Annals of Finance

, Volume 8, Issue 1, pp 97–122

Large deviations estimation of the windfall and shortfall probabilities for optimal diversified portfolios

Research Article

DOI: 10.1007/s10436-011-0182-x

Cite this article as:
Chu, B. Ann Finance (2012) 8: 97. doi:10.1007/s10436-011-0182-x


Many investors believe that they can effectively reduce risk by, among other ways, holding large combinations of investment assets. The purpose of this paper is to develop asymptotic approximations of the windfall and shortfall probabilities for an optimal portfolio of risky assets as the number of the assets becomes sufficiently large. We start by providing some heuristics to motivate our problem, then proceed to prove general large deviations theorems. We also present specific results with an application to the multivariate normal case. Both a theoretical analysis of the method and an empirical application justify the diversification tenet of the allocation strategies that many hedge funds and pension funds tend to adopt nowadays.


Diversification Large deviations Shortfall probabilities Windfall probabilities 

JEL Classification

C60 C13 G11 

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of EconomicsCarleton UniversityOttawaCanada

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