Suppose we analyze a fund manager using a 4-factor model. That is, we evaluate the manager by regressing the excess returns of the fund on a the market factor, the size factor (SMB, which buys small cap stocks and shorts large cap stocks), the book-to-market factor (HML, which buys value stocks and shorts growth stocks) and a momentum factor (WML, which buys stocks with high 2-12 month returns and shorts stocks with low 2-12 month returns).

Suppose that the expected for the market factor is 6% per year, the expected returns for SMB is 4% per year, the expected returns for HML is 6% per year and the expected returns for WML is 8% per year. The risk-free rate is 3% per year. Suppose we regress the excess return of the fund on the excess return of the market portfolio, SMB, HML and WML using the past 5 years worth of monthly data. We find that the factor loadings are 1.10 on the market, -0.20 on SMB, 0.10 on HML and 0.25 WML. Over this period, the fund manager has achieved a return of 11.0% where as the market has returned 9.0% (6% above the risk-free rate).

a) According to 4-factor model, has this fund manager produced superior returns?

b) Rather than investing in the fund, construct a portfolio that invests in the factor mimicking portfolios that produces the same risk profile as the fund. (That is, you want a portfolio that has the same risk loadings as the fund itself) Assume that you have $1Mil to invest. That is, how should the money be allocated among the market portfolio, SMB portfolio, HML portfolio and WML portfolio?

c) Given the beta estimates from the four-factor model, does the fund manager appear to have invested more in small stocks or in large stocks?

d) Given the beta estimates from the four-factor model, does the fund manager appear to have invested more in value stocks or in growth stocks?