Financial Engineering Seminar
October 10, 2008 (Fri)
Time: 4:05 PM
Place: Weil Hall 303
Traditional portfolio selection models often optimize some criteria which are estimated with historical observations. Such an in-sample optimization approach, however, faces essential difficulties in its implementation because, with a limited number of observations, the in-sample optimality does not necessarily lead to a good out-of-sample performance.
In order to improve the out-of-sample performance, we propose a new portfolio optimization approach on the basis of nonparametric upper and lower bounds of the out-of-sample loss probability. Those theoretical bounds are derived by modifying the so-called generalization theory for the nu-support vector machines (SVMs), which have been developed in the 1990s and successfully used in the context of the statistical learning. Motivated by the bounds, several fractional functions are minimized where the numerator of the ratio includes the empirical VaR or CVaR associated with adequate loss variates, while the denominator is a norm of the portfolio vector. Interestingly, this also implies that the short-sale constraint brings a theoretical underpinning to the ordinary VaR or CVaR minimization. Some computational experiments demonstrate its promising performance.