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Stochastic optimization for allocation problems with shortfall risk constraints
Author(s) -
Casarin Roberto,
Billio Monica
Publication year - 2007
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.671
Subject(s) - expected shortfall , asset allocation , portfolio optimization , econometrics , multivariate statistics , marginal distribution , multivariate normal distribution , portfolio , asset (computer security) , degrees of freedom (physics and chemistry) , constraint (computer aided design) , computer science , mathematical optimization , economics , random variable , mathematics , finance , statistics , computer security , physics , geometry , quantum mechanics , machine learning
One of the crucial aspects in asset allocation problems is the assumption concerning the probability distribution of asset returns. Financial managers generally suppose normal distribution, even if extreme realizations usually have an higher frequency than in the Gaussian case. The aim of this paper is to propose a general Monte Carlo simulation approach able to solve an asset allocation problem with shortfall constraint, and to evaluate the exact portfolio risk‐level when managers assume a misspecified return behaviour. We assume that returns are generated by a multivariate skewed Student‐ t distribution where each marginal can have different degrees of freedom. The stochasticoptimization allows us to value the effective risk for managers. In the empirical application we consider a symmetric and heterogeneous case, and interestingly note that a multivariate Student‐ t with heterogeneous marginal distributions produces in the optimization problem a shortfall probability and a shortfall return level that can be adequately approximated by assuming a multivariate Student‐ t with common degrees of freedom. Thus, the proposed simulation‐based approach could be an important instrument for investors who require a qualitative assessment of the reliability and sensitivity of their investment strategies in the case their models could be potentially misspecified. Copyright © 2007 John Wiley & Sons, Ltd.