ) ' ⋅σσ ' ⋅(ω − ωL ) = 1−

kFs

⎛

⎝⎜⎞

⎠⎟

2

the optimal portfolio policy reads:

The optimal amounts invested are:

Optimal RCI weights, by contrast, read:

In the same complete market setting, optimal weights from RCI read:

In economic capital as in RCI strategies, the allocation to the PSP is driven primarily by risk insurance, as it is a direct function of the surplus (1-k/Fs). Thus, economic capital can be interpreted as constant proportion portfolio insurance in an ALM context: the total allocation (weight ω times wealth A) to the risky assets is a fixed multiplier

times the surplus that can be simplified (think of the one-asset case) as

A*

1m⋅σ M

⋅(1−1

Fs

) =1

m⋅σ M

⋅( A − L )

For a PSP which has a volatility of σM=15% and for a regulatory multiplier m=1.96 (representing the 97.5% confidence interval of the normal law), the multiplier of the strategy is (m.σM)-1=3.4.

In RCI models, the fraction of the liabilities hedged depends on risk aversion. Economic capital models, by contrast, require the full hedging of liabilities—more precisely, when economic capital is applied to the surplus, liabilities are fully hedged, and when economic capital is applied to the funding ratio the weight allocated to the LHP is equal to the value of the assets (see appendix 5.3). Swaps are usually bought for a full hedge of interest rate risk; risky assets are bought with cash.

In economic capital models, allocation to the PSP is not sensitive to overall returns in the economy. That allocation does not depend on the risk premium shows that economic capital models are not naturally suited to stochastic opportunity sets. In RCI models, by contrast, the allocation to the PSP is a linear function of the risk premium—the allocation to the PSP depends on expected returns, proxied by such variables as dividend yield.

In economic/regulatory capital management,the asset allocation is not fully specified ex ante (it is not predictable); instead, it is left to management, which then decides which changes in asset allocation must be made to respect regulatory constraints. Models

ω = ωL

+(σσ ') −1 ⋅ (μ − r1)

(μ − r1) ' ⋅ (σσ ') −1 ⋅ (μ − r1)⋅

1

m1−

kF

s

⎛

⎝⎜

⎞

⎠⎟

ω ⋅ A = ωL ⋅ A +

(σσ ') −1 ⋅(μ − r1)

(μ − r1) ' ⋅(σσ ') −1 ⋅(μ − r1)⋅

( A − kL )m

w* = 1−1

γ1−

kF

s

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟ ω

L+

1

γ1−

kF

s

⎛

⎝⎜

⎞

⎠⎟ σσ '( ) −1

μ − r1( )



of economic/regulatory capital imply discretionary decisions and usually suit a management style in which management agreement is needed to rebalance a portfolio. Economic/regulatory capital models can be used to monitor and manage various constraints and multiple risk budgets simultaneously: practitioners then have a dashboard in which they monitor economic constraints (in the Netherlands, their real funding ratios) and their prudential constraints (on the Netherlands, their nominal funding ratios) simultaneously. Management makes discretionary investment or capital decisions in keeping with these dashboard readings.7

Allocating risks requires risk-adjusted profitability measuresIn practice, the PSP and LHP are not always fully defined ex ante in economic capital models: the definition results from the allocation of the risk budget (defined as the surplus). In a discretionary setting, for economic capital to be implemented efficiently, the risk budget (the surplus, possibly net of the current economic capital or risk consumption) must be translated into investment decisions: it must be allocated first to reference portfolios (the PSP and the LHP) and then to individual investments or funds.

Ideally, assets with poor risk-adjusted profitability (or activities in banking) must be shed, those with higher profitability increased, and the overall asset allocation must at all times respect the risk constraints. An integrated risk-management system thus involves a risk-allocation system.

Explicit factor exposures are as useful for allocating risks as they are for aggregating them. When exposures to each explicit factor are known, one can easily allocate risk across these factors as well as monitor the exposure to these risk factors.

As for any optimisation exercise, the most important tool, from a mathematical standpoint, will be the derivative of the function to be maximised. We derive below the first-order conditions for economic capital models. Though these are close to the typical portfolio optimisation problem considered in the literature, the definition of the natural and practical constraints is different.

We rely on incremental economic capital, a term coined by reference to incremental VaR. Incremental economic capital is obtained from delta economic capital, which is the vector of economic capital’s sensitivity to risk factors.

E C (ω ) = ωii∑ ∂E C (ω )

∂ωi

If it is assumed that the expected rate of return is constant (the expected return m does not depend on the size of the portfolio, a usual assumption in the investment fund industry, in which each investor is considered small in relation to the financial markets), with Qα the Value at Risk with confidence interval α, the derivation yields:

∂E C (ω )∂ωi

=∂(Q

α (ω ) − μ 'ω )

∂ωi

=∂Q

α (ω )

∂ωi

− μi

In economic approaches, when expected returns are positive, the risk budget is slightly higher than the risk measure


7 - In addition to traditional VaR measurements, financial companies usually incorporate stress-tests to quantify risks not captured by VaR methods. These stress tests usually increase the measure of risk and lead to an additional capital requirement: stress tests lower the risk budget. When a firm has excessive risk, i.e., when it lacks capital or surplus to withstand its current risks, it must either reduce risk or increase its available capital. Risk is reduced by cutting equity holdings, diversifying better, using portfolio insurance or derivatives; capital is increased by lowering liability, reducing indexation, or securitising unencumbered assets.



Qα(ω), or the economic capital is lower (EC(ω) = Qα(ω)-μ’ω). When returns are Gaussian EC(ω) = k.σ(ω)-μ’ω.

Though it is written differently, the problem is then equivalent to the Markowitz approach, since minimising EC(ω) = Qα(ω)-μ’ω with Gaussian returns and fixed expected returns is equivalent to minimising the variance.

For all i, the first-order conditions read:

μ 'i

∂Qα

(ω )

∂ωi

− μ 'i

= v

This quantity

μ 'i

∂Qα

(ω )

∂ωi

− μ 'i

is the return on economic capital (RoRAC) and it is suitable for performance measurement. This expression also shows that

ωi

∂E Cα (ω )

∂ωi

= ωi

∂Qα (ω )

∂ωi

− μ 'i ωi

is the most natural way to allocate economic capital per sub-portfolio (and to measure the performance of sub-portfolios, too).

In practice, risk allocation methods are not always readily available to those who use economic capital; even when they are, discretionary decision-making in successive investment committee meetings leads to possible delays in modifying the strategy and to subsequent losses that could have been avoided by committing more rigorously to hedging strategies. After all, failure to specify the optimal strategy ex ante often implies a failure to prepare for changes in the

environment or for hedging prudential constraints.

Economic capital without rule-based implementation entails the risk of delaysEconomic capital is better suited to the traditional organisation of pension funds and the role of the trustees in asset allocation. Unless pension funds have the means to transform a risk budget into an investment decision, pension funds relying solely on these methods run the risk of losing responsiveness and making investment changes too late. Delays are possible when discussions in investment committees on the adequate change in investment strategy are not conclusive. As La Fontaine (1668) puts it: “To argue or reline / Wise counselors abound; / The man to execute / Is harder to be found.”

As the literature shows, trustees or managers are often reluctant to implement optimal investment decisions; for instance, they are averse to selling at a loss (when market values are less than book values).

On the whole, then, when attempts to insure risks away are made, the failure to define formally an LHP and a PSP and to draw up pre-defined investment rules is a great drawback of economic capital and other techniques such as surplus optimisation.

We thus recommend that pension funds rely more heavily on rule-based strategies such as RCI to implement their economic capital models. Rule-based economic capital means that investment decisions are implemented following rules suitable




for risk insurance. They may be refined or even slightly distorted when reviewed in investment committees. They are unlikely to be totally ignored or overruled, as may be the case when discretion prevails.

Managing non-economic constraintsRegulatory constraints that are at odds with the economics of the pension fund8 also require close attention; the pension plan will shift its investment strategy to the portfolio that minimises risk as identified by these regulations. The simple and generic technique we suggest is to define a “regulatory LHP” as the projection of the regulatory liability on the universe of tradable assets. The portfolio will shift towards this LHP when the regulatory constraints become binding.

Regulations often prescribe the discount rates. For instance, as IAS 19 requires discounting liabilities at the yield of AA bonds, fixed liability cash flows require a portfolio of forward credit rate agreements as a match.

The historical standard that involved discounting liabilities at a fixed discount rate makes the duration of the regulatory LHP shorter than the duration of the liabilities; by contrast, the Dutch FTK regulation, which requires a nominal approach to real liabilities, involves a regulatory duration greater than that of the real liabilities. These regulatory standards require interest rate convexity and dynamic management of the duration.

The regulatory valuation of liabilities may also fail to take into account specific risk factors. Regulators have historically failed to take into account the risk of a longer life; the Swiss regulator does not require mandatory indexation to be measured in the regulatory value of liabilities; in most cases, the combined risks of both higher liabilities (for instance, from greater longevity) and lower interest rates are not taken into account, which tends to result in sub-optimal interest rate risk management and hedging—interest rate risk has caused even the most sophisticated pension funds, Dutch multi-industry schemes, to go underfunded in 2008.

1.1.5. Integrated ALM—Managing Sponsor Risk and Accounting riskThe sponsor of a pension fund cannot close deficits if it goes bankrupt. Thus, pension funds are short a put option on the default of their sponsors, the nominal amount of which is the deficit in the event of sponsor default. In reality, because participants in pension funds (active members) receive salaries from the sponsor, their exposure to sponsor risk is much greater than the exposure of the pension fund itself—if the sponsor defaults, they may lose part of their human capital (future wage income). Making sponsor risk part of the decision-making process is called integrated ALM for the pension fund. Managing sponsor risk is a natural approach since pension fund trustees must act in the interest of the participants.

The sponsor is subject to accounting risk, i.e., the risk of changes in the funding ratio of the pension fund resulting in a volatile P&L in the accounts of the


8 - There are accounting and prudential constraints. The volatility of the cost of providing pensions in the accounts of the sponsor is an accounting constraint; minimum funding ratios and the negative impact of recovery plans are prudential constraint, particularly binding during downturns where sponsors and participants have scarce resources. When liabilities must be discounted at a fixed or smoothed discount rate, an interest rate risk different from the natural “market” discount rate used by the pension fund must be hedged.



sponsor. The sponsor can manage the risk in its account; it also participates in the definition of the investment strategy when the pension fund is set up or the contribution policy is decided—after all, the value of the put option offered by the sponsor to the participants also depends on pension fund strategy. Sponsors can thus also take an integrated approach to their ALM.

We provide a brief review of the solutions to the problem of managing accounting and sponsor risks.

Optimal asset allocation for the sponsorSponsors are bound primarily by prudential and accounting regulations in the calculation of their reported cost of providing pensions. IAS 19 essentially prescribes the way the cost of pensions is computed in the profit and loss account independently of the actual cash contributions made to the plan. Deficits higher than 10% are amortised over the average remaining working lives of participants. In addition, liabilities are discounted at an AA rate, and Amenc, Martellini, and Sender (2009) show that a portfolio of forward interest rates swaps in the sponsor’s account makes it possible to manage the accounting discount rate.For the management of accounting volatility in keeping with IAS 19, Sender (2009b) shows that sponsors and pension funds need only agree on a risk-controlled strategy that ensures that the funding ratios fall within the IAS 19 90%-110% corridor for sponsors’ profit and loss accounts to be unaffected by the volatility of the funding ratio of

their pension funds in the current IAS 19 framework.

After all, one can take both minimum and maximum funding constraints into account very easily by imposing explicit terminal constraints; the maximisation programme thus reads:

Maxws ,t≤s≤T

Et

AT

LT

⎛⎝⎜

⎞⎠⎟

1−γ

1− γ

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

s.t. k1 ≤

AT

LT

⎛⎝⎜

⎞⎠⎟

≤ k2

The first-order condition reads:

1LT

AT

LT

⎛⎝⎜

⎞⎠⎟

−γ

− υ0 (k1 ,k2 ) ⋅ MT +υ1 (k1 ,k2 )

LT

−υ2 (k1 ,k2 )

LT

where M is the stochastic discount factor, υ0 the Lagrange multiplier associated with the budget constraint, υ1 the Lagrange multiplier with the minimum funding constraint, and υ2 with the maximum funding constraint. All multipliers depend on k1 and k2, and υ1(0,∞)=υ2(0,∞)=0 because k1=0 and k2=∞ represent the unconstrained case. υ1 and υ2 are strictly positive when the terminal funding ratio is equal to k1 and k2 respectively, and zero otherwise; thus the expression simplifies both when υ1 and υ2 are null and when they are positive, as follows:

FTk1 ,k2 ,*= Min(Max( υ0 (k1 ,k2 ) ⋅ MT ⋅ LT

⎡⎣ ⎤⎦−1/γ

,k1 ),k2 )

FTk1 ,k2 ,*= k1 + ( υ0 (k1 ,k2 ) ⋅ MT ⋅ LT

⎡⎣ ⎤⎦−1/γ

− k1 ) + − ( υ0 (k1 ,k2 ) ⋅ MT ⋅ LT⎡⎣ ⎤⎦

−1/γ

− k2 ) +

FTk1 ,k2 ,* = k1 + (ξ(k1 ,k2 )FT

u,* − k1 ) + − (ξ(k1 ,k2 )FTu,* − k2 ) +

with ξ(k1 ,k2 ) =

υ0 (k1 ,k2 )

υ0 (0,∞)

⎛

⎝⎜⎞

⎠⎟

−1/γ




and FTu,* the unconstrained funding ratio

that is obteined with k1=0 and k2=∞

ξ(k1 ,k2 ) is a budget constraint (from υo), and can be evaluated directly as such.

In the event of explicit funding constraints, the optimal funding ratio is an option on the unconstrained optimum. In terms of pricing, taking the liability as a numeraire makes the funding ratio a martingale and allows the direct pricing of the optional components of the optimal funding ratio, as follows:

Ft

k1

,k2

,* = k1

+ E QL (ξ(k

1, k

2) F

T

u ,* − k1) +⎡

⎣⎤⎦

− E QL (ξ(k

1, k

2) F

T

u ,* − k2

) +⎡⎣

⎤⎦

(Eq.1)

In the constant relative risk aversion, constant opportunity set cast above, the volatility of the unconstrained funding ratio is:

with ωu the unconstrained portfolio weights. These quantities can be used directly to compute

(di ±) for each option, with

di± =

ln(F

t

ki

) ±1

2(σ

F

u ) 2 T − t( )

σF

u T − t

Likewise, ξ must satisfy the budget constraint, i.e., must be such that (Eq.1) is satisfied.

