Reference Portfolio & Factor Investing: Advances in · PDF fileReference Portfolio & Factor...

Reference Portfolio & Factor Investing:

Advances in Global Investment Management

Global Pension Symposium, Tokyo, November 2015

SUNG Cheng Chih

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Outline

• Motivation

• Theory

• Practice

• Conclusion

SUNG Cheng Chih


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Part 1: Motivation

SUNG Cheng Chih


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Traditional Asset Allocation Model & Its Pitfalls • Traditional approach to portfolio construction centred around a quasi-

static policy portfolio with significant allocation to equities, modest level of active management & regular rebalancing

• Main shortcomings of the asset allocation-centric approach:

- tight link between policy & actual portfolios imposes structural rigidity in inclusion of new strategies/asset classes

- insufficient risk transparency on underlying drivers of risk and return beyond asset class labels while diversification benefits are often exaggerated

- performance measurement fails to distinguish between skill-based value creation and returns from beta, currency, leverage & illiquidity especially for alternatives

- active risk framework ineffective in managing risk of benchmark-agnostic strategies & private investments

SUNG Cheng Chih


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Motivation for Opportunity Cost Model • Pioneered by CPPIB under leadership of David Denison, John Ilkiw, Don

Raymond & Mark Wiseman in mid-2000s (known as ‘Total Portfolio Approach’) and later adopted with modification by GIC and NZ Super

• Starting premise: risk/return drivers of liquid publicly traded assets are better understood & cheaper to replicate compared to alternatives

• Risk of alternative investing overlaps with public market investing to varying degrees but real case for alternatives rests on embedded uncorrelated sources of returns, both systematic & idiosyncratic

• Reference Portfolio comprising only liquid assets provides an objective measure of opportunity cost for active investing in both public & private markets

• Total risk of actual portfolio governed by an expanded active risk budget relative to the Reference Portfolio

SUNG Cheng Chih


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Part 2: Theory

SUNG Cheng Chih


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Basic Construct of Opportunity Cost Model

SUNG Cheng Chih


• Reference Universe, ∏: Asset universe comprising liquid, publicly traded assets, usually nominal/real government bonds & listed equities

• Reference Portfolio, B: The optimal portfolio for the investor within the reference universe ∏ which acts as a realistic low-cost passive alternative for the fund under the given constraints

• Funding Benchmark, Bi: Each investment strategy with return Ri is funded by and managed against a funding benchmark Bi ∏ which serves as a proxy for the opportunity cost of that investment and hence basis for risk & performance measurement

• Return Projection, Pi: For each strategy with return Ri , Pi represents the projection of Ri onto the reference universe ∏ (i.e. the best liquid market proxy) such that Ri = Pi + ri = Bi + (Pi - Bi) + ri where the residual return ri is uncorrelated with assets in the reference universe, i.e. ri ⊥ ∏

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Geometric Visualisation: Strategy Return

SUNG Cheng Chih


Reference Universe ∏

Strategy Return Ri

Funding Benchmark Bi

Residual Return ri

Ri = Pi + ri = Bi + (Pi - Bi) + ri where Pi, Bi ∏ and ri ∏

Var[Ri - Bi] = Var[Pi - Bi] + Var [ri]

Return Projection Pi

Pi - Bi

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Total Fund Return & Active Return

SUNG Cheng Chih


• Total fund return can then be represented as

R = ∑i wiRi = ∑i wiBi + ∑i wi (Pi - Bi) +∑i wiri

while total active return becomes

R – B = (∑i wiBi – B )+ ∑i wi (Pi - Bi) +∑i wiri

• Since reference universe ∏ comprises liquid assets only, rebalancing and completion management can in theory be effected at low cost to ensure ∑i wiBi B at all times

• By virtue of ri ∏, active risk can be decomposed orthogonally as

TE2 = Var[R – B] Var[∑i wi (Pi - Bi)] + Var[∑i wiri]

• With a quasi-static reference portfolio, portfolio construction boils down to allocation to investment strategies that maximise total active return R – B subject to an active risk budget expressed in TE terms

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Geometric Visualisation: Total Fund Return

SUNG Cheng Chih


Total Fund Return R = ∑i wiRi

Reference Portfolio B

Residual Return r = ∑i wiri

R P + r = B + s + r where P, B, s ∏ and r ∏

TE2 = Var[R – B] Var[∑i wi (Pi – Bi)] + Var[∑i wiri ]

Return Projection P = ∑i wiPi

s = ∑i wi (Pi - Bi)

Reference Universe ∏

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Part 3: Practice

SUNG Cheng Chih


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Choice of Reference Portfolio

SUNG Cheng Chih


CPPIB GIC NZ Super

2015 2018 2015 2015

65% equities - 55% international - 10% domestic

80% global equities

65% global equities

80% equities - 65% developed - 10% emerging - 5% domestic

35% fixed income - 5% international - 30% domestic

20% global fixed income



• The total risk of the actual fund is governed indirectly by an active risk budget which typically ranges from 2% to 3.5% in annual tracking error terms relative to the Reference Portfolio

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Estimating Active Risk

SUNG Cheng Chih


• In theory, active risk in Opportunity Cost Model can be estimated in 3 steps:

- determine projected return Pi for each strategy

- estimate liquid component of TE2 = Var[∑i wi (Pi - Bi)]

