First passage times in portfolio optimization: a novel nonparametric approach

This paper introduces a portfolio optimization procedure that aims to minimize the intrahorizon (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 meanvariance 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.