It is also true for any other utility function that in the presence of explicit funding constraints the optimum funding ratio is an option on the unconstrained funding

ratio. This option-like feature enables practitioners to implement it directly, regardless of the underlying technique they use to define their (unconstrained) strategies.

With this idea in mind, practitioners can resort to even simpler heuristics to manage their constraints, for instance, fully hedging their liability risk and buying or replicating a call-spread option on the optimal portfolio of risky assets, the PSP: for €100M of final liability value, the pension fund can invest in a zero-coupon bond that pays €90M (90% being the lower end of the corridor), and replicate a call-spread option on the PSP with a €90M low strike price and a €110M high strike price. In this simple case, practitioners will simply need a European option pricer to allocate assets adequately.

The allocation to the PSP as a function of the funding ratio is illustrated in figure 4. Figure 4: Optimal allocation to risky assets as a function of the funding ratio when there is a 90%-110% corridor and when the corridor narrowsA pension fund that fully hedges its liability risk may invest in a call-spread on the optimal asset mix (the PSP) to respect its 90%-110% funding constraints. The call-spread and its delta can be priced in a Black-Scholes setting, and the amount allocated to this call option depends on the initial wealth of the pension fund. The illustration depicts a British pension fund with initial funding ratio of 99%, interest rate 0%, volatility of the PSP of 25%. The allocation to the PSP diminishes when the funding ratio approaches either the 90% or the 110% thresholds.


(σFu ) 2 = (ω u − ωL ) ' ⋅σσ ' ⋅(ω u − ωL )

(σFu ) 2 =

1

γ 2μ − r1( ) '

σσ '( ) −1μ − r1( ) + σL

' σσ '( ) −1σL − 2σL

' σσ '( ) −1μ − r1( )⎡

⎣⎢⎤⎦⎥



Managing sponsor risk at the pension fundFor a given horizon, then, the pension fund’s exposure to the risk of sponsor default is the expected deficit conditional on the default of the sponsor. Because participants have additional personal exposure to the risk of sponsor default, it is certainly in the interest of participants for the pension fund to hedge at least its own exposure to this risk. In financial terms, pensioners (and hence the pension fund that manages pension assets in their interest) are short a put option on the deficit of the pension fund, conditional to the bankruptcy of the sponsor (in a traditional corporate pension fund, pensioners will not be paid their pensions if the sponsor goes bankrupt while the pension fund is in deficit).

Sponsor bankruptcy is assumed when Y, the terminal asset value of the sponsor, falls below an exogenous threshold B (the value of assets at which bankruptcy is declared, a value determined primarily by coupon/debt values, as well as by tax rates, bankruptcy costs, and the riskiness of the firm [Leland 1994]). The pension fund, for its part, has assets value S and liability value L. A simple approximation of the value of the pension put can be derived in a very simplified setting with a fixed horizon and no possible intermediate default from the sponsor. Then, traditional corporate DB pension funds are short the following put option:

Pt (St ,Yt ) = E Q

t,S ,Y [e− r (T −t)(LT − ST ) +1Y <B ]

with

d2

X =ln( X (t) / K ) + (r − σ

X

2 / 2) ⋅ (T − t)

σX

T − t

for X= (Y, S) and K =(L,B)and

d1

S = d2S + σS T − t =

ln(S / L ) + (r +12

σS2) ⋅(T − t)

σS T − t

d1

Y = d2Y + ρ ⋅σS T − t =

ln(Y / B) + (r −12

σY2 + ρ ⋅σS σY ) ⋅(T − t)

σY T − t

where B is the bivariate Gaussian cumulative distribution function.

The pension put has two deltas, one with respect to each underlying asset. Then, the pension fund could naturally be tempted to hedge against the delta of the put option with respect to its funding ratio, but such a hedging strategy is equivalent to a change in asset allocation, and should the pension fund wish to do so, it would simply need to adopt an RCI strategy that prevents underfunding and sponsor risk in the first place. The pension fund will delta-hedge this pension put by taking the appropriate short position on the assets of the sponsor—the required short position is strongest when the sponsor’s asset value is near bankruptcy; it also decreases in the funding ratio. The formula for the delta with respect to the sponsor’s asset value is:

∂P(S ,Y ,t)∂Y

=S(t) ⋅ n(d

1

Y ) ⋅(1− N (d1

SY )) − K e− rT n(d2Y ) ⋅(1− N (d2

SY ))

YσY T − t

∂P(S ,Y ,t)∂Y

=S(t) ⋅ n(d

1

Y ) ⋅(1− N (d1

SY )) − K e− rT n(d2Y ) ⋅(1− N (d2

SY ))

YσY T − t


P(S ,Y ,t) = K e− rT B(−d2Y ,−d2

S,ρ) − S(t) ⋅ B(−d1Y ,−d1

S,ρ)




with

In general, the sponsor’s assets are not directly traded; only its equity is. A correction should be made to take into account the delta of the equity with respect to the sponsor’s asset value. Our simplified working hypothesis is consistent with the view that the sponsor’s put is hedged and that sponsor’s contributions are not impacted by the funding status of the pension fund. We have:

∂v(Y ,t)∂Y

= N (d1tradY ) and thus

∂Y∂v(Y ,t)

=1

N (d1tradY )

with

d1trad

Y =ln(Y / B) + (r +

12

σY2) ⋅(T − t)

σY T − t

Naturally, in the case of a pension insurance company, such as the PBGC in the US and the PPF in the UK, the pension fund is long a similar put option with a lower strike for the pension fund assets, L’<L. From a practical perspective, one must remember (Haug and Taleb 2008) that the Black-Scholes-Merton argument and equation

is built on the assumptions of operators working in full knowledge of the probability distribution of future outcomes. But the exact asset value that triggers bankruptcy of the sponsor is unknown to the pension fund. The value of the sponsor’s assets is not measurable even though the delta can be approximated by the change in the stock price; the same applies for volatility of the assets; the asset value that triggers bankruptcy is likewise unknown and should be calibrated using corporate bond data from the sponsor.

An alternative is to use financial instruments more closely linked to the risk of default of the sponsor than its shares. Credit default swaps (CDSs), when they are traded, are the most relevant such instrument. Bonds would be suitable as well, but shorting a bond and hedging it dynamically are harder than hedging a CDS dynamically.

A pension fund can easily set up a dynamic hedging scheme on the risk of sponsor default.

1.2. Assessment of Practices

1.2.1. Hedging Risk Away and Construction of the LHPALM is founded on the ability to hedge liability risk. This ability requires the definition of a liability-hedging portfolio, the portfolio that best replicates the liabilities. Because it is expected that this portfolio will reflect the liability structure of pension funds, we will first describe the types of liabilities in our sample.

a. Typology of respondents’ liabilitiesRespondents in continental Europe

d1

SY =

σY ln(S / K ) − σS ρ ln(Y / B)

σS σY

+ r(σY − ρσS )

σS σY

(T − t) +12

(σS (1− 2ρ 2) + ρσY )(T − t)

1− ρ 2 T − t

d2

SY =

σY ln(S / K ) − σS ρ ln(Y / B)

σS σY

+ r(σY − ρσS )

σS σY

(T − t) +12

(ρσY − σS )(T − t)

1− ρ 2 T − t

d1

SY = d2

SY + 1− ρ 2 T − tσS

∂P(S ,Y ,t)∂v(Y ,t)

=S(t) ⋅ n(d

1

Y ) ⋅(1− N (d1

SY )) − K e− rT n(d2Y ) ⋅(1− N (d2

SY ))

YN (d1tradY )σY T − t



generally have hybrid liabilities (28% in core Europe and 71% in Northern Europe), a reflection of the shift from traditional defined benefits to more hybrid forms such as funds with conditional indexation (some form of guarantee is almost systematically required).

In the UK, where flexible conditional indexation is not required but employers may provide defined contributions, the trend has been to close DB schemes and make defined contributions instead—no UK participant reports hybrid schemes. Appendix 5.1 examines these trends. Forty-three percent of survey respondents have traditionally defined liabilities, in other words, pension liabilities that result from a formula linked to the number of years of participation, wages, or amounts contributed, and variables such as inflation or the wage index, but are independent of the investment policy of the pension fund. Thirty-five percent of respondents report hybrid liabilities.

Figure 5: Type of liabilityForty-three percent of respondents have traditional liabilities and 35% hybrid liabilities. Twenty-two percent state that their liabilities are not defined, even though only a very limited number of them are fully defined contributions without specific guarantees.

No. %

Not defined 25 21%

"Traditional" (fully defined) 50 43%

"Hybrid" (conditional) 41 35%

Total 116 100%

Results naturally differ from country to country, with 91% of Dutch respondents reporting hybrid schemes. More than 60% of British and German participants report traditional liabilities. Only 38.5% of Swiss liabilities are hybrid.

These national characteristics are also reflected in the responses from sponsors (two-thirds have traditional pension plans) and fiduciary managers, which, located mainly in the Netherlands, mostly (71%) manage hybrid schemes.

Traditional liabilities are generally linked to inflation and, to a lesser extent, to wages, even though last-wage pension plans are being closed in the UK. By contrast, hybrid liabilities are usually a function of investment returns; pension funds, however, often define and target liabilities they disclose to participants (naturally, pension funds may depart from their targets in the event of extraordinary returns; this is the reason for hybrid liabilities).

More than 70% of hybrid pension plans (excluding the non-responses) define their target indexation with traditional pension funds as a benchmark: 62.5% use economic indices such as inflation and wages as their target, and a large share of “other” respondents refer to specific wage indices (such as sector indices, “base wage” indices, or wages actually paid).

Nearly 13% of pension funds that self-classified as hybrid funds use investment guidelines close to those of defined- contribution funds, as they set their targets directly as a function of the returns of market indices, and thus behave somewhat like benchmarked investment funds.

Finally, nearly 10% lack a pure “internal” target, as they rely on peer analysis and some “other” respondents do not properly define (target) liabilities; they simply define




a set of constraints on their investment policy (such as avoiding shortfalls).

Figure 6: Liability structure or designThe majority (62.5%) of liabilities are indexed to the consumer price index or to a general wage index. This figure aggregates traditional defined benefits formally indexed to such economic indices and hybrid liabilities where the pension fund makes official the target of indexing liabilities to such economic index.

No %

Peer analysis 4 10%

Market index target 5 12%

Main economic index (e.g., consumer price index or general wages)

25 62%

Tailored economic index (e.g., price of a basket of goods for retirees)

0 0%

Other 6 15%

Total 40 100%

b. Design of the liability-hedging portfolioThe characteristics of the liability are the main inputs to the design of an LHP. As it happens, we find that 45% of pension funds characterise their liabilities poorly. As illustrated previously, 25% of respondents report that their liabilities are not defined, even though they are not full DC plans.9 Most of the time, these “undefined liabilities” are in fact hybrid liabilities with limited guarantees and sponsor commitment. These guarantees should be managed—the failure take liabilities into account and to manage in an ALM framework usually leads to sub-optimal results, so these answers are an initial indication of the lack of sophistication of ALM practices in European pension funds.

More than 30% of pension funds do not define an LHP. When they define an LHP, pension funds usually use proxies rather than full characterisation of liabilities.

In the text and the figures, we put under the umbrella “pension fund stakeholders” the following categories: pension funds, participants, sponsors, fiduciary management.

Figure 7: Have you identified the LHP (portfolios below)?The LHP is formally identified by slightly more than 60% of respondents. In Northern Europe, the figure is even lower, probably because having conditional liabilities means that liabilities depend on asset allocation

PF stakeholders Core Europe All

UK Northern Europe

0

10

20

30

40

50

60

70

80

Figure 8: How do you (pension fund stakeholders) define the reference portfolios?In a similar manner to figure 7, figure 8 shows that the LHP is not always defined in terms of liability profile.

No %

Non-response 18 24%

In terms of liability profile 48 65%

As market indices 5 6%

As a bond/cash index 5 6%

Through optimisation 3 4%

73

Figure 9: Do you (pension fund stakeholders) factor in the description of the liability in the investment benchmarks? Again, the liability description is not factored in the investment benchmarks at 46% of pension stakeholders.

No %

Non-response 2 2%

No 34 46%

Yes 37 50%


9 - Ten pension funds state that their liabilities are not defined. Only two are actually “pure” defined contribution, and three have “light” guarantees typical of Eastern Europe.




Country specificities: more inflation-linked securities in the UK than in continental EuropeIn addition to the surprisingly large share of respondents who pay little or no heed to the LHP, we find country specificities in the portfolios of those who define an LHP.

In the UK, there is mandatory indexation to inflation. In addition, indexation is capped to 2.5%, 3%, or 5% depending on the year of service—the year the pension rights are acquired (Amenc, Martellini, and Sender 2009). Thus this mandatory indexation is best replicated with derivatives, as there are derivatives based on inflation in the UK, which gets around the basis risk many European countries are subject to when hedging their inflation exposure.

By contrast, in the Netherlands, most pension funds take a hybrid form, and indexation is generally conditional on the surplus. Inflation is a reference rather than something that should be perfectly replicated at all times. In addition, inflation derivatives imply basis risk as they are generally based on the European consumer price index (CPI) rather than on the Dutch CPI. On the whole then, Dutch pension funds—and, to a lesser extent, those in continental Europe—are less likely to rely on options in the construction of their LHPs than are their British counterparts.

We find that all British pension funds have at least 10% of their LHPs made up of inflation-linked bonds (ILBs), and 40% have more than 50% in ILBs. By contrast, only 37.5% of continental pension funds have more than 10% of their portfolios invested in ILBs, and only 7.5% have more than 50% invested in ILBs.

Likewise, 40% of respondents from the United Kingdom invest more than 20% of their LHPs in inflation derivatives, whereas only 12.8% of those outside the UK do so. This difference is statistically significant (see figures 10a and 10b).

