全球共同基金群組風險與績效評估—以風險值修正夏普指標之應用

The Evaluation of Off-Shore Mutual Fund Risk and Performance-the Application of VaR Adjusted Sharpe Ratio

張有若(Yu-Jou Chang)

指導教授 ： 陳若暉

中原大學/商學院/企業管理研究所/碩士(2002年)

https://doi.org/10.6840/cycu200200545

摘要

共同基金已普遍成為一般投資人重要的理財工具之一，而如何挑選出適合自身風險承受且報酬率高的共同基金，需借重各種評估指標之衡量，其中以Sharpe Ratio最常為投資人所使用，但由於Sharpe Ratio建構在報酬率呈常態分配的假設上，當共同基金報酬率呈非常態分配時，衡量之績效會產生偏誤，再者由於Sharpe Ratio以傳統標準差來衡量風險，但標準差衡量到的是波動風險而非下跌風險，因此無法真正貼近實際風險。本研究利用風險值(VaR)取代標準差，並加入標竿市場的相對風險值，改善Sharpe Ratio在報酬呈非常態分配時的偏誤，提高各類指標對風險的敏感度，應用在共同基金整體績效評估中。以全球平衡型基金、債券型基金、貨幣型基金及以上三類所組成的基金群組，所做的常態分配檢定，發現並非所有基金皆呈常態分配，在多樣化投資組合群組後，其報酬會趨近於常態分配，所有共同基金皆呈現高狹峰，表示其報酬較集中，且有厚尾現象﹔因為並非所有共同基金都呈常態分配，因此其偏態狀況不一。再者以常態檢定的結果區分風險值計算方式，發現在常態分配部分以Delta-Normal法計算較佳，而在非常態分配方面則以歷史模擬法計算為佳，所計算出的風險值以回溯測試法及向前測試法驗證皆屬合理範圍。另外比較標準差及風險值，發現標準差皆小於風險值，而共同基金的投資組合項目對風險則會產生一定程度的影響，共同基金群組在風險中確實會有降低風險的效果，但亦非絕對﹔在相對風險值部份，所選擇的標竿市場會影響其相對風險的大小。以VaR取代標準差的修正後Sharpe Ratio(V1)指標與一般化Sharpe Ratio(Sp)指標在排名會有差別，但排名差別不大的原因是由於各共同基金間的報酬率差異過大，因此產生報酬主導排名順序﹔以標竿報酬率代替無風險利率之Sharpe Ratio(V2)指標績效相較於Sp及V1為佳﹔在加入相對市場風險因素計算出的Sharpe Ratio(V3)指標則會與其他績效衡量指標差異頗大，共同基金的排名變動程度不一。在投資績效預測性方面，由Spearman等級相關係數檢定發現Sp、V1及V2具有指標預測性，其中以V1之等級相關係數最高，在以風險值取代標準差後的確會增加其預測性，因此可應用在共同基金的評選，藉以預測未來績效。

關鍵字

基金群組 ； 共同基金 ； 持續性 ； 夏普比率 ； 報酬率 ； VaR ； 風險值

並列摘要

Sharpe Ratio is a well-know method to analyze the performance of mutual funds. As it is well know, the hypothesis of Sharpe Ratio is under the normal distribution of return, it will be bias when the return is non-normality. Besides, Sharpe Ratio uses the standard deviation for the risk evaluation. The standard deviation only measures the floating risks, but not the declining risk. Thus, we cannot acquire the real risk. This article proposes the Value at Risk (VaR) to replace the standard deviation and adds the benchmark of relative risk to improve the Sharpe Ratio’s bias and to enhance the sensitivity when the return is non-normality. Firstly, testing the normal distribution of return in the global balanced funds, bond funds, currency funds and fund of funds, we found that not all of the mutual funds were normal distribution. After diversified portfolio, the distribution of return tends to approach the normality. All of the mutual funds are leptokurtosis. Therefore, it represents that the returns of mutual fund are convergence and are heave-tailed relatives to normal distribution. Secondly, we use three main approaches, Historical Simulation approach, Delta Normal approach and Bootstrap, to evaluate the VaR of four kinds of mutual funds and compares with to see which one has better performance. Apparently that the result of the Delta-Normal method in the normal distribution of return is better than others, while the Historical Simulation method is adapted to the non-normality of returns. Using back testing and forward testing to verify the VaR is reasonable. Compared with the standard deviation and the VaR, we discover that standard deviation is less than VaR. The items of mutual fund portfolio will influence the risk, and the fund of funds decreases the risk indeed. The ranking is difference between traditional Sharpe Ratio (Sp) and adjusted Sharpe Ratio (V1), but the reason that makes this raking indistinct is because the return of mutual funds makes great difference. Therefore, the return dominants the ranking. The performance of Sharpe Ratio (V2, using the benchmark return rate to replace the risk-free rate of interest) is better than Sp and V1. Besides, the Sharpe (V3, using the Benchmark-Relative VaR to replace the standard deviation) is great different from other indexes and the variation of ranking is not consistent. Finally, in the forecast of indexes, the result of Spearman testing appears that the Sp, V1 and V2 have a forecasting effect, which the Classic Correlation Coefficient of V1 is higher than others. By using the VaR to replace the standard deviation will increase the feasible of forecasting, and thus it can be applied to mutual funds selection to forecast the future performance.

並列關鍵字

Normal Disrribution ； Sharpe Ratio ； Value at Risk ； Mutual Fund ； Return Rate ； VaR ； Fund of Funds

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