Robust tests

The four-factor model used above is very popular and efficient and it can provide a very useful measurement of performance relating to the risks faced by mutual funds. However, it is not very good for measuring the investment style of mutual funds. As mentioned by Ibbotson and Patel (2002), the performance of mutual funds can largely be attributed to the capitalization or investment objective of a fund rather than manager skill. Thus any superior performance by a mutual fund can be due to the investment style that the fund has employed rather than the fund’s style consistency or past performance. In order to avoid this potential problem in this paper, rather than using the four-factor model to estimate the actual style of mutual funds (risk-adjusted performance measures are also available), the previous analysis will be extended by using Sharpe’s return-based style analysis regression to determine the mutual funds’ investment style categories.

Other than the Fama-French factor model, this research also uses Sharpe’s style analysis regression to perform the test. The reason for using Sharpe’s style analysis is that it is able to construct the customized benchmark which identifies the weights in passive indices that would be necessary to mimic the funds’ return stream over a specific period (Ibbotson and Patel, 2002). Any over- or underperformance versus the stylized benchmark can be called the style-adjusted alpha, a measure of value-added manager skill that is not attributable to the style of the fund. Thus, the performance measure from this model is the style-adjusted alpha.

The three key research questions above are focused on learning whether investors can use the style consistency of mutual funds to predict their future performance. However, the fact that some mutual funds perform better than others may only be due to their investment style. For example, balanced mutual funds may perform better than stock mutual funds during a stock market recession. To prevent these problems in the robust test (using a technique this researcher has employed previously), Sharpe’s style analysis method will be used to determine the actual investment style of each mutual fund in each year of the test period. At that point the relationship between style consistency and mutual funds’ future returns will be tested conditional on the investment style of the funds. Additionally, the selection returns calculated from Sharpe’s method will also be referred as style-adjusted returns of mutual funds. The relationship between style consistency and future performance would thus be tested within 5 investment style groups as determined by Sharpe’s return-based style analysis model.

Sharpe’s return-based style analysis

7 1 it i it i i

R

w r

e







Rit represents the actual total rate of return for mutual fund i at week t;

r

represents the return of index i at week t; Wi is the coefficient for index i，there are two constraints for those coefficients – 1) Wi is larger than 0; 2) sum of Wi equal to 1.

7 1 bt i it i

r

w r





Wi represents the coefficient to index i over a 1-year period prior to t as calculated by regression [1], and r-it is the return to index i in week t. r-bt, therefore, is the style benchmark return for mutual i at week t.

it

r

r



 

The difference between the actual return of mutual fund i and its style benchmark return at week t is the style-adjusted alpha of mutual fund i at week t.

Because 50 weeks (a 1-year period) of data is required to create the customized benchmark, the first style-adjusted alpha that is calculated is for the first week in 2006. The benchmark created for week 1 of 2006 is based on a regression that uses data from the prior 50 weeks in 2005. At week 1 of 2006, the actual return is compared to the benchmark return to determine alpha. In this manner, rolling forward out-of-sample alphas are calculated for each week from 2006 to 2008. The weekly style-adjusted alphas are then compounded into a single, annualized style-adjusted alpha for each calendar year. The RSQs for 2005, 2006, 2007 and 2008 are calculated by the regression [9] and then the two-way ranking tables would be used to show the relationship between style consistency and future mutual funds’ performance (as mentioned above). Finally, the cross-sectional regression would be used to test the relationship.

In reality, there are two methods for performing the robust tests: 1) to use Sharpe’s style analysis method to determine the style of mutual funds and to then use alpha and R-squared from the four-factors model above to test under different investment style categories; or 2) to use the style-adjusted return as the performance measure to perform the tests above. In this research the use of the first method of doing the robust test is preferred. Moreover, all the style-adjusted returns as well as the robust test results of these mutual funds have also been calculated using the second method; these results also support the conclusions of this thesis (available on request，see Appendix 6 for details).