There are two securities in the market, A and B. The price of A today is €50. The price of A next year will be €40 if the economy is in a recession, €55 if the economy is normal, and €60 if the economy is expanding. The probabilities of recession, normal times and expansion are 0.1, 0.8 and 0.1, respectively. A pays no dividends and has a correlation of 0.8 with the market portfolio. B has an expected return of 9 per cent, a standard deviation of 12 per cent, a correlation with the market portfolio of 0.2, and a correlation with A of 0.6. The market portfolio has a standard deviation of 10 per cent.

Assume the CAPM holds.

(a) If you are a typical, risk-averse investor with a well-diversified portfolio, which security would you prefer? Why?

(b) What are the expected return and standard deviation of a portfolio consisting of 70 per cent of A and 30 per cent of B?

(c) What is the beta of the portfolio in part (b)?