Figure 10a: ANOVA and Fisher tests on LHP, UK vs. non-UK respondents. Share of inflation-linked bondsRespondents from the UK have significantly more inflation-linked bonds than do non-UK respondents.

>20% <20% Fisher ANOVA

UK 4 6 + ++

Non-UK 10 68 (p=0.049) (p=0.0029)

Figure 10b: ANOVA test, share of inflation-linked bondsThe three geographies have a significantly different proportion of inflation-linked bonds in their portfolios

UK Northern Europe +

Netherlands

Core Europe

ANOVA

Means 2.727273 1.769231 1.588235 +(p=0.0184)

Figure 10c: ANOVA test, share of inflation derivativesThe UK uses significantly more derivatives than continental Europe

UK Continental Europe ANOVA

Means 2.3 1.1447 ++(p=0.0024)

The LHP and the time horizonAs we mentioned in the background, pension funds that have a long horizon and real liabilities should use real assets to match these long-term commitments, as these assets offer a good inflation hedge for the long run.

Since these assets offer very poor hedging properties over the short run, pension funds that are subject to short-term constraints usually account for these risks by classifying these real assets in the PSP, not in the LHP. After all, the LHP is a low-risk portfolio, and the term structure of risk



that makes it possible to invest in equities and other real assets involves a risk that must be accounted for.

However, 35% of respondents have more than 20% of equities in their LHPs, a figure that suggests that many European pension funds have chosen to implement these long-term hedging strategies as part of the LHP… which then is no longer a low-risk portfolio.

1.2.2. Risk Diversification and Construction of the Performance-Seeking PortfolioIn addition to hedging liabilities, pension funds must try to generate performance either to diminish future contributions or to increase the value of pension payments.

a. Investment benchmarks for individual asset classesThe design of an efficient PSP can be seen as a two-step process. One first needs to choose appropriate benchmarks for each asset class, then to combine these benchmarks into a global benchmark portfolio.

Within an asset class, one should seek exposure to the market via benchmarks that should not be market indices or other cap-weighted mechanisms, which have proven grossly inefficient.

Figure 11: How do you (all respondents, excluding non-responses; multiple choice question) define the reference portfolios?Sixty percent of respondents use market indices to define the PSP. More—66%—use market indices as benchmarks for individual funds.

PSPIndividual funds

In terms of liability profile

As market indices

As a bond/cash index

Throughoptimisation

0

10

20

30

40

50

60

70

80

Sixty percent of respondents design the PSP as a combination of market indices—and a limited fraction in terms of liability profile or bond/cash index—and two-thirds define the benchmarks for individual funds from indices, too. Only 32% of those surveyed use optimisation techniques to design the PSP (to find the appropriate mix of asset classes); only 30% of respondents (22% of all those surveyed) resort to optimisation to define the investment benchmarks of individual funds (within an asset class).

Asset management firms may be tempted to select inadequate and noisy investment benchmarks because of the usual practice of peer analysis. And individual investors lack the knowledge to select or define more appropriate benchmarks. But pension funds have the sophistication to construct efficient benchmarks or select providers that construct efficient indices. Pension fund trustees work to give




participants a fair pension and pension fund are not benchmarked against cap-weighted indices nor against their peers. Thus, pension funds have no reason not to choose optimal strategies.

b. Use of asset classes in the PSPDiversificationOnce appropriate benchmarks for each asset class have been selected, the PSP will be derived by weighting the asset classes. One-third of those surveyed invest more than 75% of their holdings in stocks and bonds (here including ILB and corporate bonds); two-thirds invest at least two-thirds of their assets in these two categories. Mortality derivatives or reinsurance are the assets that do most to diversify away the longevity risk borne by pension funds. They are not widely used, however; indeed, they are ignored by 46% of respondents.

Equity is the preferred asset class; on average, it accounts for 32% of total allocation to the PSP. Bonds seem to be relegated to hedging liabilities, as 15% of respondents have no bonds in their PSPs, even though bonds provide diversification benefits and can hedge against both real and nominal interest rate changes.

Accessing the illiquidity risk premiumOutside the most liquid listed securities, one is exposed to different degrees of uncertainty and valuation risk, liquidity risk, and other specific risks.

The average individual investor’s preference for liquidity means that he must pay a premium for it and requires assets that can be sold with low frictional

costs (transaction costs, bid/ask spreads). For this reason, the first measures of the cost of liquidity were based on bid/ask spreads (Amihud and Mendelson 1986). Liquidity costs are higher for short-term investors because the annualised impact of the trading cost, seen as a one-off cost, diminishes with the holding horizon. By the same token, long-term investors may benefit from the liquidity risk premium by investing in assets with very high bid/ask spreads and holding them for a very long period.

Anecdotal evidence suggests that the usual industry recommendation is that pension funds invest at least 30% of their holdings in alternative assets; more than 60% of Yale University’s endowment is allocated to alternative strategies, an allocation illustrative of the pursuit of liquidity risk.

Thus most of those surveyed allocate very little to other asset classes. Average cumulative investment in hedge funds, private equity, and infrastructure is 15% in continental Europe and 19% in the UK; only 10% invest 25% of their assets or more in the following potentially less liquid securities: infrastructure, private equity, hedge funds, and mortality derivatives. Combined with real estate, however, investments in these asset classes amount to nearly 25%, and only 8% of those surveyed have no real estate in their portfolios, both statistics that underscore an apparent preference for real estate as a source of the illiquidity risk premium. When real estate is accounted for, 25% of those surveyed have more than 30% in all potentially illiquid investments.




On the whole, however, investments in alternative asset classes seem to be insufficient both to maximise diversification benefits and to gain access to the illiquidity risk premium most readily accessible to pension funds.

c. Use of static risk-budgeting techniquesRespondents are more likely to report that they understand the techniques necessary for portfolio construction and static risk-budgeting techniques than they are to use them.

Eighty percent of those surveyed—as well as 80% of pension funds—report that they master LDI concepts (see figure 12a), but only 63% (57% of pension funds) report that they actually use them (see figure 12b). In addition, even though the preferred technique is LDI (see figure 13), used by more than 45% of all respondents and of pension funds, more than 45% resort to techniques such as surplus optimisation or economic capital, which do not require the identification of an LHP and a PSP. Because this identification clarifies portfolio construction and makes it possible to use rule-based strategies to manage constraints, we are surprised to find that a large majority of the 37% of respondents (and 43% of pension funds) that do not use LDI techniques assert that these techniques either add no value or are irrelevant (see figure 12c).

Bayesian and portfolio resampling techniques are by far the least understood techniques in the profession; the primary reason for their unpopularity, as for that

of robust portfolio construction, is the lack of knowledge (see figure 14c).

Figure 12a: How well are the fields/techniques below understood by your firm (all respondents)? The light and dark yellow bars represent above-average mastery, “3” or “4” on a scale from “1” or “not at all” to “4” or “very much so”). Eighty-six percent of respondents master shortfall risk, and 82% master LDI techniques. Only 35% master Bayesian and portfolio resampling techniques

(++) Very much so(+)(-)(--) Not at allNon-response

Shortfall risk Robust estimation

and simulation

Bayesian analysis/

resampling techniques

Liability-driveninvestment

0

20

40

60

80

100

Figure 12b: Are the fields/techniques below used at your firm (all respondents)? The yellow bars are the fraction of respondents that use the techniques. All techniques are less likely to be used than to be understood.

YesIn progressNoNon-response


and simulation

Bayesian analysis/



0

20

40

60

80

100




Figure 12c: If not, why not? (All respondents)The yellow and orange bars show the share of respondents not using a particular technique who think the technique is “not relevant” or “does not add value”. More than 80% of those not using LDI or shortfall risk think these techniques “do not add value” or are “not relevant”.

Not relevantDoes not add valueLack of knowledgeCosts too muchToo difficult from anorganisational standpoint


and simulation

Bayesian analysis/



0

20

40

60

80

100

120

140

Figure 13: Do you factor in the risk of shortfall/surplus with respect to liabilities in the design of the ALM strategy?Forty-five percent of respondents use LDI techniques to factor the risk of shortfall/deficit in their strategies. More than 45% of respondents and of pension stakeholders use techniques such as economic capital, Value at Risk or surplus optimisation that do not require a formal definition of the LHP and of the PSP.

All respondentsPension fund stakeholders

No Yes, with non-linear AM techniques

whithout explicit reference to liabilities

Yes, we usesurplus

optimisationtechniques

Yes, matchingcash flows

Yes, we use economic capitalor Value at Risk

Yes, option-pricingapproach forconditionalliabilities

Yes, other

Yes, with LDI(liability-driven

investment)

0

10

20

30

40

50

1.2.3. Risk-Controlled Investing and Management of Regulatory ConstraintsEnsuring that minimum funding ratios are met requires a form of dynamic asset allocation that can be called portfolio insurance. Regulatory constraints that take the form of minimum or maximum funding likewise require dynamic asset allocation, risk management, or derivatives.

Managing regulatory constraints that differ from economic constraints calls for identification of a “regulatory LHP”. IAS 19 requires discounting liabilities at the yield of AA bonds, so fixed liability cash flows require a portfolio of forward credit rate agreements as a match. The Dutch nominal framework and traditional regulations that smooth interest rates require a dynamic duration approach to be implemented with a dynamic allocation to swaps and swaptions (Amenc, Martellini, and Sender 2009).

In the current section we review the understanding and use of risk insurance, in particular for the management of economic, prudential, and accounting constraints.

Risk-insurance techniques are less well understood than static risk-budgeting techniquesRisk-insurance investing, which makes it possible to insure against the risk of shortfalls, is less well understood than static risk budgeting.

Fifty-six percent of respondents and 53% of pension funds report that they understand RCI; only 41% of respondents and 30% of pension funds use this




technique. Nearly 80% of respondents, however, report that they understand how to embed regulatory constraints in their ALM, and 70% that they do, in fact, embed them.

Figure 14a: How well are the fields/techniques below understood by your firm? (All respondents)Risk-controlled investing is well understood by 67% of respondents, yet 78% claim they understand how to embed regulatory constraints in their ALM.


Risk-controlled investing Integration of regulatoryconstraints in the ALM

strategy

0

20

40

60

80

100

Figure 14b: How well are the fields/techniques below understood by your firm? (Pension fund stakeholders) Risk-controlled investing is well understood by 53% of pension stakeholders, yet 77% claim they understand how to embed regulatory constraints in their ALM.



strategy

0

20

40

60

80

100

Figure 15a: Are the fields/techniques below used in your firm? (All respondents) Risk-controlled investing is currently used by 40% of respondents; 69% currently embed regulatory constraints in their ALM.

YesIn progressNoNon-response


strategy

0

20

40

60

80

100

Figure 15b: If not, why not? (All respondents)When respondents do not apply such techniques, they feel that they do not add value or are irrelevant (yellow and light orange). More than half the respondents who do not use RCI techniques believe that they are not relevant or that they do not add value; almost all those who do not integrate regulatory constraints in their ALM strategy also say this would not add value. This failure to consider risk insurance probably accounts for the underfunding of a fraction of respondents.

Not relevantDoes not add valueLack of knowledgeCosts too muchToo difficult from anorganisational standpoint


strategy

0

20

40

60

80

100

120





On the whole, the survey shows a wide gap between the understanding of RCI strategies and the use of these strategies.

Management of economic/regulatory capital preferred to risk-controlled investingAlthough RCI is used by only 41% of respondents, many assert that they take regulatory constraints into account in the design of their strategies. After all, many use economic/regulatory capital management, which provides risk insurance but at the same time involves discretionary decisions, and thus seems more well suited to the role of the trustees, responsible for asset allocation, and possibly to the organisation and culture of pension funds.

To manage prudential constraints, usually minimum funding constraints, 28% of respondents use dynamic LDI techniques; twice as many—56%—use risk management (see figures 17a and 17b).

Figure 17a: Which underlying strategies do you (all respondents) prefer to use to manage prudential, accounting, and economic risk? That the light orange bars are higher than the yellow bars shows that economic capital is far more popular than risk-controlled investing. Fewer than half the respondents re-evaluate their strategies frequently (dark orange bars), though frequent re-evaluation is much needed when RCI strategies are not used.



10

20

30

40

50

60

Figure 16: Understanding and using RCI techniques; use of RCI vs. economic capital techniquesRespondents understand RCI techniques more than they use them. They prefer economic capital to RCI techniques to manage their risks, and in particular to manage their prudential risks (the minimum funding constraints).

UK Core Europe Northern Europe + Netherlands

Total sample

Master RCI techniques 77% 60.5% 61% 56%

Currently use RCI techniques 54% 44% 40% 41%

Use RCI for economic, accounting, or prudential risks

75% 51.3% 72% 63%

Use economic capital for economic, accounting, or prudential risks

75% 79.5% 83% 80%

Use RCI for prudential risks 17% 18% 24% 28%

Use economic capital prudential risks 25% 56% 52% 56%




Figure 17b: Which underlying strategies do you (pension fund stakeholders) prefer to use to manage prudential, accounting, and economic risk? That the light orange bars are higher than yellow bars shows that economic capital is far more popular with pension stakeholders than is risk-controlled investing.



10

20

30

40

50

60

Swap and swaptions used more often than equity derivativesSwaps, swaptions, and caps are the instruments most commonly used to manage prudential, accounting, and economic constraints, because of large interest rate risk (and hedging demand) in pension funds. Swaps and swaptions are more popular in the Netherlands than in other countries, a popularity that reflects the specific higher interest rate risk derived from the nominal FTK framework.

Credit yielding instruments (corporate bonds or forward credit swap agreements) are not widely used to manage accounting risk, despite their usefulness in hedging the AA discount rate of pension liabilities in IAS 19. The failure to use these instruments simply reflects, in general, a failure to manage accounting risk.

Figure 18: Which underlying assets do you (all respondents) prefer to use to manage prudential, accounting, and economic risk? Swaps, swaptions, and caps (dark red bars) are the most widely used instruments. Credit instruments are not widely used to manage accounting risks.

