5. Suppose your price of risk A is 5. There are two risky assets a' and 'b'. The expected return and variance of the asset a are E[ra,t+1] = 5% and SD [ra,t+1] = 10%, respectively. The expected return and variance of the asset 'b' are E[rb,t+1] = 10% and SD [rb,t+1] = 16%, respectively. Which asset would you prefer between 'a' and 'b' if you have to invest all your wealth in either 'a' or 'b', but not both? (Hint: compute the level of happiness Urt+1) for each asset, and pick the one with higher U(r++1).) 1) Asset 'a' 2) Asset 'b' 3) They are equally preferable. 6. Suppose your professor James' price of risk 'A' is 7. Which asset would James prefer between 'a' and 'b' in the question 5? (Hint: repeat the question 5 with 'A' = 7.) 1) Asset 'a' 2) Asset 'b' 3) They are equally preferable. 7. Choose a false statement. 1) Covariance of two random variables X and Y can be larger than 1. (Hint: if X=Y, cov(X,Y) = var(X) = var(Y). Can the variance of a random variable be larger than one or not?) 2) The correlation coefficient should be between -1 and +1. 3) Correlation coefficient of two random variables X and Y is 0.34 if the correlation coefficient of two random variables (3xX) and (2xY) is also 0.34. (Hint: the correlation coefficient is scale- invariant. For example, Corr(5*X, 4*Y) =Corr(X,Y)) 4) Suppose Cov(X, Y) = 200, SD(X) = SD(Y) = 20, Cov(W, Z) = 100, and SD(W) = SD(Z) = 10. Then we can say that random variables X and Y are more correlated than W and Z because Cov(X, Y) > Cov(W, Z). (Hint: compute correlation coefficients, not covariance, and use them for comparison.) 8. To maximize the Sharpe ratio of your portfolio, what assets should you NOT include in your portfolio when other things are equal? 1) Assets with low standard deviation. 2) Assets with high expected return. 3) Assets with low covariance with other assets in your portfolio. 4) Assets with high covariance with other assets in your portfolio