Question 3. (Total: 30 point)

The following return forecasts are for two stocks, Mars and Venus:

	Bear market	Normal	Bull market
Probability	0.3	0.5	0.2
Mars	-8%	10%	35%
Venus	-5%	10%	25%

From this forecast, the expected returns of Mars and Venus are computed as 9.60% and 8.50%, respectively. The standard deviations of returns for Mars and Venus are 14.90% and 10.50%, respectively.

1. Calculate the correlation between the returns of Mars and Venus. Show all computations. (10 points)

2. (i) According to the mean-variance portfolio theory, which stock, Mars or Venus, should be chosen for a rational risk-averse, mean-variance investor whose index of risk aversion, A, is 4? Explain the reason(s) for your choice. Show your computations, if any, for full credit. (7 points)

(ii) If the investor is risk-neutral, would your answer be different from (i)? Explain. (3 points)

3. Compute the standard deviation of an equal-weighted portfolio comprising of Mars and Venus stocks.

(5 points)

4. Explain why it is easier to interpret correlation than covariance in constructing and managing a portfolio. (5 points)