Extreme returns in a shortfall risk framework

One of the most important aspects in asset allocation problems is the assumed probability distribution of asset returns. Financial managers generally suppose normal distribution, even if extreme realizations usually have an higher frequency than results in the case of normally distributed returns. Using Monte Carlo simulation, we propose and solve an asset allocation problem with shortfall constraint, evaluating the exact risk-level for managers in the case of misspecification of tails behaviour. In particular, in the optimisation problem, we assume that returns are generated by a multivariate Student-t, when in reality returns come from a multivariate distribution where each marginal is a Student-t with different degrees of freedom; this method permits us to value the effective risk for managers. In the case analysed, it is also interesting to observe that a multivariate density with different marginal distributions produces a shortfall probability and a shortfall return level that can be approximated adequately by assuming a multivariate Student-t in the optimisation problem. The present approach could be an important instrument for investors who require a qualitative assessment of the reliability and sensitivity of their investment strategies when their models are potentially misspecified. * GRETA (Venice). ** GRETA (Venice) and University of Venice. ** GRETA (Venice) and University of Venice. Extreme Returns in a Shortfall Risk Framework