Risk Management for Hedge Funds

Tackling Rare Events with an Incomplete History

A. Jaun

1,2

, S. Umansky

1

, H. El Showk

1 1 Signet Capital Management Limited 2 Assoc. Prof. Royal Institute Technology, Stockholm Contact [email protected]

Gdansk Conference, 11-12 May 2007

Uncertain returns from markets

Example: NYBOT coffee futures 1994 -2007

frost in Brazil

Markowitz’N90: risk  volatility =   (r i m ) Engle’N03: arbitrage free GARCH average 2 … but frost only happens during the winter!

Maximum likelyhood historical fit

with Normal-/Inverse Gaussian distributions Normal

log

NIG

zoom stress

Adequate description of normal , stress and rare events?

normal

rare

The perception of risk evolves

Volatility & kurtosis looking back 1-12 years

coffee sugar coffee sugar

Should coffee prices be getting more stable?

Modern tools for risk management

• Value at risk VaR a (not subadditive) • Expected shortfall ES=

1 1-

a  a

1

VaR u du prob weigthed returns probabitily 1 a of losses > VaR a (subadditive) • Simulation -VaR a -s (historical 1-10 years, Monte-Carlo) m • Extreme Value Theory to model rare events (Generalized Pareto distribution is generic, Embrechts) returns

Example: trading coffee derivatives

Daily risk budgeting

VaR95 ES95 ER Normal -1.10% -1.38% +0.34% +0.35% -0.0007% Stress -1.57% -1.84% +0.33% +0.36% -0.001

Worst case if D S=+15% 4% loss (no risk of frost in Apr)

And when there is not enough data

Ex: avalanche risk • little/no history • incomplete data Take the right decision... before it is too late!

3x3 «orthogonal» qualitative factors

• Global (from home) regional forecast.....................0

map, itinerary..........................1

level of participants.................0

• Local (from start) snow depth >15cm.................1

weather conditions.................0

orientation (NE-NW)...............1

• Zonal (every step) slope >35 deg........................1

snow consistency..................1

solidity test.............................1

Total......................6 > 4 too risky  avoid

Optimize a fund of hedge funds

Impossible to rely on the past perfomance Would need > 140 years of monthly data (A. Lo) I. Check for structural risks People, organization, administrator, infrastructure II. Estimate aggregatable market risks Identify risk factors, limit and diversify exposures Estimate returns from worst case scenarios III. Maximize risk-adjusted expected returns Generalize Sharpe ratio: S = E[Return] / Risk Details of the process are propriatery, but…

Risk budgeting with uncertainty • Estimate optimization constraints

– Exposures: gross, net, liquidity, geography, strategy – Worst losses 9/11, stock crash, rate hikes, liquidity crisis

• Account for uncertainties (work plan)

Optimum with rigid constraints goal function Range of optima with different confidence levels constraint uncertainty

Risk-adjusted expected returns

Returns from probability weighted scenarios E.g. 30% stagflation, 50% soft landing, 20% hard landing Risk from a fund = lack of confidence in Our own judgement (insufficient knowledge) Future expected returns (forward looking volatility) The preservation of capital (exposure to rare events) Estimates should be back-tested (work plan) How well does past performance match forecasts?

Example: fund of hedge funds

Fixed income strategies fund • 50 hedge funds, 6 strategies, exposures, etc • Risk management process validated over 7 years • Low correlation to market and rare events Historical performance compared to indices 2'600 2'100 1'600 1'100 600 40 30 20 10 0 JPM Gl.Gov.Bond

MSCI W TR GFI fund Return Range (%)

Conclusions

Distribution of returns to describe market risks Max likelihood to fit Normal, NIG, Pareto distributions Choice of the historical time span is the main issue When there is not enough data Identify aggregatable & orthogonal risk factors Bayesian estimate of returns for rare events Estimates can be back-tested and refined with time Rare events do happen and define our lives!

Disclaimer

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