Quantitative Asset Management for Turbulent Markets

NATIXIS EQUITY MARKETS

2

Asset Allocators have to cope with tail risk

The rewards of risk premium are wiped out by a small number of extreme risk events

3

Mitigating Tail Risk

Approach Description Remarks

Stop Loss Mechanism Divest from risky assets when themarket drops to a predeterminedbarrier

• Simple• Reactive

Use Derivatives Derivatives such as options orfutures to provide downsideprotection

• Timing sensitive• Potentially expensive

Subjective approach For example “bonus smoothing”Gradually divest from equities ingood years

• Subjective• Perceived as black

box

Quantitative Models[Reactive]

Rule based asset allocation such asCPPI or volatility target strategies

• Reactive• Objective

Quantitative Models[Forecasting]

Fundamental research basedquantitative models

Equity MarketsARPI and Risk Control

Framework

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Equity Markets - ARPI and Risk Control Framework

• Natixis Equity Markets has developed a family of investable indexes:

Rule-based

Quantitative technology developed in-house

Allocation occurs between liquid market instruments

• With these indexes, it is possible to:

Build cheap passive indexed funds

Provide increasingly sophisticated guarantees and enhance investor protection

• The investment can be structured through:

Mutual Funds

- Physical

- Synthetic

Debt Wrappers

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• Implied Volatility of Equity Markets

(VIX)

Strong and robust anti-correlation with

equity markets

Implied volatilities (vs. historical) can

anticipate / estimate future realised

volatility

IMPLIED VOLATILITY

• CDX Investment Grade non-Financials

• CDX High Yield

Risk aversion measure expressing

expectations of default rates

Quantifies the conditions of access to credit

and the cost of cash

CREDIT SPREADS US YIELD CURVE DYNAMICS

What is the Advanced Risk Perception Indicator ?

• The ARPI is an indicator of perceived market risk.

• Among the numerous potential measures of investor risk aversion (in the US market), we have selected three classesof observable indicators:

• Slope 1Y-5Y

• Difference 1Y-Annual Moving Average

1Y

Measures medium term growth expectations

Captures the effects of investor flight to

quality and movements in liquidity

preference resulting from changes in the

FED monetary policy

ARPI©

Average of Normalized Market Observables

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Extracting Regimes from ARPI– the HMM Methodology

Natixis Quantitative Research implemented an algorithm that is based on a statistical model called the HMM(Hidden Markov Model)

• A recursive filter enables us convert the time series of the ARPI into a time series of regimes

• The filter takes three types of information into account:

Where we are (the current level of ARPI gained from the new information)

Where we have come from (the level of the regime at the previous date)

How fast we are moving (incorporates the historical probability for change of regime - theinertia)

• A change of regime occurs when the current level of ARPI becomes statistically incompatible with the current regime.

HMM FilterARPI©

Regimet-1

Regimet

Insignificant Market Changes

and White Noise are ignored

Life-long learning – detects new trends

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HMM Risk Regimes Are Stable

98.98%1.02%0.00%0.00%

0.98%98.63%0.39%0.00%

0.00%0.36%99.03%0.61%

0.00%0.00%0.93%99.07%

Regime 1

Regime 1

Regime 3

Regime 2

Regime 4

Regime 2 Regime 3 Regime 4

US ARPI Distribution by regime

0,00 0,20 0,40 0,60 0,80 1,00

US ARPI

Pro

bab

ilit

yD

en

sit

y

Regime 1

Regime 2

Regime 3

Regime 4

2

0 0

23

4 4

9

0

0

2

4

6

8

10

2003 2004 2005 2006 2007 2008 2009 2010 2011

Changes of Regime per Year since Inception

• Key observations:

There is a high degree of inertia inthe HMM model (probability ofremaining in the current regimefrom one day to another over 95%)

Helps to minimize transaction costsin implementing a reallocationstrategy

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Putting it all together

Market Data

Allocation

Rule

ARPI

Regime

Assets

Proprietary Strategy

HMM

• The final step in the process is to allocate between asserts, based on theprevailing regime of the day

• The allocation weights between assets are generally fixed at thebeginning of the strategy, and are aligned with the differing perceivedrisk levels associated with each regime

• As seen, in the majority of cases there is no change to the prevailingregime

Regime 1

Regime 2

Regime 4

Regime 3

Highly Aggressive Allocation

Moderately Aggressive Allocation

Moderately Conservative Allocation

Highly Conservative Allocation

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NXS SHARPe Multi Asset Worldwide USD

