共同基金績效評估－利用風險值與左尾部分動差調整夏普指標

Evaluating the performance of mutual fund－by using VaR and LPM to adjust the Sharpe ratio

何冠陞(Kuan-Sheng Ho)

指導教授 ： 林允永

淡江大學/商學院/財務金融學系碩士在職專班/碩士(2011年)

https://doi.org/10.6846/TKU.2011.00898

摘要

共同基金儼然是現代投資人最普遍之投資工具，要如何在眾多基金商品當中選擇適合之投資標的為投資人所關注之課題，目前較常被市場採用之基金績效指標有夏普比率(Sharpe Ratio)、崔納比率(Treynor Ratio)、基金淨值報酬率等，其中又以夏普比率(Sharpe Ratio)最為常見，「承擔1單位之風險所能得到之報酬」作為投資人選擇投資標的之重要參考指標。
然夏普比率(Sharpe Ratio)仍有其所不足之處，一方面其以標準差作為評估風險之基礎，而標準差同時涵蓋上漲與下跌之風險，與一般投資人只在乎下跌風險有所差異；另一方面在報酬率非為常態分配情形下，評估出來之基金績效恐會產生偏誤。
故本研究主要採用風險值(VaR)來進行共同基金之績效評估，再利用GARCH之風險值模型來設法改進報酬分配之偏誤問題，並以左尾部分動差(LPM)來修正夏普指標，最後分析下方風險(downside risk)對共同基金績效評估所產生之影響及在不同類型之基金族群下績效之變化。

關鍵字

共同基金 ； 夏普指標 ； 一般化自我相關條件異質變異 ； 風險值 ； 左尾部分動差

並列摘要

There has been so much attention on how to choose the best investment portfolios from all kinds of funds, one of the most popular tools around the world. Some commonly used performance indices are the Sharpe ratio, the Treynor ratio, and the information ratio.

The Sharpe ratio, the most frequently used index, has some disadvantages. First, it covers both the upside and downside risks, while for investors, it is the downside risk that counts. Second, the Sharpe ratio is biased if the rate of return is not normally distributed.

In this research, hence, we evaluate the performance of mutual funds by using Value at Risk (VaR). Next, we use the generalized autoregressive conditional heteroskedasticity (GARCH) model to root out the bias and adjust the Sharpe ratio with the lower partial moment (LPM).

Finally, we analyze the downside risk influenced by the performance of mutual funds and see the variations among different groups of mutual funds.

並列關鍵字

Mutual fund ； Sharpe ratio ； GARCH ； VaR ； LPM

參考文獻

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Beder, T, 1995, “VaR: Seductive but dangerous.” Financial Analysts Journal 51, 12-24.

Bollerslev, T, 1986, “Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics 31, 306-327.

Campbell, R., Huisman, R., and Koedijk,K., 2001, “Optimal Portfolio Selection in a Value-at-Risk Framework.” Journal of Banking & Finance, 1789-1803.