Portfolio Diversification and Value At Risk Under Thick-Tailedness
We present a unified approach to value at risk analysis under heavy-tailedness using new majorization theory for linear combinations of thick-tailed random variables that we develop. Among other results, we show that the stylized fact that portfolio diversification is always preferable is reversed for extremely heavy-tailed risks or returns. The stylized facts on diversification are nevertheless robust to thick-tailedness of risks or returns as long as their distributions are not extremely long-tailed. We further demonstrate that the value at risk is a coherent measure of risk if distributions of risks are not extremely heavy-tailed. However, coherency of the value at risk is always violated under extreme thick-tailedness. Extensions of the results to the case of dependence, including convolutions of alpha-symmetric distributions and models with common shocks are provided.
|Date of creation:||01 May 2005|
|Date of revision:||01 Aug 2005|
|Contact details of provider:|| Web page: http://icf.som.yale.edu/|
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
- Dennis W. Jansen & Casper de Vries, 1988.
"On the frequency of large stock returns: putting booms and busts into perspective,"
1989-006, Federal Reserve Bank of St. Louis.
- Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
- Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
- Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
- An, Mark Yuying, 1998.
"Logconcavity versus Logconvexity: A Complete Characterization,"
Journal of Economic Theory,
Elsevier, vol. 80(2), pages 350-369, June.
- An, Mark Yuying, 1995. "Logconcavity versus Logconvexity: A Complete Characterization," Working Papers 95-03, Duke University, Department of Economics.
- Fang,H. & Norman,P., 2003.
"To bundle or not to bundle,"
18, Wisconsin Madison - Social Systems.
- Fang, Hanming & Norman, Peter, 2005. "To Bundle or Not to Bundle," Microeconomics.ca working papers norman-05-06-10-08-19-02, Vancouver School of Economics, revised 10 Jun 2005.
- Hanming Fang & Peter Norman, 2003. "To Bundle or Not to Bundle," Cowles Foundation Discussion Papers 1440, Cowles Foundation for Research in Economics, Yale University.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
- Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value-at-Risk with Heavy-Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269.
- Gneiting, Tilmann, 1998. "On[alpha]-Symmetric Multivariate Characteristic Functions," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 131-147, February.
- Loretan, M. & Phillips, P.C.B., 1992.
"Testing the Covariance Stationarity of Heavy-Tailed Time Series: An Overview of the Theory with Applications to Several Financial Datasets,"
9208, Wisconsin Madison - Social Systems.
- Loretan, Mico & Phillips, Peter C. B., 1994. "Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets," Journal of Empirical Finance, Elsevier, vol. 1(2), pages 211-248, January.
- Donald W.K. Andrews, 2004.
"Cross-section Regression with Common Shocks,"
Yale School of Management Working Papers
ysm401, Yale School of Management.
- Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
- Eaton, Morris L., 1988. "Concentration inequalities for Gauss-Markov estimators," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 119-138, April.
- McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
- Jovanovic, Boyan & Rob, Rafael, 1985.
"Demand-Driven Innovation and Spatial Competition Over Time,"
85-34, C.V. Starr Center for Applied Economics, New York University.
- Boyan Jovanovic & Rafael Rob, 1987. "Demand-Driven Innovation and Spatial Competition Over Time," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 63-72.
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-80, April.
- Jensen, D. R., 1997. "Peakedness of linear forms in ensembles and mixtures," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 277-282, October.
When requesting a correction, please mention this item's handle: RePEc:ysm:somwrk:amz2386. See general information about how to correct material in RePEc.
If references are entirely missing, you can add them using this form.