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Posted on March 8th, 2013, by

In such a way, empirical evidence reveals the fact that CAPM helps to understand that professional skills of fund managers are essential for the successful performance of mutual funds. To put it more precisely, the CAPM reveals the priority of the accurate analysis of risks associated with investments and expected returns. Therefore, the detailed and accurate risk assessment and analysis of expected returns is possible only on the condition of the high professional level of fund managers and their well-developed professional skills, whereas luck is secondary, if important at all. Therefore, the CAPM proves the priority of professional skills of fund managers as the key factor contributing to the successful performance of mutual funds. In this respect, it is important to dwell upon the empirical aspects of the CAPM test and its interpretation that will be presented in the chapter to follow along with other methods of analysis that help to reveal the impact of professional skills and luck of fund managers on the performance of mutual funds.

4. Empirical tests and interpretation

4.1 The data

On applying the CAPM model to the analysis of the impact of professional skills of fund managers and luck on the performance of mutual funds, it is important to test the CAPM. In order to test the CAPM model, data has been collected for monthly intervals between January 1995 and December 2004. The equation E(ri) = rf + Яi[E(rMarket) rf] will be tested by observing the 120 monthly holding period rate of returns on 20 stocks within the S&P 500 index. The S&P 500 will be used as an approximation of the market and monthly rates of the 3-month Treasury Bill in the Secondary Market will be used as an approximation for the risk-free rate (Scholz, 2006).

At the same time, it is possible to refer to ANOVA to test the impact of professional skills and luck on the performance of mutual funds (See App. Table 1). The data reveal the correlation between professional skills and performance of mutual funds and the possible impact of luck on their performance.

4.2 Test procedure

Before testing the above equation, a 120 x 20 matrix consisting of the stock returns was created, followed by a 20 x 20 variance-covariance matrix of the stock returns. Another 20 x 20 matrix was then created and which weighted the variance covariance matrix by the stock weights in a given portfolio. From this matrix a portfolio variance and standard deviation could be derived. Finally, the portfolio weights were adjusted until the standard deviation was minimized and the expected portfolio return was found. This gave the minimum risk (standard deviation) portfolio, with an expected return and standard deviation of (0.0142, 0.0397) (Scholz, 2006).

After plotting this point, a new portfolio was found which minimized standard deviation for a given expected return. This process was repeated for various values and each point was plotted, resulting in the following efficient frontier (Scholz, 2006).

As for the ANOVA test it presents the comparison of different mutual funds, whose performance varies consistently and whose managers rely heavily on their professional skills or luck. The null hypothesis is that the luck has no impact on the performance of mutual funds.

Hence, the performance of mutual funds depends mainly on professional skills of their managers.
4.3 Results and interpretation of the test

Returning to the CAPM, it is important to place emphasis on the fact that after finding the frontier between professional skills and luck, a 120 x 21 matrix was constructed consisting of the 20 columns of excess stock returns (rit rft) and 1 column of excess market returns (rMt rft) in order to test the expected return-beta relationship predicted by the CAPM. Each excess stock return was then regressed on the excess market returns to estimate the beta coefficient as follows:
rit rft = ai + bi(rMarket t rft) + eit

To estimate expected excess returns, the sample average excess returns were taken for each stock as well as the market. The values of bi are estimates of the true beta coefficients for the 20 stocks during the sample period. The residual ei of each estimate was squared in order to estimate the nonsystematic risk for each stock (Fama & French, 2004).

Now the SML will be constructed and its coefficients estimated to verify that our CAPM is valid. The coefficient of beta is estimated by regressing estimated expected excess stock returns on the estimates of beta (Fama & French, 2004). The estimated nonsystematic risk for each stock will also be included in the regression to see whether it is correlated with the excess returns.
S(rit rft)/n = a0 + a1bi + a2*ei^2 + ui

If the CAPM is valid, then three conditions are satisfied:
1. a0 = 0, there is no risk premium for bearing nonsystematic risk,
2. a1 = S(rmarket rf)/n, beta times the excess market return yields the excess stock return,
3. a2 = 0, expected excess return is independent of nonsystematic risk.
Testing these hypotheses produced the subsequent results (Fama & French, 2004):
Coef. Std. Err. ratio Result
a0 0.004409 1.77 Fail to reject at 95% level
a1 0.004558 1.545 Fail to reject at 95% level
a2 0.2741 0.275 Fail to reject at 95% level

The findings after the application of CAPM prove the domination of professional skills over luck. The same results were obtained in the result of the application of ANOVA. In fact, professional skills are prior condition of the successful performance of mutual funds, whereas luck is consistently less important. At any rate, mutual funds’ success depends on the ability of their managers to assess accurately risks and forecast expected returns. In addition, managers should be capable to maximize benefits of mutual funds and forecast the development of the market to assess accurately possible outcomes of investments. They cannot perform the aforementioned functions without well-developed professional skills, whereas luck can be of little importance for them in this regard.

At the same time, the ANOVA reveals the fact that the average beta of the sample mutual funds analyzed in terms of the current study varies between 0.8500 to 0.9500 and a bit more but fails to reach the 1 level (See App. Table 1). In such a way, risks associated with these funds are lower compared to average in the industry. On the other hand, the average beta is higher for mutual funds, which rely heavily on the luck of their fund managers. In addition, these funds have higher risks compared to mutual funds relying primarily on professional skills of their fund managers.

Moreover, the standard error for mutual funds discussed and analyzed in terms of the current studies is relatively low. Therefore, the findings of the study are reliable and valid. In this regard, the study proves that professional skills are prior to luck and fund managers’ professionalism plays an important, if not to say determinant, part in the performance of mutual funds.

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