以錯誤發現率控制法評估共同基金績效

Evaluating Mutual Fund Performance with False Discovery Rate Control

林汶郁(Wen-Yu Lin)

指導教授 ： 管中閔

國立臺灣大學/管理學院/財務金融學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202101144

摘要

實務與學術上，檢定共同基金績效是否較大盤更為優異是相當重要的議題。對多檔基金同時進行多重假設檢定，會面臨總體型一錯誤率膨脹的問題，藉由控制錯誤發現率 (False Discovery Rate, FDR) 則可避免此問題。本研究檢定共同基金績效，探究控制錯誤發現率在辨別真實優異基金的表現。研究結果顯示，控制 FDR 選出的優異基金在樣本外區間依然優異的比例，較未控制 FDR 更高，意味該方法有助於篩選出真正優異的基金。其次，以控制 FDR 選出的優異基金形成的資產組合在樣本外區間的績效，優於未控制 FDR 組成的資產組合，顯示該方法能建構績效更優異的基金資產組合。所以採用 Benjamini \ Hocberg (1995) 控制 FDR 的方法，較容易選出實務上具有優異表現的基金。

關鍵字

因子異常報酬 ； 全族錯誤率 ； 多重假設檢定 ； 拔靴法 ； 資產組合 ； 錯誤拒絕率

並列摘要

It is important to evaluate if there are funds outperforming the market. To select outstanding funds, multiple hypothesis tests must be performed for scientific inference. However, the overall Type I error rate would increase under this circumstance. This article explores the methods from Benjamini \ Hocberg (1995) which controls False Discovery Rate (FDR) and Bonferroni procedure which controls Family-wise Error Rate (FWER) to alleviate the problem. The result shows that the performance persistence of outstanding funds selected by controlling FDR is better than that of funds selected without controlling FDR. In addition, the out-of-sample performance of the portfolio formed by the funds selected by controlling FDR is usually better. The fact that the FDR controlling method selects more outstanding funds than the Bonferroni procedure does indicates the FDR controlling method is capable of selecting truly outstanding funds and hence practically useful. The FDR should be properly controlled while study fund performance.

並列關鍵字

Bonferroni procedure ； bootstrap ； FDR ； FWER ； multiple hypothesis test ； Type I error

參考文獻

一、外文文獻

Barras, L., O. Scaillet, R. Wermers (2010). False discoveries in mutual fund performance: Measuring luck in estimated alphas. Journal of Finance, 65(1), 179-216.

Benjamini, Y., Y. Hochberg (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society: Series B (Methodological), 57(1), 289-300.

Carhart, M. M. (1997). On persistence in mutual fund performance. Journal of Finance, 52(1), 57-82.

Cuthbertson, K., D. Nitzsche (2013). Performance, stock selection and market timing of the German equity mutual fund industry. Journal of Empirical Finance, 21, 86-101.