Suppose the CAPM holds, company A has beta A = 0.5 and volatility A = 12%, company B has beta B = 1.5 and volatility B = 25%. The market return is 6%, market volatility is 15%, and the risk-free rate is equal to zero. All assets are uncorrelated. Reminder: formulas may require variance while the question is providing a standard deviation.

1. What would be your estimate of the aggregate risk aversion in this economy?

2. What is the expected return of company A and B?

3. Suppose an investor with risk aversion = 4 has to choose how much to invest in the risk-free asset and companies A and B. What is the optimal portfolio for this investor?

4. What is the optimal portfolio in the case = 2? Compute the leverage of the investor.

5. Compute the beta of the portfolio of an investor with risk aversion equals to = 2 and = 4. Hint: the beta of a portfolio equals the average of the individual betas (weighted by the portfolio share).