6.

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

1. rA = 0.06 + 0.8F1 - 0.6F2

2. rB = 0.07 + 2F1

rC =0.04+0.7F1 +0.4F2

(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. (5 marks)

(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. (5 marks)

(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?

(5 marks)

(c) You observe a fourth well-diversified portfolio with sensitivities of 2.5 to F1 and -1.6 to F2, and a return of 14%. Show that an arbitrage opportunity exists. How would you exploit this opportunity? (4 marks)

(d) Compare the implications of the arbitrage pricing theory (APT) and the capital asset pricing model (CAPM) for optimal investment portfolios. (120 words)

(6 marks) (Total = 25 marks)