The Mathematica Journal: Volume 9, Issue 4: Skew Densities and Ensemble Inference for Financial Economics

Skew Densities and Ensemble Inference for Financial Economics

H. D. Vinod

Financial economics includes the study of the density of 'excess returns,' having skewness, fat tails, and excess kurtosis. We illustrate it using monthly data on a mutual fund. The nonnormality of

impacts measurement of potential losses by 'value at risk' (VaR). Since finance literature has mostly ignored Azzalini's [1] skew normal (SN) density, our aim is to illustrate its implementation using Mathematica and mathStatica [2]. We use a location-scale version of the SN distribution, create its likelihood function, and use maximum likelihood (ML) to estimate its parameters. We illustrate it with data for a mutual fund and report the ML estimates, quantiles of

, and the VaR.

Notebook

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1. Introduction

2. The Empirical Data

3. Model: A Generalised Azzalini Skew Normal Distribution

4. Maximum Likelihood Estimation

5. Value at Risk

6. Conclusion

References

About the Author

Professor H. D. Vinod is a professor of economics and director of the Institute for Ethics and Economic Policy at Fordham University in New York. He received his Ph.D. in economics from Harvard University, has worked at Bell Laboratories for many years, and has been an expert witness in major antitrust trials. He has published over a hundred articles in top journals in econometrics and statistics, including Econometrica, Journal of Econometrics, Journal of the American Statistical Association, Management Science, American Economic Review, Review of Economics and Statistics, International Economic Review, Journal of Economic Literature, Journal of Business, and Journal of Advertising Research. He has edited special issues and refereed many journals. In 1996, he was named a fellow of the Journal of Econometrics. Maharashtra Foundation honored him for outstanding social service in 1998. Vinod coauthored a 1981 research monograph on regression methods and a 2005 Wiley monograph, "Preparing for the worst: Incorporating downside risk in stock market investing." He co-edited volume 11 of the Handbook of Statistics with C. R. Rao, the famous statistician. Vinod manages a worldwide anticorruption project described at www.fordham.edu/economics/vinod.

H. D. Vinod
Professor
Economics Department
Fordham University
Bronx, New York 10458
Vinod@fordham.edu