以Gruber四因子模型與修正後二因子模型評估共同基金績效及其持續性之研究

Abstract

市場並非隨時處於有效率的狀態，有些投資組合表現會較其他的投資組合來的好，因此如果要將資金投資於共同基金必須設計一些方法來衡量評估投資組合的績效，以判斷不同基金或是經理人的表現。 Fama和French(1996)提出以公司規模、淨值市價比及市場風險溢酬此三因子可以解釋大部分的平均報酬，因此提出了三因子模型。Gruber (1996, 2001)發表四因子模型，提出加入債券殖利率風險溢酬因子，認為此四因子模型為一良好評估共同基金績效之模型。因此本研究運用Gruber的四因子模型，探討台灣開放式股票型基金之報酬率與市場風險溢酬、淨值市價比、公司規模及債券殖利率之間的關係。 以台灣46支開放型共同基金為研究對象，探討期間為民國八十五年十月至九十年十一月，結果顯示，不論採用平均報酬率或是基金個別報酬率分析，規模溢酬因子與公債溢酬因子均不顯著。 若修正模型為以市場溢酬及淨值市價比溢酬為二因子，發現可解釋的變異的能力較四因子模型好，且此市場溢酬為顯著大於零，淨值市價比溢酬為顯著小於零，表示經理人，較多投資於市值高而淨值低的股票。對於基金平均報酬率或是個別基金而言，不管由四因子模型或是調整後的二因子模型，計算出之超額報酬均大多為負值，表示並沒有超額報酬。 在衡量基金的持續性方面，採用投資組合建構法，在衡量期為季時，具有顯著的持續性。衡量期為半年時，具有持續性，但不顯著。衡量期為一年時並沒有持續性現象。採用Spearman等級相關性檢定，其等級亦沒有持續性。因為Spearman等級相關檢定較看不出短期之持續性效果。因此基金短期間具有持續性現象，但長期間並不具有持續性現象。

Market is not always efficient. Some mutual funds are superior to the others. We have to propose some methods to evaluate mutual fund performance. Fama and French (1996) proposed that market factor, size factor and book-to-market factor—these three factors are the keys that affect the returns of mutual funds. However, Gruber (1996, 2001) considered that the portfolios of mutual funds include stocks and bonds, so he proposes the four-factor model that includes the fourth factor, bond index. We employ Gruber’s four-factor model to evaluate the performance of mutual fund in Taiwan. The samples are the financial data of 46 mutual funds during Oct, 1996 to Nov, 2001. The results conclude that the size premium and bond index premium factor are not obvious in the model. If we only utilize two factors, market premium and market-to-book premium, we can find the R-square value of the revised model is higher than that of four-factor model. Furthermore, the market premium factor is greater than zero and the market-to-book premium is less than zero. It implies that managers tend to invest in the stocks with low book value and with high market value. The other important part of this research is to evaluate the persistence of mutual fund. We divide the evaluating period into season, half year and one year. The results reveal that the persistence obviously exists while the evaluating period is season; it un-obviously exists while the evaluating period is half year and it does not exist while the evaluating period is year. When we employ the Spearman Rank Correlation Test to evaluate the persistence, the result reveals the persistence does not exists in the long term.