Portfolio Diversification and Value at Risk Under Thick-Tailedness
23 Pages Posted: 9 May 2005
Date Written: October 2004
Abstract
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.
Keywords: value at risk, coherent measures of risk, heavy-tailed risks, portfolios, riskiness, diversification, risk bonds
JEL Classification: G11
Suggested Citation: Suggested Citation
Do you have a job opening that you would like to promote on SSRN?
Recommended Papers
-
Efficient Mechanisms for Public Goods with Use Exclusions
By Peter Norman
-
An Efficiency Rationale for Bundling of Public Goods
By Hanming Fang and Peter Norman
-
By Hanming Fang and Peter Norman
-
Monopolistic Provision of Excludable Public Goods Under Private Information
-
Toward an Efficiency Rationale for the Public Provision of Private Goods
By Hanming Fang and Peter Norman
-
Optimal Provision of Multiple Excludable Public Goods
By Hanming Fang and Peter Norman
-
Optimal Provision of Multiple Excludable Public Goods
By Hanming Fang and Peter Norman
-
The Provision and Pricing of Excludable Public Goods: Ramsey-Boiteux Pricing Versus Bundling
-
A Note on Budget Balance Under Interim Participation Constraints: The Case of Independent Types
By Tilman Borgers and Peter Norman
-
Public Goods, Participation Constraints, and Democracy: A Possibility Theorem
By H. P. Gruner