Problem 3: Go to Ken Frenchs data library (google it) and get the following data: Monthly returns, from 196307 to present, to 1) the three Farma-French factors and T-bills (link: Farma/French Factors), 2) the momentum factor, and 3) the 6 portfolios formed on size and book-to-market (2x3).

a) What is the mean-variance efficient portfolio of the three Farma-French factors (MKT, SMB and HML) and the momentum factor (MOM) over the sample? What is the portfolios Sharpe ratio?

b) What is the mean-variance efficient portfolio of the four corner portfolios from the 2x3 sort on size and book-to-market (i.e., small value, small growth, large value, large growth)? Please provide some intuition for the weights.

c) What are the average excess returns to the six portfolios sorted on size and book-to-market?

d) What are the six portfolios market loadings and abnormal returns (alphas, with test-statistics) from a CAPM type regression employing the excess market returns as the explanatory factor (MKT)

e) Repeat part b) employing all three Farma-French factors as explanatory variables.