Equity derivativesStructured productsCredit instrumentsSwapsSwaptions and caps


5

10

15

20

25

30

35

40

The pension industry fails to manage regulatory risksThe majority of pension stakeholders (as well as of respondents) have a blinkered view of the risks they face: prudential risk (the risk of underfunding) is managed by only 42% and accounting risk (the volatility from the pension fund in the accounts of the sponsor) by 30%. Only economic risk (the risk of underfunding at the investment horizon of the fund, given its own measures of liabilities) is managed by the majority of pension stakeholders.




Figure 19: Are pension fund stakeholders even attempting to measure and manage their main risks (prudential, accounting, and economic)? The dark orange bars show the proportion of pension stakeholders who manage regulatory risks, whereas the light orange bars show the proportion that simply measure risks. Prudential risks are managed by only 42% of pension stakeholders, and accounting risk by 30%.


Prudential risk(minimum funding constraints and the risk of breaching them)

Accounting risk(risk of large losses in

the P&L of the sponsor)

Economic/financial risk(surplus and risk of a shortfall)

0

10

20

30

40

50

60

70

80

British pension funds and sponsors take sponsor risk into account more frequently than their European counterparts (62% of British respondents do so, vs. 48% in core European countries and 52% in northern European countries). After all, there are more hybrid funds with multiple sponsors and limited sponsor commitment in Northern European countries.

Surprisingly, however, only 17% of UK respondents manage accounting risks—the risk of volatility of the defined-benefit obligation in the accounts of the sponsor. This is the lowest percentage of the three geographies analysed; it compares with 33% in northern European countries and 38% in core European countries; 36% of all traditional DB schemes manage this risk. This failure to manage this risk is particularly striking as the UK has the most stringent accounting standards, and as UK

sponsors have no obligation to provide their employees DB schemes. In general, our survey suggests that the failure to manage accounting risk in the UK may account, in part, for the wave of closures of DB schemes.

In addition, our survey suggests that respondents from the UK have less sophisticated practical risk measurement and allocation tools than those from Northern Europe. Again, a more highly fragmented industry, with less access to qualified resources, subject to less stringent regulation than in Northern Europe, may account for this situation.

Figure 20: From the measuring to the management of accounting risk (UK)In the UK, only 15% of respondents manage accounting risk (dark orange bar).


0

10

20

30

40

50

Ignoring sponsor riskMore than 50% of respondents ignore sponsor risk (the risk of a bankrupt sponsor’s leaving a pension fund with deficits). In general, the two greatest risks to pension funds and their sponsors are the most widely ignored: sponsor risk is a great danger for pension funds (especially for traditional DB schemes) as accounting



risk is the greatest danger for the sponsor of a DB fund. Yet these two risks are the least likely to be modelled and managed. Indeed, no more than a minority of any category of respondents model or manage sponsor risk.10

British pension funds pay the greatest attention to sponsor risk. They focus largely on the risk that contributions cannot be raised in downturns. UK respondents are more likely to fail to incorporate sponsor risk into their ALM models (figure 21c), just as they are more likely to ignore accounting risk than are respondents from other geographies (figure 20).

Figure 21a: When designing your investment strategy, do you (all respondents) take sponsor risk into account? Fifty-two percent of respondents do not take sponsor risk into account at all in their investment strategy or fail to answer this question. Figure 21b shows that 55% of pension funds fail to take sponsor risk into account.

% obs.

Non-response 13%

We take into account the risk of default of the sponsor

25%

We take into account the risk that the sponsor's contributions cannot be raised during downturns

25%

Our investment strategy accounts for the risk factors common to pension fund assets and sponsor revenues

25%

Our integrated ALM fully models sponsor risk 12%

No, we do not take sponsor risks into account 37%

Figure 21b: When designing your investment strategy, do you (pension funds) take sponsor risk into account?

% obs.

Non-response 12%


22%


20%


22%



Figure 21c: When designing your investment strategy, do you (British pension funds and sponsors) take sponsor risk into account? UK participants are keener on taking sponsor risk into account. After all, UK pension fund deficits make them more sensitive to sponsor risk than the average (non-UK) pension fund.

% obs.


42%


28%


14%



This failure to manage accounting risk and fully model sponsor risk in the UK is particularly worrying. After all, UK pension funds are more highly exposed to sponsor risk from lower funding and greater sponsor guarantees (traditional schemes, unlike the hybrid schemes in Northern Europe, usually involve unlimited sponsor commitment). Likewise, the failure to manage accounting risk in the UK, where sponsors are not obliged to provide DB schemes but are subject to stricter accounting regulations than in other countries, opens the door for the simple and definitive closure of UK pension funds.

Further evidence that sponsor risk is not sufficiently taken into account in the strategy of pension funds can be found by comparing the funding ratios of state-supported pension plans and those of corporate pension funds. These statistics are available in Switzerland, where pension funds are divided into those that enjoy the backing of the state and those that do not.


10 - Answers from pension funds and non-pension funds, or when actuaries/advisors are included in the sample, are not statistically different.



In theory, there is no risk of default of sponsors of state-backed pension funds, whereas that risk exists for corporate pension funds. Thus, corporate pension funds should at least try to prevent short-term underfunding to limit their exposure to the risk of sponsor bankruptcy, and adopt a risk-controlled strategy, whereas pension funds with state backing should follow fixed-mix strategies.

However, the Swiss data (figure 22) show only that the Swiss pension funds with state guarantees have lower funding ratios, not that they manage their assets differently.

These funding ratios reflect the failure to manage sponsor risk and to make it part of the design of pension fund investment strategy.

Conclusion on the design of ALM strategiesPension funds prefer economic/regulatory capital approaches that theoretically provide risk insurance but involve discretionary, not rule-based, changes to asset allocation. Twenty-eight percent of respondents rely on risk-controlled investing, whereas 56% use economic/regulatory capital to manage prudential constraints. But discretionary approaches to risk insurance make it very likely

that the very mechanism that makes a strategy a risk-insurance strategy is lost. Reliance on discretionary investment policies involves both the risk of delays in implementation and the risk of relying on behavioural biases that distort the theoretical strategy (pension funds may be reluctant to sell at a loss, even though they rely essentially on market values and should pay no attention to book values).

On the whole, because rule-based strategies are compatible with economic capital and prudential risk-based regulations, we recommend greater reliance on these strategies. Even though mathematical

methods such as stochastic programming are required to derive the optimal asset allocation rules for risk insurance, very simple approximations that can be derived from the CPPI approach and rules of thumb and require no minimum mathematical background insure risks efficiently.

For rule-based strategies to be efficient, pension funds must ensure that they have a comprehensive view of their risks. The reluctance to manage risks comprehensively may have severe consequences. First, it increases risks in pension funds to no purpose. And the reluctance to manage accounting risks


USA, top 100 funds

UK Netherlands Switzerland Without state guarantees

With state guarantees

Funding ratios Dec.07 109% 100% 144% 110% 114.4% 94.5

Funding ratios Dec.07 79% 80% 95% 93.7 97.5 82.3

Basis Accounting Prudential Prudential Prudential Prudential Prudential

Source Watson Wyatt (2009)

The Pension Regulator (2009)

DNB (2009) Swiss regulator Swiss regulator Swiss regulator

Figure 22: Funding ratios in 2007-2008 in various geographiesFalls in funding ratios have been fairly similar in funds with state guarantee and funds without state guarantees; the similarity reflects the lack of dynamic trading strategies at corporate pension funds



may lead to inappropriate volatility in the accounts of the sponsor and trigger the closure of pension funds in countries such as the UK, where there is no obligation to provide DB plans, or the withdrawal of sponsor support in countries such as the Netherlands, where some guarantees are mandatory.



2. Risk and Performance Measurement



2.1. Background

2.1.1. Risk Measurement and Aggregation of Pension Fund RiskBecause asset allocation in a framework with constraints relies on risk budgeting, these techniques require both risk measurement and risk allocation.

In practice, however, when firms are unable swiftly to translate their risk budgets into investments, economic/regulatory capital will not prevent deficits.

There is a large body of academic literature on optimal portfolio construction techniques that investigates optimal risk measurement at portfolio level. It usually involves structured estimates of the variance-covariance matrix and the use of implicit factor exposures. Software providers tend to rely on explicit factor exposures; regulators tend to require aggregating the Value-at-Risk estimates computed for each risk types.

Most relevant methods for constructing a single portfolio and measuring its risk rely on structured estimates of the variance-covariance matrix. These methods, however, are impractical for aggregating risks from various portfolios. After all, the implicit factors found in different portfolios will also differ, which makes aggregation impossible (a new correlation matrix or new factors must be found for such an aggregation).

The difficulty of aggregating exposure to implicit risk factors accounts in part for the popularity of software applications that rely on explicit factor exposures. Factors are usually those most often

identified in the literature (the Fama-French factors, level, slope, and curvature of the yield curve, market volatility). Explicit factor exposures may lead to less accurate computation of the Value at Risk of any given portfolio; however, they allow easy aggregation of risks as well as clear comparability of VaR figures and of the risk exposures to the identified factors. These models used for investment risk, however, do not always incorporate the additional factors that can be found in institutional investors’ balance sheets (longevity and other biometric risks, liability risks).

The regulatory approaches usually require the direct aggregation of VaR figures; they are inspired by the Basel-II notion of risk types. In insurance (Solvency II) and pension funds (the Dutch FTK), diversification of risk types is allowed. These models usually include a measure of what could be called aggregate risk, that is, risks that arise in the aggregate that may not be visible in the portfolio. For instance, concentration risk, liquidity, and counterparty risks arise because of the overlap of the holdings (or risks) of individual portfolios. These measures of risk require a look-through approach to portfolio holdings. In Solvency II, the exposure to each risk type can also be seen as an exposure to explicit factors.

There are, however, technical failings in regulatory models as well as in those adopted by many financial institutions, as they do not measure risk comprehensively. The failure of regulatory models to measure risk comprehensively is worrying because capital/funding ratio requirements are usually more closely watched than any other measure.




Thus, failure to take into account some risks, such as the combined risks of having both high liability value and low asset value at the same time, or, in banking, having lower housing prices and higher default rates, means that in some cases risks are clearly underestimated, and the balance sheets are riskier than they seem.

The necessity of thinking in terms of risk factorsFor a risk budget to be allocated, one must be able to take its derivatives with respect to relevant assets or risk factors. There is a dimensionality curse; the number of factors in the covariance matrix expands with the square root of the number of assets. Estimates then become particularly noisy or even impossible. In addition, when one expands the universe with similar assets, the matrix becomes quasi-singular, which poses deep optimisation problems (investment funds have the same benchmarks, and low tracking error may be strongly correlated).

From a practical standpoint, ALM managers must rely on factor exposures. Reliance on these exposures limits the size of the matrix to be estimated and prevents problems of co-linearity. Because the same factors must apply for all assets, one must resort to the explicit factor.

The optimisation problem, or, for practitioners, the allocation of the risk budget, is solved as above; one then decides for a given risk factor how much to allocate to each investment fund with traditional fund screening/selection processes.

2.1.2. Value Added of Asset Allocation and the Necessity of Performance MeasurementPerformance attribution is standard in asset management. By contrast, academic prescriptions for the measurement of the value added of ALM are still missing. We argue, first, that performance measurement techniques from the asset management industry can be used in the LHP and the PSP. Second, we argue that for the performance of the ALM departments to be measured properly, the funding ratio constraints (minimum and maximum) should be taken into account to derive a dynamic “benchmark” allocation strategy, from either economic capital or risk-insurance methods.

Performance measurement techniques in asset management and the findings of Brinson, Hood, and Beebower (1986) Brinson, Hood, and Beebower’s (1986) conclusion that more than 90% of the average time-variation in returns is explained by strategic asset allocation has led to wide recognition of the importance of asset allocation in institutional investors’ returns and, by extension, in pension fund performance.

Since their study, asset management (AM) and ALM techniques have undergone marked changes: many institutions now allocate a significant proportion of their portfolios to alternative asset classes such as listed and unlisted real estate, commodities, infrastructure, and hedge funds. Stricter regulations and accounting standards have led to the development of ALM techniques that formally embed liabilities in the asset allocation decision.




Modern ALM techniques also focus on risk control through state-dependent asset allocation whose aim is to ensure that minimum funding constraints are respected.

Perhaps the best known approach to performance attribution is the Brinson method, as illustrated by Brinson, Hood, and Beebower (1986) and described in Laker (2002).

Figure 23 shows the quadrant that the Brinson, Hood and Beebower (1986) measure relies on. The benchmark and portfolio returns for each fund are considered weighted sums of the sector benchmark and portfolio returns.

Quadrant 1 calculates the fund benchmark returns, whereas quadrant 4 calculates the fund returns as the weighted sum of sector benchmark weights and sector benchmark returns.

Quadrant 2 calculates the pure effect of asset allocation (here, to sectors) by calculating the return that would have been obtained if the fund had an active allocation to sectors but tracked the benchmark exactly in each sector.

Similarly, by multiplying benchmark sector weights and portfolio sector returns, thus capturing the return that would have been realised if the asset allocation had been strictly neutral but the stock selection active, quadrant 3 captures the pure effect of stock selection.

Finally, an interaction term captures the non-linear pattern in asset allocation and stock selection: overweighting sectors

with positive stock selection leads to outperformance even though the asset allocation and the stock selection effects may offset each other.

To sum up, we have the following:Asset allocation = Q2 – Q1Stock selection = Q3 – Q1Interaction = Q4 – Q3 – Q2 + Q1Total value-added = Q4 – Q1

Based on the very same principle, Brinson, Hood, and Beebower (1995) introduce a model that, with a similar quadrant arrangement, makes it possible to take into account market timing ability.

Bikker, Broeders, and de Dreu (2009) examine the impact of asset allocation on the performance of Dutch pension funds.


