Risk Management for Hedge Funds Tackling Rare Events with an Incomplete History

A. Jaun1,2, S. Umansky1, H. El Showk1

1 Signet Capital Management Limited2 Assoc. Prof. Royal Institute Technology, Stockholm

Contact info@signetmanagement.com

Gdansk Conference, 11-12 May 2007

Uncertain returns from markets

Markowitz’N90: risk volatility = (ri -)2 Engle’N03: arbitrage free GARCH average… but frost only happens during the winter!

Example: NYBOT coffee futures 1994 -2007

frost in Brazil

Maximum likelyhood historical fitwith Normal-/Inverse Gaussian distributions

Adequate description of normal-, stress- and rare events?

stress

zoom

logNormal

NIG

rare

normal

The perception of risk evolvesVolatility & kurtosis looking back 1-12 years

coffeecoffee

sugar

sugar

Should coffee prices be getting more stable?

Modern tools for risk management

• Value at risk VaR

(not subadditive)

• Expected shortfall

(subadditive)-VaR

returns

prob weigthed returns

• Simulation(historical 1-10 years, Monte-Carlo)

• Extreme Value Theory to model rare events (Generalized Pareto distribution is generic, Embrechts)

1

1-

1

VaRu duES=

probabitily 1- of losses > VaR

Example: trading coffee derivativesDaily risk budgeting

Normal Stress

VaR95 -1.10% +0.34% -1.57% +0.33%

ES95 -1.38% +0.35% -1.84% +0.36%

ER -0.0007% -0.001

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

And when there is not enough dataEx: 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.....................0map, itinerary..........................1level of participants.................0

• Local (from start)snow depth >15cm.................1weather conditions.................0orientation (NE-NW)...............1

• Zonal (every step)slope >35 deg........................1snow consistency..................1solidity 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 risksPeople, organization, administrator, infrastructure

II. Estimate aggregatable market risksIdentify risk factors, limit and diversify exposures

Estimate returns from worst case scenarios

III. Maximize risk-adjusted expected returnsGeneralize 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

Range of optima with different

confidence levels

goal function

uncertainty

constraint

Risk-adjusted expected returns

Returns from probability weighted scenariosE.g. 30% stagflation, 50% soft landing, 20% hard landing

Risk from a fund = lack of confidence inOur 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 fundsFixed 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

600

1'100

1'600

2'100

2'600

J-99

J-00

J-01

J-02

J-03

J-04

J-05

J-06

Ba

se C

urr

en

cy

JPM Gl.Gov.Bond MSCI W TR GFI fund

0

10

20

30

40

-5 to

-4

-3 to

-2

-1 to

0

1 to

2

3 to

4

Return Range (%)

Nu

mb

er

of m

on

ths

Conclusions

Distribution of returns to describe market risksMax likelihood to fit Normal, NIG, Pareto distributions

Choice of the historical time span is the main issue

When there is not enough dataIdentify 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!

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