投資組合選擇-考慮偏態(Skewness)

Abstract

本篇研究發現，在民國八十年七月至民國八十六年六月這段期間，台 灣股票市場的報酬呈現非常態分配。 當偏態存在時，投資組合選 擇就是競爭和衝突目標之間的取捨，也就是要最大化投資組合的預期報酬 和偏態，且對規避風險的投資者而言要最小化投資組合的風險。 利用多項式目標規劃來決定台灣八種分類股票指數投資組合成分的選擇； 在投資組合選擇中應用多項式目標規劃的特色是：1. 存在最佳的解，2. 併入投資者對偏態偏好的可行性，和 3. 計算上的要求，相對的簡單。 實證發現提示，併入偏態到投資者的投資組合決策，將引起最佳投資組合 結構的改變；實證也指出投資者以預期報酬換取偏態。 如同預期 的，本篇研究發現禁止融券放空的投資組合效率前緣位於允許融券的投資 組合效率前緣的內側；因此，有允許融券放空對投資者而言將境遇更佳， 因為他們能夠達到更高的滿意水準。 This paper finds that the return of the Taiwan's stock market are not normally distributed during the July 1991-June 1997 time period. In the presence of skewness, the portfoilo selection is a trade-off competing and conflicting objectives, such as maximizing both its expected returns and skewness, and minimizing its risk for risk-aversion investors. Since it is unlikely that a portfolio can solve the multiple-objectives problem simultaneously, a portfolio selection must depend on the investor's preference among objectives. Polynominal goal programming is utilized to determine the optimal portfolio consisting of the choices of Taiwam's 8 category stock indexes. The features of applying polynomial goal programming in portfolio selection are 1. the existence of an optimal solution, 2. the flexibility of the incorporation of investor preference for skewness, and 3. the relative simplicity of computational requirements. The empirical findings suggest that the incorporation of skewness into an investor's portfolio decision causes a major chang in the construction of the optimal portfolio. The evidence also indicate that investors trade expected return of the portfolio for skewness. As was expected, This study finds that efficient frontiers of no-short- sales portfolio lie within the frontiers of short-sales portfolio. Thus, with short sales allowed, investors will be better off, as they are able to achive a higher level of satisfation.