Question 2

Suppose that we live in a very small world with only two risky assets in the market, namely, Stock U and Stock Q. Suppose also that CAPM holds in this world. Stock U has a price of $85 today. Its price next year will be $65 if the economy is in a recession, $90 if the economy is normal, and $130 if the economy is in a boom. The probabilities of recession, normal times, and boom are 5%, 80%, and 15%, respectively. Stock U pays no dividends and has a correlation of 0.85 with the market portfolio. Stock Q has an expected return of 15%, a standard deviation of 30%, a correlation with the market portfolio of 0.25, and a correlation with Stock U of 0.45. The market portfolio in this small world has a standard deviation of 25%.

1. Suppose that you are a typical, risk-averse investor with a well-diversified portfolio. Which stock would you prefer? Briefly explain why. [6 marks]
2. What are the expected return and standard deviation of a portfolio consisting of 65% of Stock U and 35% of Stock Q? [2 marks]
3. What is the beta of the portfolio in part (b) above? [2 marks]