Intelligent Hedge Fund Investing
Successfully Avoiding Pitfalls through Better Risk Evaluation
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CHAPTER 10

INTRODUCTION

BIBLIOGRAPHY

ERRATA AND OTHER MATERIAL

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ALTERNATIVE APPROACHES TO ESTIMATING VAR FOR HEDGE FUND PORTFOLIOS
Turan G. Bali and Suleyman Gokcan

INTRODUCTION

Non-Normally distributed returns are the norm in financial return series. The most widely documented departure from Normality is too many large returns, both positive and negative (and high autocorrelation in large returns). This non-Normal reality is a problem for traditional parametric risk measurement, which relies on the assumption of Normality.

If returns were Normally distributed, then a 2.5 daily standard deviation loss event would happen about one day a year. In practice, a rule of thumb is to expect a 4 standard deviation loss event about once a year.

Bali and Gokcan put forward an alternative parametric approach to VaR estimation that is robust to these types of deviations from the Normal probability distribution.

In the usual parametric VaR calculation, the standard deviation of portfolio returns is multiplied by a constant, e.g., 2.33, which is based on the known quantiles of the Normal distribution. In their alternative method, this multiplicative constant is modified to incorporate information about the skewness and excess kurtosis in the return distribution.

Bali and Gokcan examine the returns to 17 hedge fund strategy indexes, all of which exhibit statistically significant departures from Normality, including the negative skewness we have come to expect in hedge fund returns.

They show that their alternative to the standard parametric VaR results in a very close correspondence to the empirically observed tail percentiles they examine, much closer than the usual parametric approach, which significantly underestimates the empirical tail percentile. Their estimates are also better than when they estimate VaR using an extreme value approach, a result they argue that is further enhanced by the greater ease of applying their approach.

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BIBLIOGRAPHY

  1. Agarwal, V., and N. Naik, 2000, “Performance Evaluation of Hedge Funds with Option Based and Buy-and-Hold Strategies.” Review of Financial Studies, 17(1), pp. 63-98.
    http://www.GloriaMundi.org/picsresources/rb-vann.pdf
  2. Amin G., and Kat H., 2003. "Hedge Fund Performance 1990-2000: Do The “Money Machines” Really Add Value?" Journal of Financial and Quantitative Analysis 38, pp. 251-274.
    http://www.GloriaMundi.org/picsresources/rb-gahk.pdf
  3. Andersen, T. G., T. Bollerslev, and S. Lange, 1999. “Forecasting Financial Market Volatility: Sampling Frequency vis-à-vis Forecast Horizon,” Journal of Empirical Finance 6(5), 457-477.
  4. Asness, C. S., R. J. Krail, and J. M. Liew, 2001. “Do Hedge Funds Hedge?” Journal of Portfolio Management, Fall, pp. 6-19.
  5. Bali, T. G., 2003, “An Extreme Value Approach to Estimating Volatility and Value at Risk,” Journal of Business, 76(1), pp. 83-108.
    http://www.GloriaMundi.org/picsresources/rb-tb.pdf
  6. Castillo, E., 1988, Extreme Value Theory in Engineering, (San Diego: Academic Press).
    view at Amazon.com
  7. Cornish, E.A., and Fisher, R.A., 1937, “Moments and Cumulants in the Specification of Distributions.” Review of the International Statistical Institute, pp. 307-320.
  8. De Souza C., and Gokcan S., 2004, "Allocation Methodologies and Customizing Hedge Fund Multi-Manager Multi-Strategy Products." Journal of Alternative Investments, 6(4), pp. 7-21.
  9. Dickey, D., and W. A. Fuller, 1979, “Distribution of the Estimates for Autoregressive Time Series with a Unit Root,” Journal of the American Statistical Association, 74, pp. 427-431.
  10. Dowd, K., 1998, Beyond Value at Risk: The New Science of Risk Management (John Wiley & Sons).
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  11. Duffie, D., and J. Pan, 1997, “An Overview of Value at Risk.” Journal of Derivatives (Spring), pp. 7-49.
  12. Embrechts, P., C. Kluppelberg, and T. Mikosch, 1997, Modeling Extremal Events (Berlin: Springer-Verlag).
    view at Amazon.com
  13. Fung, W., and D. A. Hsieh, 1999, "Is Mean-Variance Analysis Applicable to Hedge Funds," Economics Letters 62, 53-58.
    http://www.GloriaMundi.org/picsresources/rb-fh.pdf
  14. Geman, H., and Kharoubi, C., 2003, “Hedge Funds Revisited: Distributional Characteristics, Dependence Structure and Diversification,” Journal of Risk, 5(4).
  15. Gourieroux, C., and J. Jasiak, 1999, “Truncated Local Likelihood and Nonparametric Tail Analysis,” DP 99, CREST.
  16. Gourieroux, C., Laurent, J. P., and O. Scaillet, 2000, “Sensitivity Analysis of Values at Risk,” Journal of Empirical Finance 7, pp. 225-245.
    http://www.GloriaMundi.org/picsresources/rb-gour.pdf
  17. Gumbell, E.J., 1958, Statistics of Extremes (New York: Columbia University Press).
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  18. Gupta, A., and B. Liang, 2001, “Do Hedge Funds Have Enough Capital? A Value at Risk Approach,” Working Paper, Case Reserve Western University.
    http://www.GloriaMundi.org/picsresources/rb-gbl.pdf
  19. Harrel, F., and C. Davis, 1982, “A New Distribution Free Quantile Estimation,” Biometrica 69, pp. 635-640.
  20. Hull, J, and A. White, 1998, “Value at Risk When Daily Changes in Market Variables Are Not Normally Distributed.” Journal of Derivatives, 5(3), pp. 9-19.
    http://www.GloriaMundi.org/picsresources/rb-hw.pdf
  21. Jorion, P., 1996, “Risk2: Measuring the Risk in Value at Risk,” Financial Analysts Journal, 52, pp. 47-56.
  22. Jorion, P., 2000, “Risk Management Lessons From Long Term Capital Management,” European Financial Management 6, pp. 277-300.
    http://www.GloriaMundi.org/picsresources/pjltm.pdf
  23. Jorion, P., 2001, Value-at-Risk: The New Benchmark for Controlling Market Risk (Chicago: McGraw-Hill).
  24. Leadbetter, M.R., G., Lindgren, and H.Rootzen, 1983, Extremes and Related Properties of Random Sequences and Processes (New York: Springer-Verlag).
  25. Longin, F. M., 2000, “From Value at Risk to Stress Testing: The Extreme Value Approach,” Journal of Banking and Finance 24(7), pp. 1097-1130.
  26. McNeil, A. J., and R. Frey, 2000, “Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach.” Journal of Empirical Finance, 7, pp. 271-300.
  27. Pickands, J., 1975, “Statistical Inference Using Extreme Order Statistics.” Annals of Statistics 3, pp. 119-131.
  28. Venkataraman, S., 1997, “Value at Risk for a Mixture of Normal Distributions: The Use of Quasi-Bayesian Estimation Techniques.” Economic Perspectives, Federal Reserve Bank of Chicago, (March/April), pp. 2-13.
    http://www.GloriaMundi.org/picsresources/rb-subu.pdf

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ERRATA AND OTHER MATERIAL

  1. Other research by Turan G. Bali:
    SSRN website
  2. Homepage of Turan G. Bali:
    http://faculty.baruch.cuny.edu/tbali/

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Introduction

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Hardcover: 470 pages
ISBN: 19044339220

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