This paper applies Talpaz, Harpaz, and Penson's (THP) (Talpaz, H., A. Harpaz, J. B. Penson, Jr. 1983. Risk and spectral instability in portfolio analysis. Eur. J. Oper. Res. 14 262--269.) mean-variance-instability portfolio selection model to eight selected Taiwan stocks during 1980--89 to demonstrate how instability preference affects the traditional mean-variance frontier. In contrast to THP's finding, the empirical results show that Taiwan's high-frequency stocks have high, not low, variance. This indicates that Taiwan investors, unlike U.S. investors, prefer to speculate in high-variance stocks. The empirical results also show that short selling may increase the risk of the portfolio when the investor is instability preferred.