First passage times in portfolio optimization: A novel nonparametric approach

Abstract

This paper introduces a portfolio optimization procedure that aims to minimize the intra-horizon (IH) risk subject to a minimum expected time to achieve a target cumulative return. To estimate the first passage probabilities and the expected time a novel nonparametric method and a new Markov chain order determination approach are developed. The optimization framework proposed allows us to include novel path-dependent measures of risk and return in the asset allocation problem. An empirical application to S&P 100 companies, a risk-free asset and stock indices is provided. Our empirical results suggest that the proposed framework exhibits more consistency between in-sample and out-of-sample performance than the mean-variance model and an alternative optimization problem that minimizes the MaxVaR measure of Boudoukh et al. (2004). Overall, the portfolio optimization approach we introduce results in higher out-of-sample annualized returns for relatively low levels of IH risk.