DETECTING HIDDEN RISKS

Why Factor Analysis?

UNDERSTAND • ANTICIPATE • ACT

Raphael Douady, CNRS and Riskdata

THE DATA PARADOX OF HEGDE FUND ANALYSIS

Too Many Data Gigabytes processed Heavy Model Calibration, Optimization

Too Few Data Only a few Hedge Fund returns Only some returns are meaningful, bear information

Why Computing Power and Memory Capacity

are so Inefficiently used?

How to “break the data wall”

What is Risk Management about?

Is it Returns Distribution? Performance: Sharpe, Skew, Kurtosis, Omega etc. etc. Risk: Value at Risk, CVaR

Or understanding Reaction to Market Moves? Correlation, Betas, Factor Analysis

Or Anticipating Potential Losses due to

Markets? Stress Testing, Hedge policy, Overlay

3 QUESTIONS OF RISK MANAGEMENT

Question 1: “What is the Range of possible Future

returns?” Answers: Expectations, Value-at-Risk, ex-ante Volatility

Question 2: “How Returns are Related to Markets?” Answers: Factor models, stress tests

Question 3: “How Returns are Inter-related?” Answers: Diversification, Portfolio construction

What is the Range of possible Future returns?

Observed ex-post performance

TodayPast Future

Observed ex-post volatility

Future performance expectation

VaR = Pessimistic scenario

Optimistic scenario

Statistical methods to estimate future returns, not to observe past

ones

A Risk Measure is an Ex-ante

measure

PERFORMANCE vs. RISK MEASURES

Using Performance Measures as Risk Measures is

making 2 Assumptions:1) Future will look like the Past2) No Other Information than past performances is Relevant

Risk Measurement CANNOT rely on these assumptions

A fortiori Risk Management Aggregate Risk Measures Take Action (Allocation, overlay with Market Instruments…)

PURPOSE OF A RISK SYSTEM

Compute Risk Measures Reporting Communication Warning system

Take Action Discard Highly Risky ones Keep Good Risk Takers Avoid Hidden Risk Identify and Hedge Dangerous Market Scenarios,

incl. Correlation breaks

HEGDE FUND RISK FOR THE INVESTOR

Survive Through Crises ANTICIPATE!

Identify Risk Sources Holdings, Exposures Leverage Liquidity, Concentration Vanishing Diversification

Dangerous Market Scenarios Extreme Risk Systemic Risk

Position based risk analysis miss a key aspect of hedge fund risk:

a significant part of it stems from dynamic portfolio management

What Does This Snapshot Tell Us?

• We know the exact position of every subject at a given point in time.

• Do we really understand what’s going on?

Dali Atomicus by Philippe Halsman

Hiding Risk: Writing Put option

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mid August 07

Long-Short Equity: Think Gamma & Theta

Mid-Aug 07 Return

Jul 07 Return

Theta

Gamma

REAL LEVERAGE: Returns vs. S&P 500

Downside Leverage = 3

Long-Short Equity Aug 05 - Aug 07

Jul 07

mid-Aug 07

-8%

-6%

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-4% -3% -2% -1% 0% 1% 2% 3% 4% 5%

EQMAIN_USAD

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Downside Beta = 3

Linear Beta = 0.6

Upside Beta = 0

Sources of Nonlinearity (by order of importance)

1) Liquidity Gaps They are Systematic Create Correlation Breaks

2) Dynamic Trading Positions change with market Mimic Option Replication

3) Nonlinear Relation between Assets 3.1) Bonds vs. Stocks (credit spreads increase when the

stock declines) 3.2) Small caps vs. Large caps ( increases for large

moves) 3.3) Options

HEGDE FUND RISK FOR THE INVESTOR

Survive Through Crises ANTICIPATE!