Figure 23: The Brinson, Hood, and Beebower (1986) quadrant methodThe quadrant method attempts to separate two effects. The 1986 quadrant method identifies stock selection and asset allocation as two active features. Brinson, Hood, and Beebower (1995) use a similar method to evaluate the market timing ability of fund managers

Portfolio sector returns Benchmark Sector Returns

Portfilio sector weights (Q4) Portfolio

wj

P ⋅ rjP

j∑

Q2) Active asset allocation fund

wj

P ⋅ rjb

j∑

Benchmark sector weights (Q3) Active stock selection fund

wj

b ⋅ rjP

j∑

(Q1) Benchmark

wj

b ⋅ rjb

j∑



They use the proprietary database of the Dutch national bank, a database that makes it possible to see the funding ratios and asset allocation of each pension fund. First, they analyse how asset allocation moves with stock market performance, and find that pension funds do not continuously rebalance their funds to maintain what they claim to be their strategic asset allocation (the target allocation over a three- to five-year period). They find that the average pension fund behaves 40% like a continuously rebalancing investor and 60% like a buy-and-hold investor. These first two components make pension funds trend followers (with excessive lag). In addition, the strategic weights are positively correlated with stock returns. Last, Bikker, Broeders, and de Dreu (2009) show that pension funds seem to cut equity exposure at the bottom of the business cycle in what the authors call a tactical move with negative returns. On the whole, these three components contribute to pension funds’ underperformance of a continuously rebalancing benchmark.

Performance measurement techniques for risk insurance and the need for dynamic performance attributionBikker, Broeders, and de Dreu (2009) ignore the dynamic nature of optimal strategies when there are liability constraints. In other words, once the appropriate liability-hedging and performance-seeking benchmarks have been defined, the pension fund’s optimal asset allocation should involve dynamically rebalancing the weight allocated to each benchmark as a function of the distance to its constraints (for instance, as a function of

its surplus when it has minimum funding ratio constraints).

This is the case in the Netherlands, where the FTK requires pension funds to have a minimum 105% nominal funding ratio.11

Because the authors rely on a static framework (the assumption that the optimal portfolio is a fixed-mix), their resulting performance attribution is not risk adjusted and does not conform to the modern objectives of performance attribution.

EDHEC thus recommends taking the minimum funding constraints into account when measuring performance. Performance is then relative to a dynamic benchmark that results from a risk-insurance programme (economic capital, where liabilities are fully hedged and the allocation to risky assets a function of the funding ratio and of a regulatory multiplier, or risk-controlled investing, in which the allocation to the PSP and to the LHP depends on the funding ratio and on risk aversion).

In short, because dynamic asset allocation is welfare enhancing, for any dynamic asset allocation different from that considered, one should measure its impact not only on the average performance of the fund but above all on the utility of the pension fund. Bikker, Broeders, and de Dreu’s (2009) assertion that rebalancing is much greater after negative equity returns and that this strategy leads to negative excess returns should be revisited in light of these arguments.


11 - See Amenc, Martellini, and Sender (2009) and Sender (2009) for more detail on these constraints.



In this respect, we must underscore the lack of public databases of returns and asset allocation of pension funds. Some central banks have databases but consider them private, as is typical of European regulatory secrecy. This culture of secrecy was deemed important in banking, since regulators traditionally feared that revealing the true state of bank balance sheets, even sanitised, could provoke bank runs. There should be no such fear in pension funds, since they are non-commercial entities that do not fear runs, and since the number of pension funds makes it hard to recognise a pension fund by its asset allocation. More transparency would enable researchers to provide more concrete insight.

2.2. Assessment of Aggregate Risk-Measurement PracticesThe EDHEC survey suggests that the aggregation of risk and the management of economic capital (and still more, dynamic asset allocation) are still a nascent science in the European pension fund industry.

Not only do relatively few survey respondents measure and monitor all risks (section 1.1.2, figure 12c) but those who fail to do so also express doubts about the utility of comprehensive risk management.

This section shows that risk aggregation and risk allocation are still in their infancy at European pension funds. We find it particularly worrying that only a minority use risk aggregation and disaggregation methods that allow clear views and disclosure of risk.

Respondents from the UK measure aggregate risk more often than respondents from Northern Europe; Northern European countries, however, use explicit risk factors to aggregate risks, which seems more appropriate. The guidelines provided by the Northern European regulators, generally inspired by Solvency II, have influenced practice greatly. These guidelines require first that exposure to such factors such as equity risk be assessed, that, in an initial aggregation, the VaR of a risk-type such as market risk be computed, and, finally, that all risk types be aggregated.

Failure to measure risk makes it impossible to manage risk; inefficient allocation of risk means risk measurement cannot be translated into efficient risk management. Either may result in significant deficits following market crashes.

It turns out that 35% of survey respondents—answers are similar for pension funds—do not aggregate risk from individual funds to building blocks such as the PSP and LHP or to the overall investment risk; 28% do not measure aggregate risk.

Nearly 40% of those who responded to at least one of the questions do not measure overall investment risk, and nearly 30% do not measure aggregate “balance sheet” risk, which can be defined as the aggregate of asset and liability risk.


12 - Because it is likely that participants who did not answer any question on risk measurement do not measure aggregate risk, this failure to measure risk is likely to be even greater than what the survey suggests.



Figure 24: How do you (all respondents) calculate aggregate risk in actual positions?The fraction of respondents who do not aggregate risk is at least equal to that shown in light and dark grey (those who did not answer this group of questions are not likely to measure aggregate risk). Thus, between 39% and 45% of participants do not measure aggregate investment risk. Pension stakeholders display a similar pattern (figure not shown).

Non-responseNo aggregationAggregation of VaR figuresAggregation via factor exposures(aggregation of sensitives to explicit risk factors)

From individual fundsto classes or blocks

of funds

From blocks to overallinvestment

From investment to overall risk

0

20

40

60

80

100

Figure 25a: How do you (respondents from the UK) calculate aggregate risk in actual positions?Respondents from the UK are more likely than any other group of respondents to aggregate individual VaR measures—all those who aggregate positions from individual funds to blocks of funds aggregate VaR figures.

No aggregationAggregation of VaR figuresAggregation via factor exposures(aggregation of sensitives to explicit risk factors)


of funds



0

20

40

60

80

100

Figure 25b: How do you (respondents from Northern Europe) calculate aggregate risk in actual positions? Respondents from Northern Europe are less likely to calculate aggregate risks; when they do so, they are more likely to aggregate risks with sensitivities to explicit factors.

Non-responseNo aggregationAggregation of VaR figuresAggregation via factor exposures(aggregation of sensitives to explicit risk factors)


of funds



0

20

40

60

80

100

Figure 25c: The UK as statistically different from core Europe UK respondents have statistically different methods of aggregating.

Bloc

ks

(PSP

, LH

P)

No

aggr

egat

ion

of ri

sk

Aggr

egat

ion

on

VaR

Aggr

egat

ion

via

fact

or e

xpos

ures

2x3

Fish

er’s

exac

t tes

tUK 1 9 2 +

ContinentalEurope 39 30 22 (p=0.0108)

When it comes to practical tools, 40% of respondents aggregate VaR measures, a somewhat ad hoc method that does not allow the reverse disaggregation and allocation of risk. After all, a VaR figure may be indicative of an amount of risk of a specific item, but it does not indicate exposure to risk factors, and without this information, VaR figures are blind.

On the whole, we find that only 25% of respondents use explicit factors—factors that would be defined in a similar manner across all asset classes—to aggregate risk.




Thus, the large majority of participants use inappropriate methods to aggregate risk, which severely diminishes the ability to manage the balance sheet efficiently. Having appropriate practical methods to measure, aggregate, and allocate risks is especially important when economic capital is used, because these tools do not lead to a predictable asset allocation strategy.

2.3. Implementation of Risk LimitsRisk limits serve two purposes. Tracking error limits ensure that investment funds do not deviate significantly from their mandates; aggregate risk limits ensure the respect of the design and assumptions of the investment strategy: that overall equity risk is limited to 32%, and overall investment risk to 20%, for instance. Aggregate risk measures used are usuallyVaR-CVaR limits or extreme risk measures. Respondents are more likely—but not significantly so—to use VaR for aggregate measures and tracking error for individual funds. More than 50% of the respondents, however, do not set risk limits in building blocks; only 30% use measures derived from the economic capital framework (VaR or extreme risk) to do so. We also find that more than 60% of pension stakeholders do not set risk limits for building blocks and that 25% use VaR or extreme risk measures. In the UK, 55% of respondents do not set risk limits for building blocks; nearly 40% use VaR or extreme risk measures to set risk limits for building blocks.

Figure 26: Do you (all respondents) use risk limits, and if so, where?Thirty percent use measures derived from the economic capital framework (VaR or extreme risk) to define risk limits, and more than 50% of the respondents do not set risk limits in building blocks.

None or non-responseTEVaRCVaR or extreme risk

Fund Asset class Building blocks

or "strategies"

For all investment

activities

For the entire pension fund

0

10

20

30

40

50

60

ConclusionIn short, the use of risk limits and of measurement techniques that allow aggregation and allocation of risks seems to lag that of risk-insurance techniques such as RCI and economic capital. Finance, of course, is both an art and a science, and it is of no avail to master academic concepts if inappropriate organisation and infrastructure keep knowledge from being put rigorously into practice.

2.4. Analysis of Performance Measurement Techniques The performance of the ALM function is often not measured, although the definition of main portfolios and the asset allocation processes are the most important decisions and sources of value




added in pension funds. The lessons from Brinson, Hood, and Beebower (1986) have not been learnt, and more attention is still dedicated to less important aspects such as the monitoring and performance attribution of countless individual investment funds.

In most cases, those surveyed use simple, rather than risk-adjusted, outperformance measures to evaluate the performance of their investments. Such measures are clearly inappropriate, especially for the PSP. They do not make it possible to assess the suitability of the design of the PSP. Only 14.3% of survey respondents attempt to assess the efficiency of the design of their PSPs with respect to other benchmarks or portfolios (11.5% assess the efficiency of the implementation).

Figure 27: Evaluation of the design of the PSP (all respondents who answered a question on performance measurement)Twenty-seven percent of respondents do not assess the suitability of the design of the PSP. When they do so, crude outperformance is their preferred performance measure—risk-adjusted performance is used by only 20% of respondents, and only 15% explicitly try to assess the risk-return efficiency of the design of their PSP. Pension stakeholders respond in much the same way as all respondents, or, if anything, they may be less likely to measure the suitability of the design and more likely to rely on outperformance (figure not shown).

%

Non-response 27%






7%


14%

The implementation of the investment strategy is also generally measured with the same crude estimator, outperformance, even though the standard practice for

individual investment funds is to measure performance on a risk/return basis. The discrepancy pointed at by Brinson, Hood, and Beebower (1986) persists: performance is measured most where least relevant.

Figure 28: Evaluation of the implementation of individual funds (all respondents who answered a question on performance measurement)Risk-adjusted performance measures are used more often for individual funds than for the PSP. Outperformance remains the preferred measure. Pension stakeholders respond in much the same way as all respondents (figure omitted).

%

Non-response 23%






12%

We access its risk return efficiency with respect to other benchmarks

12%

Figure 29: Evaluation of the implementation of the PSP (all respondents who answered a question on performance measurement)Outperformance is the preferred measure for the PSP. Again, pension stakeholders respond in much the same way as all respondents and their specific answers are not shown.

%

Non-response 30%






5%


11%

The LHP design simply attempts to mimic liabilities; the primary criterion is to minimise risk. Outperformance is a minor design concern, and as the LHP is meant to be implemented with a low risk budget, outperformance is even less of an implementation concern. Forty percent of respondents fail to evaluate the design of their LHPs and 40% simply assess the




outperformance of the LHP with respect to a liability index or to other market indices.

Figure 30: Evaluation of the design of the LHP (all respondents who answered a question on performance measurement)Forty percent of respondents do not assess the adequacy of the design of the LHP. And 38% try to assess whether the LHP outperforms liabilities, even though the objective of the LHP is to track liabilities. Pension stakeholders are less likely to assess the adequacy of the LHP, and more likely to use crude outperformance measures (figure omitted).

%

Non-response 40%






3%

We access its risk- return efficiency with respect to other benchmarks

10%

On the whole, then, only a very small fraction of respondents attempt to assess the design of the portfolios, and when they do they are highly unlikely to use sophisticated measures. The use of outperformance measures is clearly unsophisticated; it tends to lead to unstable measures, since returns are noisier than risk.

The same rationale seems to apply for the frequency of performance measurement: most investment funds are required to report weekly, monthly, or quarterly performance measures; by contrast, the performance of the PSP and the LHP is analysed at a yearly or tri-yearly frequency. The red sections, reflecting a frequency of one year or higher, are larger for aggregate data than for individual funds—nearly 40% of respondents assess performance of the PSP at yearly or tri-yearly intervals, or do not assess it at all.

Figure 31: Evaluation frequency of the implementation of the strategy (all respondents who answer this group of questions)red sections represent an evaluation frequency of yearly or lower. Forty percent of the respondents measure the performance of the PSP once per year or less. The performance of individual funds is measured at a higher frequency, despite the lower importance of individual funds in ALM.

WMQY3YNon-response

For individual funds For PSP For the investment strategy

For LHP0

20

40

60

80

100



2. Implementing Efficient Indexation


3. Does Being Knowledgeable Help?



For academics, life is sometimes all too simple: knowledge of modern ALM techniques is bound to ensure superior risk-adjusted returns. After all, even in efficient markets and in the absence of return predictability, risk can be managed (portfolios can be insured), so superior risk management alone ensures superior risk-adjusted returns.

In the asset management industry, there have been empirical tests of the ability of qualified asset managers to beat the market (including the famous and disputed test showing that a monkey throwing darts at a dartboard would beat the average fund manager). The general conclusions from these studies seem to be that markets are efficient on the whole: generating alpha requires processing information for a cost similar to alpha, and very few funds13

consistently beat the market.

This section attempts to analyse the empirical benefits of risk management. One could think that, because of the great benefits of risk management, empirical tests are likely to show that those using risk management will have superior results. The conclusion, as we will see, is more complex.

3.1. Evidence from Survey RespondentsWe attempt to split our sample into sophisticated and unsophisticated users of portfolio construction techniques and portfolio insurance strategies, our two major criteria. We then compare the ex post risk-adjusted performance of the sophisticated and unsophisticated respondents.

We have two measures for the performance of pension funds. We use the average funding ratio from 2005 to 2008 to proxy long-term performance. This proxy is imperfect but, in the absence of more detailed financial data,14 acceptable. The relative change in funding ratios from 2007 to 2008 makes it possible to assess how pension funds and their risk management have withstood the crisis.

