風險調整後共同基金績效評估

Risk-Adjusted performance of mutual fund

陳俞臻(Yu-Chen Chen)

指導教授 ： 林允永

淡江大學/商學院/財務金融學系碩士班/碩士(2005年)

https://doi.org/10.6846/TKU.2005.00558

摘要

共同基金已普遍成為一般投資大眾重要的理財工具之一，那麼該如何挑選出適合自身所能承受之風險且報酬率高的共同基金，便需借重各種評估指標之衡量。傳統衡量共同基金的績效指標中，最常使用的是夏普指標(Sharpe Ratio)，但是夏普指標是建構在報酬呈常態分配的假設前題下，然而並非所有的資產報酬皆服從常態分配，因此，所衡量出的績效便會產生偏誤。再者，夏普指標以傳統標準差來衡量風險，描述的只是波動風險的程度而非投資人所關心的下跌風險，故無法真正貼近實際風險的狀況。

本研究為了改善以標準差衡量風險及受限常態分配的假設，因此利用風險值(Value at Risk)與左尾部分動差(Lower Partial Moment)來補抓下方風險(downside risk)的現象，爾後針對傳統的績效評估指標進行修正，再分析傳統績效指標與修正後的績效指標間所評估的差異。最後更進一步說明基金長短期績效的變化與績效指標的穩定性。實證結果發現藉由下方風險修正後的基金績效皆與傳統夏普指標有著顯著性的差異，而在兩項修正指標中則以LPM修正後的績效排序變異程度較小，究其原因乃是LPM考量了投資人的風險趨避程度與資產報酬的偏度，而建立出一套更為完善的衡量機制。

關鍵字

共同基金 ； 夏普比率 ； 變異數-共變異數法 ； 指數加權移動平均法 ； 左尾部分動差

並列摘要

Mutual fund is becoming one of the important tools for managing money generally. How to select a suitable one that conforms to investor’s requirement, need to rely on the measurement of various kinds of indexes. In the traditional performance index of mutual fund, most often the ones used is Sharpe Ratio, but it assume that all assets are under normal distribution, however not all ones are. So the Sharpe Ratio may mislead the performance measure of mutual fund. Moreover, the standard deviation of mutual fund return that describes the rise and fall of return fluctuation is introduced to measure risk, but investors care about the downside risk more, so it is unable to disclosure to the state of the real risk.

First, in order to improve with the risk measurement with standard deviation and the normality assumption of stock return, we apply VaR (Value at Risk) and LPM (Lower Partial Moment) to catch the downside risk. Second, we revise the tradition performance index, analyzing the differences among Sharpe Ratio and performance index after revising. Finally, we further state the change of mutual fund’s performance with time and the stability of the performance index.

The empirical evidence shows that the performance of mutual fund after revising by the downside risk with apparent difference of the Sharpe ratio. Among the revising performance indexs, the performance after revising with LPM makes a variation smaller in an order, tracing to its cause that LPM consider the degree of risk that investor bears, so it set up a set of more perfect measurement mechanisms.

並列關鍵字

Mutual Fund ； Sharpe Ratio ； Delta-Normal Method ； EWMA ； LPM

參考文獻

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