Identify Risk Sources Holdings, Exposures Leverage Liquidity, Concentration Vanishing Diversification

Dangerous Market Scenarios Extreme Risk Systemic Risk

Average Skew by Strategy

Hedge Fund

Skew is 0 in

average

Funds of

Funds have

Negative

Skew

-80% -60% -40% -20% 0% 20% 40% 60% 80%

Convertible Arbitrage

Distressed Securities

Emerging Markets

Equity Hedge

Equity Market Neutral

Equity Non-Hedge

Event-Driven

Fixed Income Arbitrage

Fixed Income Non Arbitrage

Foreign Exchange

Macro

Managed Futures

Market Timing

Merger Arbitrage

Relative Value Arbitrage

Sector

Short Selling

Total

Fund of Funds

Hedge Funds returns source: Hedge Fund Research, Inc., © HFR, Inc.

Average Skew

The Negative Skew of Funds of Funds

indicates:

Positive months are uncorrelated Due to specific factors

Negative months are correlated Due to systematic factors Alternative Betas in Extreme Conditions

Risk Models must Capture Nonlinearities

3 RISK APPROACHES

Position Based Analysis Collect Hedge Fund Holdings Analyse the Joint Distribution of financial assets Aggregate Risks for each Fund, then for the Portfolio

Return Based Analysis Analyse, for each fund, the distribution of Past Returns Analyse the Joint Distribution of funds past returns Aggregate Risks for the Portfolio

Factor Based Analysis Analyse the joint distribution of Market Factors For each fund, identify Relevant Factors Determine its Behaviour with respect to Market Factors Aggregate Risks at the Portfolio level

How Returns are Related to Markets?

Holdings vs. Factors: Different Purposes

Short Term (days): Positions Holdings Based Analysis

• Hedge Fund Managers Independent risk control• Middle Office, Risk Control Limits• FoHF Concentration risk, immediate strategy confirmation

Long Term (months): Strategy • Incorporate Strategy and Dynamic Trading Risks

Factor Based Analysis• Investors, FoHF Structured Investment Process• Multi-strategy funds Management of heterogeneous managers

Allocation

Risk Analysis must rely on what is Persistent in the Fund

Power of Factor Analysis

Allow to Re-inject long-term past history

of markets into short lived Hedge Funds Are Black Swans always really unexpected? Often bad stories are just history repeating itself…

Efficient for Stress Testing Past Crises Market Scenarios Aggregation of Risk Profiles Cross Asset Class

Pure Return Based Analysis

Credit driven fund: Long AAA bonds, Short T-bonds, duration 10Y

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Sharpe = 1.3Annualised Volatility = 2.4%Annualised return = 6.5%VaR 99 = 0.9% (1.3 sigma)Peak to valley = 1.1%Skew = +0.6Excess Kurtosis = 0.2

Pure Return Based Analysis

Credit driven fund: Long AAA bonds, Short T-bonds, duration 10Y

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Sharpe = -0.25Annualised Volatility = 3.4%Annualised return = 2.6%VaR 99 = 3.5% (3.5 sigma)Peak to valley = 12.2%Skew = -1.0Excess Kurtosis = 3.0

Factor Analysis

Credit driven fund vs. AAA spread over T-Bonds This fund was just surfing the good wave during the analysis

period Will it last?

Variety of Hedge Fund Strategies

No a priori Reduced Set of Factor Large number of possible factors Aggregation: All funds must be analyzed through all factors Open system: the user must be able to enter custom factors

No a priori Rigid Model Correlation Breaks Nonlinear Models Illiquid Assets and Funds Lagged Effects Significance Factor Scoring

A system that doesn’t propose its own broad

analysis of factors and markets is a Toy, not

professional

Anticipate Time Bombs

Specific Bets, Leverage

Systemic Risk: one or several classes

blowing up

The only technique to use all information Compare the funds to markets Use long term history to assess what may happen to it Possibly compare to similar investments under past crises

Other approaches miss predictive value Examples: Performance measures as Risk measures (Sharpe, Omega…) Correlation matrix of fund returns only