Although a limited number of funding ratios is available to us, our results highlight some salient facts.

Long-term performance seems positively correlated with our proxy for portfolio diversification (and very slightly with the use of risk management), even though the predicting power is poor. Correlation, of course, is not causality: it is possible that the pension funds with the highest funding ratios pay higher salaries and make better hires; equally possible is that sponsors that have sufficient resources to fund their pension fund adequately may also staff it adequately.

Efficient protection from falls in funding ratios seems, in practice, to be more highly correlated with risk management than with the use of dynamic asset allocation techniques. When linear regressions are done, we find that the use of dynamic asset allocation techniques is positively correlated with the fall in funding ratios in 2008. By contrast, risk management seems more instrumental.


13 - Famous surveys are based on funds, not on fund managers. Funds fail to outperform the market consistently; further studies are needed to evaluate whether some managers consistently outperform the market.14 - The absolute value of funding ratios might be less meaningful than the relative drop in funding ratios in the 2008 financial crisis—their initial situation is different, and funding ratios are not fully comparable across countries and firms.



Figure 32: Univariate regressions of funding ratios and changes in funding ratiosThis figure shows the regression of long-term performance and protection from falls in funding ratios against the reported use of “dynamic strategies such as dynamic LDI”. Those who report that they use dynamic ALM posted greater falls in funding ratios in 2007-2008, and economic capital seems to yield better results.

RCI explains: Economic capital without RCI explains:

Long-term performance

Protection against fall in funding

ratios

Protection against fall in funding ratios

T-stat -0.05 -0.89 0.8

Coefficient -0.84 -0.07 0.03

R-square 0% 7.3% 6%

This counterintuitive finding that dynamic asset allocation seems to offer no protection from falls in funding ratios requires clarification. Dynamic strategies are efficient to the extent that they are used in what could be called an integrated fashion. Some sophisticated respondents are not using these strategies at the balance sheet level, but only in some specific funds. Alternatively, pension funds do not have a holistic view of their risks and may neglect interest rate risk or sponsor risk.

Despite their size and sophistication, for example, Dutch pension funds have experienced drops in funding ratios larger than those of pension funds in other European countries, partly because they failed to take convexity into account. One could argue that for rule-based strategies to be efficient rules need to be adequately defined

This incomplete use of dynamic asset allocation techniques affords incomplete protection. The inconsistency of some respondents is visible in our survey: some report that they do not take liabilities into account when defining their strategy investment process, yet they report that they use dynamic asset allocation strategies. Likewise, Sender (2009b) argues that many Dutch pension funds failed to take into account the convexity of the duration of their liabilities in their investment strategy, and were hurt by growing interest rate sensitivity when falls in equity markets lowered their funding ratios.


Figure 33: Dutch funding ratiosThe average funding ratio of sophisticated industry-wide pension funds fell under the regulatory minimum in 2008.



The use of RCI techniques is thus not sufficient to insure against risks; respondents must use these techniques in a consistent manner. We also find that the pension funds that best withstood the crisis are those that used risk management, in the form of RCI strategies or economic capital.

That the most well protected pension funds are among those that master risk insurance techniques bolsters our view that risk management is essential to the definition of the investment strategy. In the recent crises, the increased correlations of asset classes have reduced the benefits of diversification and increased the benefits of risk insurance.

Qualitative evidence from the field To seek qualitative evidence of the benefits of risk management, we have analysed reports from the pension funds that have been named best pension funds by IPE or been mentioned in the press as having performed very well, and tried to assess their use of risk management, dynamic asset allocation, and derivatives.

In most cases strategies rely primarily on techniques inspired by economic capital management rather than on dynamic asset allocation. Pension funds are generally reluctant to apply fully dynamic asset allocation schemes, either because of organisational problems (Sender 2009c) or simply because their processes are not sufficiently quantitative. After all, a more qualitative process that relies partly on investment committees is more consistent with their culture; so is economic capital management.

Although there are not always direct mentions of LHPs in their annual reports, these pension funds mention clear processes for managing their liability risks (mainly interest rate risk). They often use swaps or swaptions to manage their interest rate exposure.

Some survey respondents (ATP, for instance, named best European pension fund and best innovation pension fund, and best risk management pension fund in 2009 by IPE) calculate their risks on a daily basis, and hedge their exposures accordingly.

One respondent manages interest rate risk dynamically; a Dutch respondent (Rabobank), by contrast, relies on hybrid derivatives, where the payoff of a receiver swaption is linked to equity performance. Such a hybrid derivative can be seen as a proxy for the replication of an interest rate sensitivity conditional on the funding ratio. After all, in the Dutch framework, interest rate risk falls when equities have performed well (since equities have a positive influence on funding ratios), so this joint option is equivalent to managing interest rate risk dynamically.

3.2. ConclusionPension funds, sometimes called the new financial giants, have gained a reputation for superior approaches to investing that allow them to outperform other investors. At the same time, abysmal pension deficits are also making the news, defined-benefit pension funds are being closed down, and workers are taking losses when sponsors go bankrupt. The pension fund industry as a whole experienced sharp drops in funding ratios at the end of 2008, even




at institutions that would qualify as very sophisticated: the average funding ratio of Dutch industry-wide pension funds fell from 150% in mid-2007 to 89% in Q1-2009, well below the strict minimum funding ratio of 105%, and despite the risk-based regulation that requires the use of economic capital to prevent the possibility of underfunding.

The EDHEC survey of the ALM practices of European pension funds, made possible with the support of AXA Investment Managers, part of a research chair on the impact of regulation on the financial management of European pension funds, has attempted to shed light on this situation.

Our first conclusion is that, despite the great professionalisation of ALM in pension funds and their service providers, risk-controlled strategies are not used by European pension funds as often as they should be.

Pension funds prefer economic/regulatory capital approaches that theoretically provide risk insurance but involve discretionary, not rule-based, changes to asset allocation. Twenty-eight percent of respondents use risk-controlled investing (RCI) strategies, whereas 56% use economic/regulatory capital to manage prudential constraints. But discretionary approaches to risk insurance make it very likely that the very mechanism that makes a strategy a risk insurance strategy is lost. Reliance on discretionary investment policies involves the risk of delays in implementation and the risk of relying on behavioural biases that distort the theoretical strategy.

As it happens, respondents do not always use the strategy implied by their risk-management tools or models. Many

Dutch pension funds have failed to reduce risk as significantly as the FTK regulation commands (they kept a larger share of risky assets than allowed by their funding ratio).

In addition, discretionary strategies may be riskier than thought because of organisational challenges. Qualitative feedback shows that risk is often managed in silos (with departments acting separately) at pension funds, as it often is in banking. A silo approach generally leads to sub-optimal results, because, at best, risk measures are sub-additive, so managing risk budgets independently is less suitable than managing them jointly (above all, when the risk allocation and the limits set for each department are revised too infrequently).On the whole, because rule-based strategies are compatible with economic capital and prudential risk-based regulations, we recommend greater reliance on these strategies. Even though mathematical methods such as stochastic programming are required to derive the optimal asset allocation rules for risk insurance, very simple and intuitive approximations can be derived, and rules of thumb that require no minimum mathematical background can prove to be an efficient way to insure risks.

For rule-based strategies to be efficient, pension funds must ensure that they have a comprehensive view of their risks, which the survey suggests is not always the case: prudential risk (the risk of underfunding) is managed by only 40% of respondents, accounting risk (the volatility from the pension fund in the accounts of the sponsor) by 31% of respondents. More than 50% of the respondents ignore sponsor risk (the risk




that a bankrupt sponsor’s leaving a pension fund with deficits).

Pension funds’ reluctance to manage their risks comprehensively may have severe consequences. First, this reluctance increases risk to no purpose. And the reluctance to manage accounting risks may also lead to inappropriate volatility in the sponsor’s books, volatility that may trigger closure of pension funds in countries such as the UK, where there is no obligation to provide DB plans, or to limit the support of sponsors in countries such as the Netherlands, where some guarantees are mandatory.

Last, although performance measurement for the overall ALM may require dynamic tools that are not the industry standard, measuring the performance of individual portfolios—the LHP and the PSP—is easy, as standard industry methods are appropriate. The survey shows that 30% of respondents do not assess the suitability of the design of the PSP, and that more than 50% of respondents use crude outperformance measures. The failure to measure performance may lead to sub-optimal decisions’ being taken again and again.



4. Bibliography



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• Amenc, N., and F. Goltz, and V. Le Sourd, 2009. The performance of characteristics-based indices. European Financial Management 15 (2): 241-78.

• Amenc, N., F. Goltz, L. Martellini, and P. Retkowsky. 2010. Efficient indexation: An alternative to cap-weighted Indices. EDHEC publication (January).

• Amenc, N., L. Martellini, and S. Sender. 2009. Impact of regulations on the ALM of European pension funds. EDHEC publication (January).

• Amihud, Y. 2009. How much is liquidity worth? (It depends when). Liquidity premium conference held in London (12 November).

• Amihud, Y., and H. Mendelson. 1986. Asset pricing and the bid-ask spread. Journal of Financial Economics 17 (2): 223-49.

• Aragon, G. 2004. Share restrictions and asset pricing: Evidence from the hedge fund industry. Working paper, Boston College.

• Arnott, R., J. Hsu, and P. Moore. 2005. Fundamental indexation. Financial Analysts Journal 61 (2): 83-99

• Arnsdorf, I. 2009. From coffers to cash. Yale Daily News (17 April).

• Ball, M. 2008. Risk sharing consultation, deregulatory review of private pension. Department of Work & Pensions, United Kingdom

• Barberis, N. 2000. Investing for the long run when returns are predictable. Journal of Finance 55 (1): 225-64.

• Bikker, J., D. Broeders, and J. de Dreu. 2009. Stock market performance and pension fund investment policy: Rebalancing, free float, or market timing. International Journal of Central Banking 6 (2): 53-79.

• Binsbergen, van J., and M. Brandt. 2007. Optimal asset allocation in asset and liability management. Working paper.

• Black, F. 1980, The tax consequences of long-run pension policy. Financial Analysts Journal 36:21-8.

• Blitz, D., and L. Swinkels. 2008. Fundamental indexation: An active value strategy in disguise. Working paper.

• Brinson, G., L. Hood, and G. Beebower. 1986. Determinants of portfolio performance. Financial Analysts Journal (July-August): 39-44.

• Brinson, G., L. Hood, and G. Beebower. 1995. Determinants of portfolio performance. Financial Analysts Journal (January-February): 133-37.

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• Campbell, J., and L. Viceira. 2005. The term structure of the risk-return tradeoff. Financial Analysts Journal 61:34-44.

• Cox, J., and C. Huang. 1987. Optimal consumption and portfolio policies when asset prices follow a diffusion process. Journal of Economic Theory 49 (1): 33-83.

• DeMiguel, V., L. Garlappi, and R. Uppal. 2007. Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? Review of Financial Studies 22 (5): 1915-53.

• Engle. R. 2002. Dynamic conditional correlation: A simple class of multivariate GARCH models. Journal of Business and Economic Statistics 20 (3): 339-50.

• Engle, R., and B. Kelly. 2009. Dynamic equicorrelation. May. NYU working paper no. FIN-08-038.

• Gilboa, I., and D. Schmeidler. 1989. Maxmin expected utility with non-unique prior. Journal of Mathematical Economics 18:141–53.

• Haug, E., and N. Taleb. 2008. Why we have never used the Black-Scholes-Merton option pricing formula. Wilmott Magazine 1:1-10.

• Hoevenaars, R., R. Molenaar, P. Schotman, and T. Steenkamp. 2008. Strategic asset allocation with liabilities: Beyond stocks and bonds. Journal of Economic Dynamics and Control 32 (9): 2939-70.

• Jagannathan, R., and T. Ma. 2003. Risk reduction in large portfolios: Why imposing the wrong constraints helps. Journal of Finance 58:1651-84.

• Jobson, J., and R. Korkie. 1981. Performance hypothesis testing with the Sharpe and Treynor measures. Journal of Finance 36:889–908.

• Karatzas, I., J. Lehoczky, and S. Shreve. 1987. Optimal portfolio and consumption decisions decisions for a "small investor" on a finite horizon. SIAM Journal on Control and Optimization 25:1557-86.

• La Fontaine, J. 1668. The council held by the rats. Translated by Elizur Wright. Accessed on: http://neptune.esc.k12.in.us/socratic/resources/TheCouncilHeldbytheRats.html

• Laker, L. 2002. Fundamentals of performance attribution: The Brinson model. PRA Newsletter. Accessed on: www.mscibarra.com/research/articles/2002/PerfBrinson.pdf

• Ledoit, O., and M. Wolf, 2003. Improved estimation of the covariance matrix of stock returns with an application to portfolio selection. Journal of Empirical Finance 10 (5): 603-21.

• Ledoit, O., and M. Wolf. 2004. Honey, I shrunk the sample covariance matrix. Journal of Portfolio Management 30 (4): 110-19.

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• Levy, S. 2008. Occupational pension schemes annual report. Office for National Statistics, 2007 Edition, No. 15, United Kingdom.

• Loderer, C., and L. Roth. 2003. The pricing discount for limited liquidity: Evidence from SWX Swiss Exchange and the Nasdaq. Freiburg University conference.

• Maer, L., and D. Thurley. 2009. Defined benefit pension schemes. House of Commons, Library Standard Notes: SN/BT/1759, United Kingdom.

• Marchenko, V., and L. Pastur. 1967. The eigenvalue distribution in some ensembles of random matrices. Math. USSR Sbornik 1:457-83.

• Martellini, L., and V. Milhau. 2009. Measuring the benefits of dynamic asset allocation strategies in the presence of liability constraints. EDHEC publication.

• Miksa, B. 2007. Central Eastern European pensions 2007: Systems and markets. Allianz Global Investors.

• Munaretto, N., and L. Bertschi. 2008. Pensions in Switzerland: Setting the rate. Investment & Pensions Europe (October): 38

• Ponds, E., and B. Van Riel. 2007. The recent evolution of pension funds in the Netherlands: The trend to hybrid DB-DC plans and beyond. Working paper

• Rozinka, E., and W. Tapia. 2007. Survey of investment choice by pension fund members. OECD working papers on insurance and private pensions, no. 7, OECD Publishing.

