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Alternative Investments and Risk Measurement

This article explores the benefits and disadvantages of alternative investments, such as hedge funds, commodities, and real estate. It discusses the limitations of traditional risk measurement tools and proposes a model that incorporates skewness and kurtosis to accurately assess portfolio risk. The model utilizes the Normal Inverse Gaussian distribution and Student copulas to model the returns and dependence structure between the traditional and alternative portfolios. Monte Carlo simulation is used to compute Value at Risk and Expected Shortfall. The findings suggest that a substantial allocation to alternative investments can optimize risk and return.

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Alternative Investments and Risk Measurement

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  1. Alternative Investments and Risk Measurement Paul de Beus AFIR2003 colloquium, Sep. 18th. 2003

  2. Contents • introduction • the model • application • conclusions

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

  4. skewness kurtosis Jarque-Bera statistic reject normality* Non-normality equity -0.62 0.67 8.19 yes bonds 0.41 0.67 4.61 no hedge funds -0.55 2.81 37.54 yes commodities 0.38 0.44 3.15 no high yield -0.76 3.35 55.88 yes convertibles 0.05 0.05 0.05 no real estate -0.50 0.70 6.11 yes em. markets -2.04 9.27 422.85 yes Monthly data, period: January 1994 - March 2002 * 95% confidence

  5. 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

  6. 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.

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. Application • traditional portfolio: 50% equity, 50% bonds • alternative portfolio: 100% hedge funds Period: January 1990 - March 2002

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

  15. Optimal variance

  16. Optimal Value at Risk

  17. Optimal Expected Shortfall

  18. 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

  19. Contacts Paul de Beus Paul.de.Beus@nl.ey.com Marc Bressers Marc.Bressers@nl.ey.com Tony de Graaf Tony.de.Graaf@nl.ey.com Ernst & Young Actuaries Asset Risk Management Utrecht The Netherlands Actuarissen@nl.ey.com

  20. Questions?

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