Risk management for hedge funds tackling rare events with an incomplete history
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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.

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

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Risk management for hedge funds tackling rare events with an incomplete history

Risk Management for Hedge FundsTackling Rare Events with an Incomplete History

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

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

Uncertain returns from markets

Example: NYBOT coffee futures 1994 -2007

Markowitz’N90: risk  volatility =   (ri -m)2

Engle’N03: arbitrage free GARCH average

… but frost only happens during the winter!

frost in Brazil


Maximum likelyhood historical fit

Maximum likelyhood historical fit

with Normal-/Inverse Gaussian distributions

normal

Normal

log

NIG

zoom

rare

stress

Adequate description

of normal-, stress- and rare events?


The perception of risk evolves

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

1

1-a

Modern tools for risk management

prob weigthed returns

  • Value at risk VaRa

    (not subadditive)

  • Expected shortfall

    (subadditive)

probabitily 1-a of

losses > VaRa

1

ES=

 VaRu du

a

returns

m

-s

-VaRa

  • Simulation

    (historical 1-10 years, Monte-Carlo)

  • Extreme Value Theory to model rare events

    (Generalized Pareto distribution is generic, Embrechts)


Example trading coffee derivatives

Example: trading coffee derivatives

Daily risk budgeting

Worst case if DS=+15%

4% loss (no risk of frost in Apr)


And when there is not enough data

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

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

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

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

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

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


Conclusions

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

Disclaimer


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