Assume that stock returns are generated by a two-factor model. The returns on three well-diversified portfolios, A, B and C, are given by the following representations:

rA = 0.10 + F1 - 0.5F2

rB = 0.08 + 2F1 + F2

rC = 0.05 + 0.5F1 + 0.5F2 .

Determine the portfolio weights you need to place on A, B and C in order to construct the two factor-replicating portfolios plus a portfolio which has zero exposure to both factors. What are the expected returns of the factor-replicating portfolios and what is the expected return of the risk-free portfolio?