CASE STUDY 1: L/S Equity Europe

Created in April 03. In June 07, track record is very attractive: Average monthly performance = 3.8% Monthly volatility = 2.8% Worst Month = - 5.9%

An investor deciding to invest based on this wonderful track record would have had

the following nasty surprise: Performance from July 07 to March 08 = - 31% Worst Month after July is January 08 = - 16%

A good factor analysis run in June 07 would have help demonstrating this fund was

simply lucky: Beta+ = +3.3% for Eurostoxx +5% Beta- = -6.6% for Eurostoxx -5%

From Fund inception to June 07 Eurostoxx worst month = -5% in May 06 Average perf = 1.4%

If we look now at the entire history of the factor, going backward to 1987, one can

see that this period was simply exceptional – meaning the manager was mainly lucky: Worst month on long period was Black Monday: -23% in October 1987. Extrapolating to this scenario the fund relationship with the factor show it could loose as much as 30% in a

market like Black Monday. Between July 07 and march 08, the Eurostoxx dropped by 18%, with a worst month in January 2008: down

12% - half Black Monday.

An investor having use a good factor model should not have been surprised!

CASE STUDY 2: US Fixed Income

Created in June 04. In June 07, track record is very attractive: Average monthly performance = 0.8% Monthly volatility = 0.4% Worst Month = - 0.7%

An investor deciding to invest based on this wonderful track record would have had

the following nasty surprise: Performance from July 07 to March 08 = - 28% Worst Month after July is January 08 = - 9%

A good factor analysis run in June 07 would have help demonstrating this fund was

simply lucky: Beta+ = -1.7% for TB Spread 10Y – 1Y widen +22 bps Beta- = -0.1% for TB Spread 10Y – 1Y narrow -22 bps

From Fund inception to June 07 TB Spread 10Y – 1Y worst month = +22 bps in June 07 Average = -7bps / month

If we look now at the entire history of the factor, going backward to 1987, one can

see that this period was simply exceptional – meaning the manager was mainly lucky: Worst month on long period was +96 bps in June 2003. Extrapolating to this scenario the fund relationship with the factor show it could loose as much as 24% in a

market like June 03. Between July 07 and march 08, the TB Spread 10Y-1Y widened by 150 bps, with a worst month in January

2008: up 95 bps, same as June 03.

An investor having use a good factor model should not have been surprised!

CASE STUDY 3: Equity USA Stat. Arb. (quant. market neutral)

Created in January 05. In June 07, track record is very attractive: Average monthly performance = 1.5% Monthly volatility = 2.1% Worst Month = - 2.7%

An investor deciding to invest based on this wonderful track record would have had

the following nasty surprise: Performance from July 07 to March 08 = - 10% Worst Month after July is January 08 = - 7%

A good factor analysis run in June 07 would have help demonstrating this fund was

simply lucky: Beta+ = -3.2% for S&P500 -3% Beta- = -2% for Eurostoxx +3%

« Market Neutral » = Short Gamma and Short Volatility !

From Fund inception to June 07 S&P500 worst month = -3% in May 06 Average perf = 0.9%

If we look now at the entire history of the factor, going backward to 1987, one can

see that this period was simply exceptional – meaning the manager was mainly lucky: Worst month on long period was Black Monday: -22% in October 1987. Extrapolating to this scenario the fund relationship with the factor show it could loose as much as 23% in a

market like Black Monday. Between July 07 and march 08, the S&P500 dropped by 12%, with a worst month in January 2008: down

7%

An investor having use a good factor model should not have been surprised!

