A. Suppose there are three states of nature and three

a. Suppose there are three states of nature and three risky securities with payoffs A = (1, 0, 0),

B = (0, 1, 0), and C = (0, 0, 1). Explain whether this is a complete market and why.

b. An investor holds an efficient portfolio with mean return of 12% and standard deviation of 15%. Assume that the risk-free rate is 8%, that the mean return on the market portfolio is 11.2%, and that the CAPM holds. Answer the following questions:

i. What is the beta of this portfolio (show all the details of your calculations and display the results with four decimal places)?

ii. Suppose that the investor’s total wealth is £100, invested entirely in market shares. Considering your answer in (a) above, is this investor borrowing or lending and how much?

c. Suppose that FaceLook and and Macrosoft wish to borrow $100 million for a period of ten years and that they have been offered the rates per annum shown below. FaceLook requires a floating-rate interest and Macrosoft wants a fixed-rate investment. Assume that a bank, acting as intermediary, requires 0.3% p.a.

Explain in detail how both companies can benefit from a swap.