利用Riskiness衡量台灣上市股票與共同基金績效

Abstract

一般投資人以及基金經理人常使用夏普比率(Sharpe Ratio)衡量基金或股票的表現，然而夏普比率隱含著一些缺點，如未符合一階隨機優越的特性，造成衡量資產孰優孰劣時的偏誤。因此本研究使用Aumann and Serrano在2008年提出的Riskiness index取代夏普比率指標內標準差的位置，做成一個新的績效指標EPM。採用實證分析的方法對台灣境內共163檔共同基金以及台灣市值排名前20大的上市公司進行研究，觀察兩倍夏普比率的平方、常態分配下的EPM、EPM這三個指標之值的相關性，以及值的排名之相關性，以提供投資人在選擇投資標的的新基準。 結論為這三種不同的指標具有極高的相關性，不論從值的角度或是排名的角度看皆如此。因此若要衡量台灣境內共同基金與大型股的時候，純粹使用夏普比率並不會出現太多偏誤，因為這些資產雖然在JB檢定中皆不符常態分配，但是雖不中亦不遠矣，這些資產的月報酬分配仍相當接近常態分配，造成三種指標之相關性極高。因此，用夏普比率與EPM衡量資產表現結果近似。

General Investors and Fund Managers often use Sharpe Ratio to measure performance of funds and stocks; however, some pitfalls implied in Sharpe Ratio. For instance, Sharpe Ratio does not meet the feature of Stochastic Dominance (SD), which causes bias when measuring performance of assets. Therefore, this paper utilizes a new performance measure Economic Performance Measure by substituting standard deviation in Sharpe Ratio with Riskiness Index in Aumann and Serrano (2008). This paper conducts empirical research to analyze data from 163 Taiwanese mutual funds and top 20 listed companies. This paper examines the correlation of three Index: 2 times square of Sharpe Ratio, EPM when normal distribution, and EPM, in order to provide a new measurement for investors’ investment choice. The empirical results indicate that these three indices have strong correlations, no matter observing from value or rank of these three indices. Thus, little bias would occur when utilizing Sharpe Ratio to measure performance of Taiwanese mutual funds and large companies. Although JB normality test shows that almost all the assets are not normally distributed, the monthly return distribution of these assets is close to normal distribution, so the correlation of these three indices are extremely strong. Therefore, the result between using Sharpe Ratio and EPM is similar.