The stability of portfolio investment in stock crashes.

The stability of portfolio investment in stock market crashes with Markowitz portfolio is investigated by the method of theoretical and empirical simulation. From numerical simulation of the mean escape time (MET), we conclude that: (i) The increasing number of stocks in Markowitz portfolio induces a maximum in the curve of MET versus the initial position; (ii) A critical value of in the behavior of MET versus the long-run variance or amplitude of volatility fluctuations maximumlly enhances the stability of portfolio investment. When takes value below the critical value, the increasing enhances the stability of portfolio investment, but restrains it when takes value above the critical value. In addition, a good agreement of both the MET and probability density functions of returns is found between real data and theoretical results. [ABSTRACT FROM AUTHOR]