Study of the dynamic mean-variance portfolio optimization with regard to bankruptcy

Abstract

The mean-variance formulation by Markowitz in the 1950s paved a foundation for portfolio selection analysis in a single period. This was subsequently extended to multi-period portfolio selection by Li and Ng [4] and multi-period portfolio selection with inter-temporal constraints by Costa and Nabholz [5]. The solutions of both papers were implemented and backtested on the Singapore and US stock market. It was found that incredulous gains and exceptional losses were just as likely with both models. The empirical analysis further revealed that bankruptcy is a prevalent problem with the optimal portfolio policy of [7]. This problem was ameliorated by the addition of inter-temporal restrictions [8] but the improvements were marginal and only restricted to the Singapore market. The empirical studies also provided strong statistical evidence for an inverse relationship between the expected terminal wealth and the observed terminal wealth for certain portfolios. This is contrary to the intended purpose of the models as one would expect the observed terminal wealth to increase with the expected terminal wealth. © 2010 IEEE.