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4. Bibliography


5. Appendices



5.1. Evolution of Pension SchemesPension schemes have changed significantly in recent decades. The most pronounced change is certainly the shift from defined-benefit (DB) to defined-contribution (DC) pension provision. DB plans have suffered from serious underfunding, with low interest rates and an increase in life expectancy increasing the liability value. DC plans effectively transfer the risk of falling short of investment objectives to employees (Yermo 2007). In Europe, occupational pension plans were once mainly pure DB schemes, but in recent years more DC schemes and hybrid plans have appeared on the scene.

In the UK, there has been a trend away from the provision of defined benefits since the early 1980s. The number of active members in private-sector DB schemes (open and closed) fell from no more than 6 million in 1979 to 3.4 million in 2006 (Ball 2008). Moreover, from 1987 to 2007, the share of employees with DB pension schemes fell from 47% to 31%, while membership in DC schemes increased markedly (Maer and Thurley 2009; Levy 2008). After all, British regulation requires mandatory indexation to inflation but does not allow the more flexible hybrid funds (with conditional indexation). Sponsors that desired a more flexible regime have closed DB schemes and offered DC schemes instead. In other countries, where some guarantees on pension liabilities are mandatory but where indexation may be conditional, pension funds have modified the nature of their liabilities. The most salient example is that of the Netherlands, where liabilities used to be unconditionally indexed to inflation or sector wages, but became conditional after the Financieel Toetsingskader (FTK)

was passed (Amenc, Martellini, and Sender 2009).

In Germany and Switzerland, DC plans are required by law to offer workers some sort of guarantee (Germany) or minimum benefits (Switzerland). In hybrid DB-DC plans known as cash balance, benefits are based on contributions plus a fixed, guaranteed return (Abraham 2009; Munaretto and Bertschi 2008). In the Netherlands, occupational schemes have switched from last-wage to average-wage plans. This plan is partly DB, because of the specification of accrued pension rights, and partly DC, as the indexation is dependent on the financial return of the funds (Ponds and Van Riel 2007).

As part of recent pension reforms, most Central and Eastern European countries introduced mandatory occupational schemes with fully funded defined contribution plans (Miksa 2007). In some cases, however, as in Poland and Slovakia, the mandatory occupational schemes are structured technically as DC plans but with legal requirements on returns or benefit guarantees that defines either the liability or the way risk management must be done (Rozinka and Tapia 2007).

5.2. Statistical MethodIn the survey, we have tested and reported whether respondents’ answers were statistically significant or not.

Three tests have been used throughout the survey, as described below. In all cases, one star indicates significance at the 5% level and two stars significance at the 1% level.

5. Appendices



Binomial testTo assess whether respondents’ agreement or disagreement with EDHEC’s main conclusions is statistically significant, we use a two-tailed binomial test, grouping in one category those who report that they agree somewhat or very much, and in another those who disagree strongly or somewhat.

The binomial test is an exact test of the distribution of outcomes classified in two categories, with the number of draws, the number of outcomes in each category, and the null (implied) probability of each draw for the test used as input. In this document, the null (implied) probability tested is 50%; that is, we test the assumption that respondents as a group have no opinion, so each respondent has a random probability of agreeing or disagreeing with EDHEC’s view.

We use a two-tailed test; in other words, we assess not only the probability under the null that there are at least as many respondents that agree as observed but also the probability of the opposite extreme (disagreement with EDHEC’s views).

The two-tailed test, of course, is more powerful than the single-tailed test, which assesses only the probability that there at least as many respondents agreeing with EDHEC’s views.

With N the number of respondents, p the number of positive answers, and d the number of negative answers, with the notation m=min (p,d), the p-value reads P=2*B(m, N, 50%), where B is the cumulative distribution function of the binomial probability.

Fisher’s exact testWhen two samples need to be compared, we use either Fisher’s exact test or an analysis of variance (see next sub-section).

General Fisher testFisher’s exact test assesses the equality of binomial probabilities. If two variables X and Y have m and n observed states respectively, they form an m x n matrix in which the entries ai,j represent the number of observations in which x = i and y = j. With the sum of the row Ri and the column Cj, the total sum is given as follows,

N = Ri

i∑ = C j

j∑

The general formula to obtain the conditional probability of getting the actual matrix given in the particular row and column sums is given by:

p =R1!R2 !...Rm !( ) C1!C2 !...Cn !( )

N! ai , j !i , j∏

where n!=factorial(n)

Two-by-two Fisher exact testIn most cases, as we test whether one sub-sample (for instance, one country or the group of pension funds as a whole) has an opinion different from that of another sub-sample (for instance, the rest of the sample), we use a two-by-two test; i.e., we assess whether the binomial probability of the first sub-sample is equal to that of the other sub-sample. When there are three sub-samples, two-by-three tests are sometimes used.

5. Appendices



The logic of the test is as follows: assuming two samples with two binomial probabilities,

negative positive

Geography 1 a b

Geography 2 c d

Fisher showed that the probability of obtaining any such set of values was given by the hypergeometric distribution:

where n=a+b+c+d and

nk

⎛

⎝⎜⎞

⎠⎟is the binomial

coefficient.

Fisher’s exact test is exact when the marginals, that is, a+b and c+d, are known, as they are here (the number of respondents for each geography is given at the end of the survey; only the distribution function of the two sub-samples is unknown).

Two-by-three Fisher exact testThe two-by-three test is derived as follows:

Group I

Group II

Group III

Total

Group i a c e a+c+e

Group j b d f b+d+f

Total a+b c+d e+f a+b+c+d+e+f

The probability of obtaining any such set of values was given by the hypergeometric distribution, as in the two-by-two test:

ANOVA – Analysis of varianceThe simple ANOVA test assesses whether the means of different sub-samples are equal, under the assumptions that they have the same variance.

When there are only two samples to compare, the Student two-sample t-test is adapted and can be viewed as a specific case of the ANOVA method. The more general one-way ANOVA tests for differences in the mean of independent groups, assuming the same variance.

The ANOVA method compares the variance of the groups’ means and the mean of the variances of observations of each group (the within-group variance), after adjusting for the numbers of degrees of freedom.

F =

variance of the group meansmean of the within-group variance

F * =

MSTRMSE

where:

MSTR=

SSTRI −1

, I=number of "treatments" (groups)

and

MSE =

SSEnT − I

nT= total number of cases

When the samples are not independent, their means will differ, so both F and F* will be high. F* has a Fisher distribution.

The test is based on the four possible answers to the questions; blanks and “I don’t know” responses are filtered out. We assume that the variable of interest can have a quantitative interpretation, since

5. Appendices

p =a + b

a⎛⎝⎜

⎞⎠⎟

c + d

c⎛⎝⎜

⎞⎠⎟

e + f

e⎛⎝⎜

⎞⎠⎟

a + b + c + d + e + f

a + c + e⎛⎝⎜

⎞⎠⎟

=(a + b)!(c + d )!(e + f )!(a + c + e)!(b + d + f )!

(a + b + c + d + e + f )!a!b!c!d!e!f !

p =

a + b

a

⎛

⎝⎜⎞

⎠⎟c + d

c

⎛

⎝⎜⎞

⎠⎟n

a + c

⎛

⎝⎜⎞

⎠⎟=

(a + b)!(c + d)!(a + c)!(b+ d)!n!a!b!c!d!

p =a + b

a⎛⎝⎜

⎞⎠⎟

c + d

c⎛⎝⎜

⎞⎠⎟

e + f

e⎛⎝⎜

⎞⎠⎟

a + b + c + d + e + f

a + c + e⎛⎝⎜

⎞⎠⎟

=(a + b)!(c + d )!(e + f )!(a + c + e)!(b + d + f )!

(a + b + c + d + e + f )!a!b!c!d!e!f !



it represents the intensity of participants’ beliefs, from “strongly disagree” to “very much agree”.

5.3. Economic Capital As a Risk-Insurance ProgrammeLet ωL be the weights of the replicating portfolio, i.e., Lt=ωL * Pt in the complete market case. In that case, σ' *ωL = σL and ωL = (σ')-1 σL. Non-hedgeable liability risk is introduced as σL,ε that adds to the tradable liability risk σL defined above.

a) The normal caseRegulatory bodies usually make normal assumptions regarding returns, rather than log-normal assumptions. In other words, they look not at the volatility of the funding ratio but at that of the surplus. If one assumes that the asset and liabilities follow normal distributions (rather than log-normal ones), the natural objective is to maximise the expected surplus, subject to the regulatory VaR constraint. Because regulators usually require that a covariance matrix be used to the aggregate the Value at Risk, the risk constraint can be understood as a total volatility.

The expected change in the terminal surplus, one-year ahead, reads:(ω.A−ωL.L)’* (μ−r1) + σL,ε*σL. L if a specific risk premium is attributed to the non-hedgeable liability risk

With m the multiplier (which transforms the volatility of an asset class into the one-year-ahead 97.5% confidence interval), the regulatory constraint reads:

m⋅ (ω ⋅ A − ωL ⋅ L ) ' ⋅σσ ' ⋅(ω ⋅ A − ωL ⋅ L ) + L2σL ,ε

2

or m2 (ω − ωL / Fs ) ' ⋅σσ ' ⋅(ω − ωL / Fs ) + σL ,ε

2 / Fs2⎡⎣ ⎤⎦


μ − r1= νm2 ⋅σσ ' ⋅(ω − ωL / Fs )

The budget constraint reads:

m2 1

ν 2m4(μ − r1) ' ⋅(σσ ') −1 ⋅(μ − r1) + σL ,ε

2 / Fs2⎡

⎣⎢

⎤

⎦⎥

= (1− k / Fs ) 2

The optimal portfolio policy reads:

ω = ωL / Fs +

(σσ ') −1 ⋅(μ − r1)

(μ − r1) ' ⋅(σσ ') −1 ⋅(μ − r1)⋅

(1− k / Fs ) 2

m2−

σL ,ε2

Fs2


ω ⋅ A = ωL ⋅ L +

(σσ ') −1 ⋅(μ − r1)

(μ − r1) ' ⋅(σσ ') −1 ⋅(μ − r1)⋅

( A − kL ) 2

m2− σL ,ε

2 ⋅ L2

b) The log-normal case For an illustration of the respective properties of economic capital and RCI, we derive an economic capital programme applied to the funding ratio: the regulatory constraint is a multiplier of the volatility of the funding ratio, not of the surplus. If the pension fund takes the classic view that assets and liabilities follow a log-normal process, the drift in the funding ratio reads and its volatility reads

and its volatility reads

(ω − ωL ) ' ⋅σσ ' ⋅(ω − ωL ) + σL ,ε

2

5. Appendices

μF S = (r − μL + σL

' σL + σL ,ε2 ) + ω '(μ − r1− σσL )




(μ − r1) +12

σσ ' ⋅(ω − ωL )

−νm2 ⋅σσ ' ⋅(ω − ωL ) = 0

The budget constraint reads:

ν 2 =1

m2

(μ − r1) ' ⋅ (σσ ') −1 ⋅ (μ − r1)

(1− k / Fs) 2 − m2σ

L ,ε

2⎡⎣

⎤⎦

And the optimal portfolio policy reads:


Comparison with the optimal RCI weights:In the complete market setting, optimal weights from log-normal economic capital read:

whereas weights from RCI read:

c) Conclusion: We see that, in economic capital as in RCI, the allocation to the PSP is driven primarily by risk insurance, as it is a direct function of the surplus (1-k/Fs). We also see that, unlike RCI models, where hedging also depends on risk aversion, economic capital models require the full hedging of liabilities.15 Finally, we see that, unlike allocation to

the PSP in RCI models, a linear function of the risk premium, allocation to the PSP in economic capital models is not sensitive to overall returns in the economy. Economic capital is not internally consistent since it assumes a strategy (usually buy-and-hold or fixed-mix over one year) that, when the exercise is repeated at a higher frequency, is not, in practice, followed. On the whole, economic capital is a naturally myopic programme. RCI strategies, by contrast, allow the easy incorporation of additional hedging demands when the parameter set is stochastic.

The main advantage of economic capital is that it allows the easy incorporation into strategy of non-hedgeable risks and higher moments.

5. Appendices

15 - When economic capital is applied to the surplus (the “normal” case), liabilities are fully hedged. When economic capital is applied to the funding ratio (and the constraint is on the volatility of the funding ratio, the “log-normal” case), the weight allocated to the LHP is equal to the value of the assets.

ω = ωL +

(σσ ') −1 ⋅(μ − r1)

(μ − r1) ' ⋅(σσ ') −1 ⋅(μ − r1)⋅

(1− k / Fs ) 2

m2− σL ,ε

2

ω ⋅ A = ωL ⋅ A +

(σσ ') −1 ⋅(μ − r1)

(μ − r1) ' ⋅(σσ ') −1 ⋅(μ − r1)⋅ A

(1− k / Fs ) 2

m2− σL ,ε

2

ω = ωL +

(σσ ') −1 ⋅(μ − r1)

(μ − r1) ' ⋅(σσ ') −1 ⋅(μ − r1)⋅

(1− k / Fs )

m

w* = 1−1

γ1−

kF

s

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟ ω

L+

1

γ1−

kF

s

⎛

⎝⎜

⎞

⎠⎟ σσ '( ) −1

μ − r1( )


About EDHEC-Risk Institute




The Choice of Asset Allocation and Risk ManagementEDHEC-Risk structures all of its research work around asset allocation and risk management. This issue corresponds to a genuine expectation from the market. On the one hand, the prevailing stock market situation in recent years has shown the limitations of diversification alone as a risk management technique and the usefulness of approaches based on dynamic portfolio allocation. On the other, the appearance of new asset classes (hedge funds, private equity, real assets), with risk profiles that are very different from those of the traditional investment universe, constitutes a new opportunity and challenge for the implementation of allocation in an asset management or Asset/Liability management context. This strategic choice is applied to all of the centre's research programmes, whether they involve proposing new methods of strategic allocation, which integrate the alternative class; taking extreme risks into account in portfolio construction; studying the usefulness of derivatives in implementing Asset/Liability management approaches; or orienting the concept of dynamic “core-satellite” investment management in the framework of absolute return or target-date funds.

