An Empirical Study of a New Risk Index Riskiness"" on Mutual Fund in Taiwan""

本研究使用Aumann and Serrano (2008)提出一個新的風險衡量指標Riskiness，該指標具有許多良好的經濟性質，包括對偶性、正齊次性、一階隨機優越及二階隨機優越。 本論文將這些良好的性質運用在境內基金績效之衡量，希望提供投資人更有效的標的選擇依據。傳統上較常使用的基金衡量指標如Sharpe ratio在計算上僅考慮平均數及標準差，此新的風險衡量指標將Sharpe ratio中的標準差以Riskiness替代，將投資人較關心的偏態及峰態左尾的極端風險考量進去。 本篇選取五個境內基金的類別，其中三類為股票型基金、兩類為平衡型基金，將其Sharpe ratio及新風險指標計算出來的結果排名比較。研究結果顯示股票型基金兩者排名結果差異性相較平衡型基金大，而平衡型基金因為極端風險較低，兩者的排名結果幾乎相同，顯示Riskiness使用在風險較高的標的上效果較為顯著。This research employs a new risk index “Riskiness” proposed by Aumann and Serrano (2008). “Riskiness” contains a lot of good characters including duality, positive homogeneity, first-order stochastic dominance and second-order stochastic dominance. In this paper, we apply “Riskiness” on the performance measure of mutual fund in Taiwan. Currently, people usually use Sharpe ratio as a performance measure index which only considers mean and variance. However, the new performance measure index accounts for not only mean and variance but also higher moments of the return distribution, skewness and kurtosis. It can measure left-tailed extreme risk which most investors care about. We choose five categories of mutual fund in Taiwan, three of them are equity fund, the other two are balanced fund. By ranking and comparing the results of Sharpe ratio and the new index in each category, we can find out which one is better to measure performance. Research results illustrate that the ranking of Sharpe ratio and the new index on equity fund is more different from that on balanced fund. Moreover, the ranking of both indexes are almost identical on balanced fund due to low extreme risk. It is more evident to apply “Riskiness” on high-risk assets