도달실패확률의 커널 확률 추정법을 이용한 2단계 포트폴리오 최적화 문제

A popular portfolio optimization method has been based on mean-variance optimization or expected utility functions during the past decades. This paper studies an alternative and competing method based on shortfall probability, that is, the chance of realizing a return that is equal to or less than a target return value. The recent research on the shortfall-based method used simple nonparametric density estimation with Silverman’s rule-of-thumb. This simple method assumes that an unknown data distribution to estimate belongs to the family of Gaussian distributions. However, because it is well-known that financial assets never follow Gaussian distributions, the rule-of-thumb method is not as effective in terms of density estimation. Therefore, in order to sidestep the assumption, this paper proposes a modified two-stage portfolio optimization method, which shows similar or better performance with two experiments about toy data from three non-Gaussian distributions as well as empirical data from stocks in Korea Exchange than the simple estimation method and the two optimizations method with Sharpe Ratio and Stutzer’s PPI (Portfolio Performance Index).