There are three assets with returns r1, r2, r3, whose variation is completely explained by two factors F1 and F2:
r1 = 0:04+2F1 F2 r2 = 0:11+3F1
r3 = 0:08 6F1+3F2
Suppose that the factors are demeaned (E(F1) = E(F2) = 0) and uncorrelated.
1. Construct two portfolios with the three assets that have factor loadings (1;0) and (0; 1) respectively (one portfolio has exposure only to F1, and the second has exposure only to F2)? What is the portfolios expected return?
2. Construct a portfolio with the three assets that have factor loadings (0; 0).
3. What is the risk free rate in the economy? What are the portfoliosi´risk premia?