FACTOR VaR

Select a large Factor Set

Analyze the Fund with respect to each Factor Fi

Collection of 1-factor models:Fund = i(Fi) + specific

Use available data of the fund, restricted to recent Nonlinear functions, possibly with lags

Estimate the return distribution of factors 99% confidence interval Ji = [min99Fi , max99Fi] Use long term (> 20 years), daily data

Factor VaR Single factor: FactorVaR(Fi) = maxJi -i(Fi) Discard factors with p-value > threshold Whole Factor Set: FactorVaR = max FactorVaR(Fi)

FACTOR VaR

Capture Funds Optional Behavior + Lags

Pairwise Models No colinearity issues Can combine factors to get new ones

Input Factor long term experience Include Fat Tails from past Crises

Factor VaR by types of factors (e.g.

equity risk)

Contribution of a line to a portfolio

Robustness, yet Tail dependence

TIME BOMB STUDY

Performance of Hedge Funds during recent

market turmoil: July 07 – March 08

Ex Post Classification #Funds %Funds Avg Perf

Perf Attribn.

A: No Loss or Loss < 2 389 12% 8.7% 1.0% B: Loss < Past losses 2098 65% 1.7% 1.1% C: Unexpected Loss 729 23% -9.4% -2.1% Grand Total 3216 100% 0.0% 0.0%

Hedge Funds returns source: Hedge Fund Research, Inc., © HFR, Inc.

A: Peak to Valley in Turmoil < 2.3 x Past volatility B: PtoV in Turmoil > 2.3 x Past Vol but < 2 x Past PtoV C: PtoV in Turmoil > 2.3 x Past Vol and > 2 x Past PtoV

TIME BOMB STUDY

Pure Return filtering Analyze Fund Returns: Distribution, Fat Tails, Skew,

Kurtosis, Max Draw Down (MDD), etc. Compute Risk (e.g. VaR) Keep only funds with “regular” distribution:

• Past MDD < 2.3 x Volatility 1082 Funds (34%)

Nonlinear Factor-based filtering Analyze Fund Returns vs. Market Factors Project Long-term Factor Distribution onto Fund Risk Compute Factor VaR Keep only funds with regular Factor Driven distribution

• Max Factor VaR < 2.3 x Volatility• Max Factor VaR < 2 x Past MDD 868 Funds

(27%)

TIME BOMB STUDY

Performance after Pure Return filtering

Ex Post Classification %Funds Avg Perf

Perf Attribn. Rel. to

Benchmark A: No Loss or Loss < 2 36% 8.7% 2.1% B: Loss < Past losses 24% -0.9% -1.3% C: Unexpected Loss 40% -6.2% -0.3% Grand Total 100% 0.4% 0.4%

Performance after Nonlinear Factor-based filtering

Ex Post Classification %Funds Avg Perf

Perf Attribn. Rel. to

Benchmark A: No Loss or Loss < 2 21% 10.5% 1.1% B: Loss < Past losses 58% 6.5% 2.5% C: Unexpected Loss 21% -8.0% 0.5% Grand Total 100% 4.0% 4.0%

Cumulated Returns

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All Funds

Return Based

Factor VaR

RISK BASED ALLOCATION

Benchmark: equal allocation on all HRF

funds from Jul 07 to Mar 08

Given a Risk Measure Mi = Risk(Fundi) Keep the less risky quartile Equal Risk Allocation: /Mi in Fundi

Adjust leverage to match Benchmark total risk Mi

Risk Measures Past Volatility (standard deviation of past returns) Fat Tails: Past Volatility + Past Peak-to-Valley Factor VaR (linear and nonlinear versions)

Monthly Rebalancing

RISK BASED ALLOCATION

RISK BASED ALLOCATION

Rebalancing every 6M

CONCLUSIONS

Beware of Simplistic Models, Risk Management is meant

for Crisis Times! There is a lot of info in data, needs to be properly extracted Learn from past crises, project them into the future Take informed investment decisions

Factor Models, Factor VaR are the most efficient Provided using long-term factor history

Beware of Linear Models Linearity works most of the time… except when really needed!

It’s not because some maths don’t work that all don’t

work Don’t throw away the baby with the bath water!

Advanced Risk Management pays for itself and is

profitable Higher Long-term Performances Higher Alpha The ROI can be enormous with respect to the cost!

Good Risk Anticipation = Insurance against Redemptions