- estimate illiquid component of TE2 = Var[∑i wiri] where ri = Ri - Pi

• For an investment strategy within the reference universe, ri = 0 and Ri = Pi in which case the strategy only contributes to Var[∑i wi (Pi - Bi)] which can be readily estimated by most risk engines provided the fund owner has full position-level transparency

• For alternatives, funding benchmark Bi is usually chosen via regression analysis while projected return Pi is tacitly assumed to be Bi

• Hence, in practice, residual return ri from alternatives is taken to be Ri – Bi

and contribution to liquid component of TE2 is ignored

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Modelling Residual Risk

SUNG Cheng Chih


• Even though the residual returns ri associated with individual strategies are orthogonal to ∏, they need not be orthogonal to each other, i.e. they may exhibit factor structure of their own: ri = ∑j xijFj + θi where θi represents the ‘true’ asset-specific returns and θi ⊥ Fj

• If such alternative risk factors Fj are present, then the illiquid component of TE2 can be further decomposed into Var[∑i wi(∑j xijFj + θi)] = Var[∑j yjFj]+ ∑i wi Var[θi]

• In the case of private equity, there is strong evidence that there are no associated alternative risk factors and residual risks are essentially asset-specific in nature, hence diversifiable in large portfolios

• Empirical evidence for existence of real estate factors appears to be mixed but even if present, their contribution is likely to be modest compared to the asset-specific components

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Completion Management

SUNG Cheng Chih


• Frequent rebalancing & judicious completion management are needed to ensure that choice of funding benchmarks does not create unintended or unmanaged tilts in the actual portfolio versus the reference portfolio

• In practice, the situation is more manageable if the funding benchmarks are made up of broad components of the reference portfolio, such as global equities or global government bonds. When the funding benchmark goes into specific sub-segments such as sectors (e.g. US healthcare stocks), the job of portfolio completion becomes more laborious and costlier. Even more vexing is when the strategy has style tilts such as value or momentum

• In general, the more ‘micro’ the choice of the funding benchmark, the greater the difficulty in completing the portfolio

• Ultimately, a reasonable trade-off needs to be struck between precision and practicality

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Investment Accountability

SUNG Cheng Chih


• In addition to challenges in completion management, the choice of funding benchmarks could also lead to accountability issues in some cases:

1) when the manager refuses to take ownership for the assigned funding benchmark (e.g. insist on Libor + benchmark despite significant betas)

2) when the strategy involves large orthogonal risks not captured by the risk system

3) when the manager refuses to provide position-level transparency even though the underlying assets are all publicly traded

• In such cases, cheap-to-replicate betas may be disguised as alphas and procured at much higher costs while active risk could be under-estimated

• If the fund owner chooses to invest in a strategy despite one or more of the above, then there needs to be clear internal points of accountability for components of risk and returns that the manager is unwilling or unable to assume versus the funding benchmark for the strategy

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Fund Governance

SUNG Cheng Chih


• With no pre-determined allocation targets for alternatives (e.g. real estate), the Opportunity Cost Model calls for much greater delegation of investment authority from owner or trustees to the investment manager

• Such concerns have led some investors to modify the original CPPIB model by introducing a strategic or policy portfolio between the actual & reference portfolios

Reference Portfolio Strategic

Active Risk Budget

Operational Active Risk

Budget

Strategic Portfolio

Actual Portfolio

Increasing complexity

Increasing time horizon

Owned by trustees Jointly owned by trustees & manager

Owned by manager

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Organisation & Mind-set

SUNG Cheng Chih


• Under the Opportunity Cost Model, inclusion of new strategies, choice of funding benchmarks & allocation of active risk budget should logically come under one central decision-making body at senior management level (e.g. investment committee), aided by an expanded strategy research function

• Operationally, it also makes sense to combine trade execution, funding, hedging & completion management under one central ‘treasury’ function

• Although familiar to public market portfolio managers, the use of funding benchmarks, active risk budget and performance measurement that distinguishes skill-based value creation from liquid, cheap-to-replicate beta returns are novelties in private market investing

• Thus the burden of adjustment in terms of investment practices & mind-set falls disproportionately on the private market investment teams, which could be highly divisive if not managed well

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Part 4: Conclusion

SUNG Cheng Chih


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Concluding Remarks • The Opportunity Cost Model has gained growing traction among leading

global investors as it offers better balance among risk transparency, investment accountability & operational flexibility

• It draws a clear distinction between cheap-to-replicate liquid publicly traded assets & uncorrelated sources of risk/return from alternatives

• Compared to full factor-driven approaches, the opportunity cost model is more intuitive; in fact, it can be thought of as a liquid factor model

• However, this approach places much greater demands on risk modelling, portfolio rebalancing, completion management & investment accountability

• More importantly, it calls for greater degree of delegated authority to management, thoughtful adjustments in governance structure & mind-set change within the investment organisation

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Useful References • Review of the Active Management of the Norwegian Government

Pension Fund Global, Jan 2014, A. Ang, M. Brandt & D. Denison

• Factor Investing: The Reference Portfolio and Canada Pension Plan Investment Board, Columbia Business School Case Study, May 2012, A. Ang

• 2015 Annual Report, Canada Pension Plan Investment Board (www.cppib.com)

• Report on the Management of the Government’s Portfolio for the Year 2014/2015, GIC (www.gic.com.sg)

• 2014 Annual Report, New Zealand Superannuation Fund (www.nzsuperfund.co.nz)

SUNG Cheng Chih


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