40% Strategic Asset Allocation45.5% Tactical Asset Allocation11% Stock Picking3.5% Fees

Source EDHEC (2002) and Ibbotson, Kaplan (2000)

An Applied Research ApproachIn an attempt to ensure that the research it carries out is truly applicable, EDHEC has implemented a dual validation system for the work of EDHEC-Risk. All research work must be part of a research programme, the relevance and goals of which have been validated from both an academic and a business viewpoint by the centre's advisory board. This board is made up of internationally recognised researchers, the centre's business partners and representatives of major international institutional investors. The management of the research programmes respects a rigorous validation process, which guarantees the scientific quality and the operational usefulness of the programmes.

Six research programmes have been conducted by the centre to date: • Asset allocation and alternative diversification• Style and performance analysis • Indices and benchmarking• Operational risks and performance• Asset allocation and derivative instruments• ALM and asset management

These programmes receive the support of a large number of financial companies. The results of the research programmes are disseminated through the three EDHEC-Risk locations in London, Nice, and Singapore.

In addition, EDHEC-Risk has developed close partnerships with a small number of sponsors within the framework of research chairs. These research chairs involve a three-year commitment by EDHEC-Risk and the sponsor to research themes on which the parties to the chair have agreed.

Founded in 1906, EDHEC is one of the foremost French

business schools. Accredited by the three main international

academic organisations, EQUIS, AACSB, and Association

of MBAs, EDHEC has for a number of years been pursuing

a strategy for international excellence that led it to set up

EDHEC-Risk in 2001. With 47 professors, research

engineers and research associates, this centre has the

largest asset management research team in Europe.




The following research chairs have been endowed to date:• Regulation and Institutional Investment,in partnership with AXA Investment Managers (AXA IM)• Asset/Liability Management and Institutional Investment Management, in partnership with BNP Paribas Investment Partners• Risk and Regulation in the European Fund Management Industry, in partnership with CACEIS• Structured Products and Derivative Instruments, sponsored by the French Banking Federation (FBF)• Private Asset/Liability Management,in partnership with ORTEC Finance• Dynamic Allocation Models and New Forms of Target-Date Funds, in partnership with UFG• Advanced Modelling for Alternative Investments, in partnership with Newedge Prime Brokerage• Asset/Liability Management Techniques for Sovereign Wealth Fund Management, in partnership with Deutsche Bank• Core-Satellite and ETF Investment,in partnership with Amundi ETF• The Case for Inflation-Linked Bonds: Issuers’ and Investors’ Perspectives, in partnership with Rothschild & Cie

The philosophy of the institute is to validate its work by publication in international journals, but also to make it available to the sector through its position papers, published studies and conferences.

Each year, EDHEC-Risk organises a major international conference for institutional investors and investment management professionals with a view to presenting the results of its research: EDHEC-Risk Institutional Days.

EDHEC also provides professionals with access to its website, www.edhec-risk.com, which is entirely devoted to international asset management research. The website, which has more than 35,000 regular visitors, is aimed at professionals who wish to benefit from EDHEC’s analysis and expertise in the area of applied portfolio management research. Its monthly newsletter is distributed to more than 400,000 readers.

Research for BusinessThe centre’s activities have also given rise to executive education and research service offshoots.

EDHEC-Risk's executive education programmes help investment professionals to upgrade their skills with advanced risk and asset managementtraining across traditional and alternative classes.

EDHEC-Risk Institute: Key Figures, 2008-2009

Number of permanent staff 47

Number of research associates 17

Number of affiliate professors 5

Overall budget €8,700,000

External financing €5,900,000

Number of conference delegates 1,950

Number of participants at EDHEC-Risk Executive Education seminars

371




The EDHEC-Risk Institute PhD in FinanceThe EDHEC-Risk Institute PhD in Finance at EDHEC Business School is designed for professionals who aspire to higher intellectual levels and aim to redefine the investment banking and asset management industries. It is offered in two tracks: a residential track for high-potential graduate students, who hold part-time positions at EDHEC Business School, and an executive track for practitioners who keep their full-time jobs. Drawing its faculty from the world’s best universities and enjoying the support of the research centre with the greatest impact on the European financial industry, the EDHEC-Risk Institute PhD in Finance creates an extraordinary platform for professional development and industry innovation.

The EDHEC-Risk Institute MSc in Risk and Investment ManagementThe EDHEC-Risk Institute Executive MSc in Risk and Investment Management is designed for professionals in the investment management industry who wish to progress, or maintain leadership in their field, and for other finance practitioners who are contemplating lateral moves. It appeals to senior executives, investment and risk managers or advisors, and analysts. This postgraduate programme is designed to be completed in seventeen months of part-time study and is formatted to be compatible with professional schedules.

The programme has two tracks: an executive track for practitioners with significant investment management experience and an apprenticeship track for selected high-potential graduate students who have recently joined the industry. The programme is offered in Asia—from Singapore—and in Europe—from London and Nice.

FTSE EDHEC-Risk Efficient IndicesFTSE Group, the award winning global index provider, and EDHEC-Risk Institute launched the first set of FTSE EDHEC Risk Efficient Indices at the beginning of 2010. Initially offered for the UK, the Eurobloc, the USA, Developed Asia-Pacific, ex. Japan, and Japan, the index series aims to capture equity market returns with an improved risk/reward efficiency compared to cap-weighted indices. The weighting of the portfolio of constituents achieves the highest possible return-to-risk efficiency by maximising the Sharpe ratio (the reward of an investment per unit of risk).

EDHEC-Risk Alternative IndexesThe different hedge fund indexes available on the market are computed from different data, according to diverse fund selection criteria and index construction methods; they unsurprisingly tell very different stories. Challenged by this heterogeneity, investors cannot rely on competing hedge fund indexes to obtain a “true and fair” view of performance and are at a loss when selecting benchmarks. To address this issue, EDHEC Risk was the first to launch composite hedge fund strategy indexes as early as 2003.

The thirteen EDHEC-Risk Alternative Indexes are published monthly on www.edhec-risk.com and are freely available to managers and investors.


About AXA Investment Managers



AXA Investment Managers is an active asset manager fully owned by the AXA Group, a world leader in financial protection. AXA IM is acknowledged as a key player and thought leader in the asset management industry owing to the quality of its solutions and services. It is one of the largest European-based asset managers with 506 billion euros under management as of 31 March 2010, and employs more than 2,500 employees operating in 23 countries.

AXA IM offers products and solutions across all major asset classes and alpha strategies. Its business model is one of multi-expertise, reflecting its investment belief that, for all of its clients—institutional investors, distributors and the AXA Group:• Specialisation is key to sustainable performance;• The integration of expertises and the collaboration of specialists is at the source of optimal, tailored investment solutions.

The model is composed of the following specialised and autonomous expertises, whose teams are backed by the strength and scalability of shared support functions such as research, investment strategy, risk management or trading. These expertises form the bricks with which the Investment solutions team builds, for AXA IM’s clients, the most adapted solutions aligned with the highest industry standards:

About AXA Investment Managers


EDHEC-Risk Institute Publications and Position

Papers (2007-2010)



2010• Goltz, F., A. Grigoriu, and L.Tang. The EDHEC European ETF survey 2010 (May)

• Martellini, L., and V. Milhau. Asset-liability management decisions for sovereign wealth funds (May).

• Amenc, N., and S. Sender. Are hedge-fund UCITS the cure-all? (March).

• Amenc, N., F. Goltz, and A. Grigoriu. Risk control through dynamic core-satellite portfolios of ETFs: Applications to absolute return funds and tactical asset allocation (January).

• Amenc, N., F. Goltz, and P. Retkowsky. Efficient indexation: An alternative to cap-weighted indices (January).

• Goltz, F., and V. Le Sourd. Does finance theory make the case for capitalisation-weighted indexing? (January)

2009• Sender, S. Reactions to an EDHEC study on the impact of regulatory constraints on the ALM of pension funds (October).

• Amenc, N., L. Martellini, V. Milhau, and V. Ziemann. Asset/Liability management in private wealth management (September).

• Amenc, N., F. Goltz, A. Grigoriu, and D. Schroeder. The EDHEC European ETF survey (May).

• Sender, S. The European pension fund industry again beset by deficits (May).

• Martellini, L., and V. Milhau. Measuring the benefits of dynamic asset allocation strategies in the presence of liability constraints (March).

• Le Sourd, V. Hedge fund performance in 2008 (February).

• La gestion indicielle dans l'immobilier et l'indice EDHEC IEIF Immobilier d'Entreprise France (February).

• Real estate indexing and the EDHEC IEIF Commercial Property (France) Index (February).

• Amenc, N., L. Martellini, and S. Sender. Impact of regulations on the ALM of European pension funds (January).

• Goltz, F. A long road ahead for portfolio construction: Practitioners' views of an EDHEC survey. (January).

2008• Amenc, N., L. Martellini, and V. Ziemann. Alternative investments for institutional investors: Risk budgeting techniques in asset management and Asset/Liability management (December).

• Goltz, F., and D. Schroeder. Hedge fund reporting survey (November).

• D’Hondt, C., and J.-R. Giraud. Transaction cost analysis A-Z: A step towards best execution in the post-MiFID landscape (November).

EDHEC-Risk Institute Publications (2007-2010)



• Amenc, N., and D. Schroeder. The pros and cons of passive hedge fund replication (October).

• Amenc, N., F. Goltz, and D. Schroeder. Reactions to an EDHEC study on Asset/Liability management decisions in wealth management (September).

• Amenc, N., F. Goltz, A. Grigoriu, V. Le Sourd, and L. Martellini. The EDHEC European ETF survey 2008 (June).

• Amenc, N., F. Goltz, and V. Le Sourd. Fundamental differences? Comparing alternative index weighting mechanisms (April).

• Le Sourd, V. Hedge fund performance in 2007 (February).

• Amenc, N., F. Goltz, V. Le Sourd, and L. Martellini. The EDHEC European investment practices survey 2008 (January).

2007• Ducoulombier, F. Etude EDHEC sur l'investissement et la gestion du risque immobiliers en Europe (November/December).

• Ducoulombier, F. EDHEC European real estate investment and risk management survey (November).

• Goltz, F., and G. Feng. Reactions to the EDHEC study "Assessing the quality of stock market indices" (September).

• Le Sourd, V. Hedge fund performance in 2006: A vintage year for hedge funds? (March).

• Amenc, N., L. Martellini, and V. Ziemann. Asset/Liability management decisions in private banking (February).

• Le Sourd, V. Performance measurement for traditional investment (literature survey) (January).

EDHEC-Risk Institute Publications (2007-2010)



2010• Lioui, A. Spillover effects of counter-cyclical market regulation: Evidence from the 2008 Ban on Short Sales (March).

• Amenc, N., P. Schoefler and P. Lasserre. Organisation optimale de la liquidité des fonds d’investissement (March).

2009• Till, H. Has there been excessive speculation in the US oil futures markets? (November).

• Amenc, N., and S. Sender. A welcome European Commission consultation on the UCITS depositary function, a hastily considered proposal (September).

• Sender, S. IAS 19: Penalising changes ahead (September).

• Amenc, N. Quelques réflexions sur la régulation de la gestion d'actifs (June).

• Giraud, J.-R. MiFID: One year on (May).

• Lioui, A. The undesirable effects of banning short sales (April).

• Gregoriou, G., and F.-S. Lhabitant. Madoff: A riot of red flags (January).

2008 • Amenc, N., and S. Sender. Assessing the European banking sector bailout plans (December).

• Amenc, N., and S. Sender. Les mesures de recapitalisation et de soutien à la liquidité du secteur bancaire européen (December).

• Amenc, N., F. Ducoulombier, and P. Foulquier. Reactions to an EDHEC study on the fair value controversy (December). With the EDHEC Financial Analysis and Accounting Research Centre.

• Amenc, N., F. Ducoulombier, and P. Foulquier. Réactions après l’étude. Juste valeur ou non : un débat mal posé (December). With the EDHEC Financial Analysis and Accounting Research Centre.

• Amenc, N., and V. Le Sourd. Les performances de l’investissement socialement responsable en France (December).

• Amenc, N., and V. Le Sourd. Socially responsible investment performance in France (December).

• Amenc, N., B. Maffei, and H. Till. Les causes structurelles du troisième choc pétrolier (November).

• Amenc, N., B. Maffei, and H. Till. Oil prices: The true role of speculation (November).

• Sender, S. Banking: Why does regulation alone not suffice? Why must governments intervene? (November).

• Till, H. The oil markets: Let the data speak for itself (October).

EDHEC-Risk Institute Position Papers (2007-2010)



• Amenc, N., F. Goltz, and V. Le Sourd. A comparison of fundamentally weighted indices: Overview and performance analysis (March).

• Sender, S. QIS4: Significant improvements, but the main risk for life insurance is not taken into account in the standard formula (February). With the EDHEC Financial Analysis and Accounting Research Centre.

2007 • Amenc, N. Trois premières leçons de la crise des crédits « subprime » (August).

• Amenc, N. Three early lessons from the subprime lending crisis (August).

• Amenc, N., W. Géhin, L. Martellini, and J.-C. Meyfredi. The myths and limits of passive hedge fund replication (June).

• Sender, S., and P. Foulquier. QIS3: Meaningful progress towards the implementation of Solvency II, but ground remains to be covered (June). With the EDHEC Financial Analysis and Accounting Research Centre.

• D’Hondt, C., and J.-R. Giraud. MiFID: The (in)famous European directive (February).

• Hedge fund indices for the purpose of UCITS: Answers to the CESR issues paper (January).

• Foulquier, P., and S. Sender. CP 20: Significant improvements in the Solvency II framework but grave incoherencies remain. EDHEC response to consultation paper n° 20 (January).

• Géhin, W. The Challenge of hedge fund measurement: A toolbox rather than a Pandora's box (January).

• Christory, C., S. Daul, and J.-R. Giraud. Quantification of hedge fund default risk (January).

EDHEC-Risk Institute Position Papers (2007-2010)

For more information, please contact: Carolyn Essid on +33 493 187 824 or by e-mail to: [email protected]

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