本文藉由獨特性風險之估計以了解基金風險分散的程度、基金績效與獨特性風險之關係，以及基金經理人風險調整之行爲。實證研究發現在樣本期間中，科技類及一般類開放型共同基金的獨特性風險平均約占總風險的20%，顯示我國開放型共同基金並未完全消除可分散風險。其次，本研究發現在全樣本期間中，基金的獨特性風險與獨特性風險溢酬具有正向關係，亦即基金賺得獨特性風險溢酬的補償。在獨特性風險與績效關係的實證結果上，顯示績效好的基金的確存有較高的獨特性風險，隠含採取積極性投資組合策略的基金其績效較好。此外，本文亦發現我國基金經理人會視距競賽結束期間的長短，而調整基金的獨特性風險或系統風險，以求較佳的年度績效。

Portfolio theory states that a well-diversifIed portfolio has zero or far small part of the idiosyncratic/diversfiable risk. Lee (1997) examined the issue that how many stocks should be bought in Taiwan's stock market to construct a well-diversified portfolio. Lee (1997) find that the number of stocks an investor needs to buy is far less than the number suggested by the traditional wisdom. Lee (1997) indicates that an investor needs only 4～5 stocks to reach the risk level specified by Bird and Tppett. According to Lee's finding, we can infer that domestic open-end mutual funds in Taiwan, holding 20 stocks on average, may eliminate a large portion of the idiosyncratic risks of their portfolios. However Brown, Harlow, and Starks (1996) demonstrate that managers of investment portfolios likely to end up as losers will manipulate fund risk differently than those managing portfolios likely to be winners when their compensation is linked to relative performance. Their empirical results show that mid-year losers tend to increase fund volatility in the latter part of an annual assessment period to a greater extent than mid-year winners. Besides, Yu and Yao (2000) show that there exists a significant positive relation between the fund managers' positive-feedback strategy and the funds' performance. These two studies above imply that mutual fund managers could choose stocks with highly expected returns in order to obtain better performance but ignore risk diversification. How is the power of diversification of mutual funds in Taiwan stock market? Can fund managers effectively diversify portfolio risk and earn enough return for investors? Such an important issue, concerned by the investors of mutual funds, has been ignored by Taiwan's financial scholars for a long time. In this paper, we investigate the degree of mutual fund diversification and discuss the relation between idiosyncratic risk and fund performance, risk-adjusted behavior of fund managers. The primary contribution of this paper is that we analyze these three issues above via an analysis of idiosyncratic risk, which differs from previous literatures. Second, to estimate the size of mutual fund diversification, in this paper, following Malkiel and Xu (2003) approach, we propose a modified direct decomposition method, which takes into account for GARCH effect in return process, to estimate the idiosyncratic risks of mutual funds. This study uses a sample of Taiwan domestic open-end mutual funds consisting daily returns from 2001 to 2003. The sample of this period contains 105 open-end mutual funds in all, where including 30 technology-type stock funds and 85 general-type stock funds. Our empirical results show that in sample periods the idiosyncratic risks of both technology-type funds and general-type funds account for 20% of the total risks on average, thereby indicating that Taiwan open-end mutual funds have not eliminated all of the idiosyncratic risks. Furthermore, we find that there is no significant difference in reducing the relative degree of the diversifiable risk between technology-type funds and ordinary-type funds; however we find that the performances of risk diversification are little different among securities investment trust companies. Moreover, this study demonstrates that the idiosyncratic risks of mutual funds positively correlate with their idiosyncratic risk premiums, implying that the mutual funds can undertake idiosyncratic risks to gain risk premiums. Also, the evidence reveals that there is a positive relation between the idiosyncratic risk and mutual fund performance. It indicates that mutual fund managers can successfully adopt active portfolio strategy to obtain better performance. Finally, the empirical results show that fund managers will actively adjust systematic or idiosyncratic risk of their portfolio to gain better yearly performance according to the length of the tournament period. For example, fund managers tend to increase fund idiosyncratic risk when the term-to-maturity of annual assessment period is still long. However they tend to adjust systematic risk when the term-to-maturity of an annual assessment period is short. In this paper our above empirical results, which were not presented in the previous papers, suggest that there is much more interesting work to be done. Incorporating idiosyncratic risk into the analysis of mutual fund behavior is a fruitful area for future research.