detecting hidden risks why factor analysis? understand anticipate act raphael douady, cnrs and...
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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
80
90
100
110
120
130
140
150
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%
-4%
-2%
0%
2%
4%
6%
8%
-4% -3% -2% -1% 0% 1% 2% 3% 4% 5%
EQMAIN_USAD
LS
Eq
uit
y F
un
d
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
95
100
105
110
115
120
125
130
135
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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
-2%
-1%
0%
1%
2%
3%
4%
5%
juin
-07
juil-
07
août
-07
sept
-07
oct-
07
nov-
07
déc-
07
janv
-08
févr
-08
mar
s-08
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