Alternative Investments and Risk Measurement

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Alternative Investments and Risk Measurement

• Paul de Beus
• AFIR2003 colloquium, Sep. 18th. 2003

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Contents

• introduction
• the model
• application
• conclusions

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Alternative Investments

• The benefits
• lower risk
• higher return
• The disadvantages
• risks that are not captured by standard deviation
  (outliers, event risk etc)

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Non-normality
Monthly data, period January 1994 - March
2002 95 confidence
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Implications of non-normality

• portfolio optimization tools based on normally
  distributed asset returns (Markowitz) no longer
  give valid outcomes
• risk measurement tools may underestimate the true
  risk-characteristics of a portfolio

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The model

• Two portfolios
• traditional portfolio, consisting of equity and
  bonds
• alternative portfolio, consisting of
  alternative investments
• Given the proportions of the traditional and
  alternative portfolios in the resulting master
  portfolio, our model must be able to compute the
  financial risks of this master portfolio.

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Assumptions for our model

• the returns on the traditional portfolio are
  normally distributed
• the distribution of the returns on the
  alternative portfolio are skewed and fat tailed
• The returns on the two portfolios are dependent

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Modeling the alternative returns

• We model the distribution of the returns on the
  alternative portfolio with a Normal Inverse
  Gaussian (NIG) distribution
• Benefits
• adjustable mean, standard deviation, skewness
  and kurtosis
• Random numbers can easily be generated

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The NIG distribution
skewness -1.6 kurtosis 6.9
Example of a Normal Inverse Gaussian distribution
and a Normal distribution with equal mean and
standard deviation
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Modeling the dependence structure

• We model the dependence structure between the two
  portfolios using a Student copulas, which has
  been derived form the multivariate Student
  distribution
• Benefits of the Student copula
• the dependence structure can be modeled
  independent from the modeling of the asset
  returns
• many different dependence structures are possible
  (from normal to extreme dependence by adjusting
  the degrees of freedom)
• well suited for simulation

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Risk measures

• To measure the risks associated with including
  alternatives in portfolio, our model will
  compute
• Value at Risk(x) with x confidence, the
  return on the portfolio will fall above the Value
  at Risk
• Expected Shortfall(x)the average of the
  returns below the Value at Risk (x)
• Together they give insight into the risk of large
  negative returns

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Monte Carlo Simulation

• generate an alternative portfolio return from the
  NIG distribution
• using the bivariate Student distribution and a
  correlation estimate, generate a traditional
  portfolio return
• repeat the steps 10.000 times and compute the
  Value at Risk and Expected Shortfall

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Application

• traditional portfolio 50 equity, 50 bonds
• alternative portfolio 100 hedge funds

Period January 1990 - March 2002
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Computation

• Computation of Value at Risk and Expected
  Shortfall
• Method 1, our model
• Method 2, bivariate normal distribution
• Objective minimize the risks

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Optimal variance
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Optimal Value at Risk
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Optimal Expected Shortfall
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Conclusions

• returns on many alternative investments are
  skewed and have fat tails
• using traditional risk measuring tools based on
  the normal distribution, risk will be
  underestimated
• based on mean-variance optimization, an extremely
  large allocation to alternatives such as hedge
  funds is optimal
• using Value at Risk or Expected Shortfall, taking
  skewness and kurtosis into account, the optimal
  allocation to hedge funds is much lower but still
  substantial

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Contacts

• Paul de Beus
• Paul.de.Beus_at_nl.ey.com
• Marc Bressers
• Marc.Bressers_at_nl.ey.com
• Tony de Graaf
• Tony.de.Graaf_at_nl.ey.com
• Ernst Young Actuaries
• Asset Risk Management
• Utrecht The Netherlands
• Actuarissen_at_nl.ey.com

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Questions?