利用高階矩的基金績效指標在中國大陸的應用

Applications of Fund Performance Evaluation Indicators Using Higher Moments in China

徐梓凱(Zi-Kai Xu)

指導教授 ： 石百達

國立臺灣大學/管理學院/財務金融學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201900032

摘要

自 20 世紀 90 年代以來,大陸的基金業迅速發展。根據美國投資公司協會的資料,大陸的基金總規模在 2018 年一季度已經超越了日本,位列全球第 8 位。如今,基金已經是居民投資的一個重要渠道。雖然基金的整體規模發展很快,但業界在基金評價方面卻仍以傳統的績效評價指標為主,如夏普指數。這些傳統指標在評價基金績效時,主要使用的是收益的一階矩和二階矩。這樣就導致了一個問題,那就是沒有充分考慮極端情況的影響,對基金績效的評價會有失偏頗。在黑天鵝事件頻發的現在,投資者在評估基金時更需要將收益的高階矩納入考慮當中。
本文研究了 Aumann and Serrano (2008)及 Foster and Hart (2009)提出的兩個利用收益高階矩的績效指標在大陸基金市場的應用。首先,本文通過 SMB 組合與模擬組合的對比,闡述了收益的高階矩在績效評價中的重要性。接著,本文驗證了這兩個指標在基金挑選上的能力。一方面,本文分別根據指標來將所有基金分成五檔,通過檢驗這些組合的收益在樣本外的單調性來驗證這兩個指標挑選基金的能力。結果表明,這兩個指標具有不錯的挑選基金的效果。另一方面,本文比較了根據這兩個指標和夏普指數挑選出來的基金組合的收益。結果表明,根據這兩個指標挑選出來的基金組合均優於根據夏普指數挑選出來的基金組合。最後,本文將這兩個指標加入四因子組合,驗證了其對挑選出 alpha 的幫助。

關鍵字

基金 ； 績效評價階矩 ； 黑天鵝事件 ； 大陸市場

並列摘要

Since the 1990s, mainland Chinese fund industry has developed rapidly. According to the Investment Company Institute, the total size of mainland Chinese funds has surpassed Japan in the first quarter of 2018, ranking eighth in the world. Today, fund is already an important channel for residents to invest. Although the overall scale of the fund has developed rapidly, investors still focuses on traditional performance evaluation indicators such as the Sharp Index. Traditional indicators mainly use the first moment and the second moment. This has led to the problem that the impact of extreme conditions is not fully considered and the evaluation of fund performance will be biased. Nowadays, the black swan incident is frequent and investors need to take into account the higher distribution moments of return when evaluating funds.
This paper examines the application of two performance indicators using the higher distribution moments of return proposed by Aumann and Serrano (2008) and Foster and Hart (2009) in the mainland China. First of all, this paper illustrates the importance of higher distribution moments in performance evaluation through the comparison of SMB portfolio and simulation portfolio. Next, the paper verifies the ability of these two indicators to select funds. On the one hand, this paper divides all funds into five groups according to the indicators, and verifies the ability of these two indicators to select funds by testing the monotony of the return of these portfolios out of sample. The results show that these two indicators have a good ability of selecting funds. On the other hand, this paper compares the returns of the fund portfolios selected based on these two indicators and the Sharp Index. The results show that the fund portfolios selected based on these two indicators is superior to the fund portfolio selected according to the Sharp Index. Finally, this paper adds these two indicators to the four-factor model to verify its help in capturing alpha.

並列關鍵字

Fund ； Performance evaluation ； High distribution moment ； Black swan incident ； Mainland China market

參考文獻

Aumann, R., Serrano, R., 2008. An economic index of riskiness. Journal of Political Economy 116, 810–836.

Avramov, D., Wermers, R., 2006. Investing in mutual funds when returns are predictable.Journal of Financial Economics 81, 339-377.

Brinson, G.P., Fachler, N., 1985. Measuring non-US equity portfolio performance. Journal of Portfolio Management 11, 73-76.

Brinson, G.P., Hood, L.R., Beebower, G.L., 1986. Determinants of portfolio performance. Financial Analysts Journal 42, 39-44.

Carhart, M., 1997. On persistence in mutual fund performance. Journal of Finance 52,57–82.