Suppose that the returns on three well-diversified portfolios A, B and C are determined by the following two-factor model:

rA = 0.06 + 0.8F1 - 0.6F2

rB = 0.07 + 2F1

rC = 0.04 + 0.7F1 + 0.4 F2

(a)

(i) Determine the portfolio weights you need to place on A, B and C in order to replicate the portfolio returns on F1 and F2 respectively. Explain briefly the rationale for the calculation approach you have used.

(ii) Determine the portfolio weights you need to place on A, B and C in order to construct a portfolio with zero exposure to both factors. Explain carefully why this portfolio must be risk-free.

(b) What are the expected returns of the two factor-replicating portfolios and the risk-free portfolio? What are the premiums associated with F1 and F2?