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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 [email protected]
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!
DisclaimerUnited Kingdom. This document has been issued and approved for the purposes of Section 21 of the Financial Services & Markets Act 2000
(“FSMA”) by Signet Capital Management Limited (“SCML”), which is authorised and regulated by the UK's Financial Services Authority. Neither the receipt of the document by any person nor any information contained herein or supplied with it or subsequently communicated to any person is to be taken as constituting the giving of investment advice by SCML to any such person. The document has been issued in the United Kingdom solely for the information of persons authorised under the FSMA to carry on investment business and may only be issued or passed on by such persons to other authorised persons and/or to other categories of investor to whom unregulated collective investment schemes can be marketed without contravening Section 238 of the FSMA. The issue of this document in the United Kingdom to any other person may be an offence. An investment in any security described herein must only be made in conjunction with the most recent Offering Memorandum pertaining to such security and particular attention must be paid to the information contained therein. This document is confidential and provides general advice only. It is not an information memorandum nor is it an offer, solicitation or recommendation to apply for or invest in securities. The information in this document has been derived from sources believed to be accurate and reliable and its contents have been produced in good faith. Nevertheless, no representation or warranty, expressed or implied, is given by SCML as to the accuracy or completeness of the information and opinions contained herein and no responsibility or liability is accepted for the accuracy or sufficiency of any of the information or opinions. The document shall not and does not form the basis of any contract.
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