Offensive Profile

25%

25%

50%1

Dynamic Profile

35%

25%

20%

10%

10%

7

Balanced Profile

10%

10%

10%

25%

0%10%

35%

7

Conservative Profile

50%

30%

20%

Equity

Real-Estate

Commodity

Hedge Funds

Bond MLT

Bond ST

Cash

• Dynamic reallocation between 4 distinct management profiles

• Offensive, dynamic, balanced and conservative

• 7 asset classes in the worldwide markets through liquid indices• Equity : US, Europe and Emerging Markets

• Real-Estate : Listed REITsindex (US & Europe)

• Commodities : Listed Commodity index

• Hedge Funds : Natixis HF replicating Index ie NXS-AIR Index (Ticker Bloomberg : IQHGIXIS Index)

• Medium Long Term Bonds : LT US and Europe Government bond index (duration > 3 years)

• Short Term Bonds : LT US and Europe Government bond index (duration < 3 years)

• Cash : Compounded overnight US rate

• A portfolio fully invested at any time, without leverage and no short positions

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NXS SHARPe Multi Asset Worldwide USD – Performance

Com parison of the annual r isk / re turn

betw een asset classes

Equity

Real-EstateCommodity

Hedge

Funds

Bond MLT

Bond ST

Cash

SHARPe

Multi Asset

Worldw ide

0%

2%

4%

6%

8%

10%

12%

0% 5% 10% 15% 20% 25% 30%

Volatility

An

nu

al

retu

rnInvestment in the strategy and asset classes achieved from 01/7/99 to 02/12/11

Com parison of perform ances

0

100

200

300

400

500

600

19992000

20012002

20032004

20052006

20072008

20092010

2011

SHARPe Multi Asset Worldw ideStatic StrategyEquityReal-EstateCommodityHedge FundsBond MLTBond STCash

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● Layer 1 – Risky Asset Allocation :

The Risky Asset Allocation is designed to embed a Natixis SHARPe Quantitative Allocation

● Layer 2 – Performance Engine:

The performance engine implements a Volatility Control mechanism

A Systematic rebalancing occurs between the Natixis SHARPe Allocation and a Safe Asset

The rebalancing follows the ratio of the Target Volatility to the Realised Volatility

● Layer 3 – Smart CPPI on the Performance Engine :

A classic CPPI portfolio management technique is at risk of Cash-lock

Using Natixis ARPI and HMM, the Cash-lock is eliminated for higher risk regimes

3 Protection Layers for a Resilient Investment Solution

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● Basic Structure:

The CPPI Protects a fixed percentage (typically 80%) of the maximum observed NAV by

dynamically re-balancing between risky and risk-free assets, on the basis of a predefined

mechanism

In the most simple case, the difference between current NAV and the protection level (the

“cushion”) is calculated. A constant proportion of the cushion is then invested in the risky asset

As the risky asset moves, the portfolio is rebalanced in accordance with the cushion available

Constant Proportion Portfolio Insurance (CPPI)

CASH

RISK ASSET

FUND NAV = 100%

PROTECTION = 80%

CUSHION =

NAV – PROTECTION = 20%

MULTIPLIER = 3

60%

40%

FUND NAV = 125%

PROTECTION = 100%

CUSHION =

NAV – PROTECTION = 25%

MULTIPLIER = 3

FUND NAV = 90%

PROTECTION = 80%

CUSHION =

NAV – PROTECTION = 10%

MULTIPLIER = 3

CASH

RISK ASSET75%

25%

CASH

RISK ASSET30%

70%

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● The Smart CPPI makes use of the ARPI for allocation purposes. Allocation is made according to a variable Multiplier. The

Multiplier is scaled according to the ARPI

Allocation is conservative during periods of high risk aversion

Allocation is aggressive during periods of low risk aversion

Smart CPPI using the ARPI

Regime 1

Regime 2

Regime 4

Regime 3

Highly AggressiveAllocation

HighlyConservative Allocation

Moderately AggressiveAllocation

Moderately ConservativeAllocation

3

0

1

5

VariableMultiplier

80%

20%Cushion

BondFloor

X

3RiskAsset60%

RISK ASSET EXPOSURE = CUSHION x VARIABLE MULTIPLIER

Function of Risk Regime

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0

20

40

60

80

100

120

140

160

180

05/0

1/19

99

04/0

1/20

00

03/0

1/20

01

03/0

1/20

02

03/0

1/20

03

05/0

1/20

04

04/0

1/20

05

04/0

1/20

06

05/0

1/20

07

07/0

1/20

08

06/0

1/20

09

06/0

1/20

10

05/0

1/20

11

NA

V

0

10

20

30

40

50

60

70

80

90

100

Ris

kA

sse

tA

llo

ca

tio

n(%

)

Risk Asset Allocation SPX TR SHARPe SPX80Max

Protected Level Ordinary CPPI

Smart CPPI using the ARPI

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Resilience of a Smart CPPI in Higher Risk Regime

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