1Given an investor utility function U = E(r) - 0.5 * A * Var(r), calculate the risk aversion coefficient (A) for an investor who is indifferent between a risky portfolio (expected return 0.15, standard deviation 0.15) and a risk-free asset with a 6% return.
2An investor allocates 30% of her wealth to a risky asset (E(r) = 0.15, variance = 0.04) and 70% to a risk-free asset (rf = 0.06). What are the portfolio's expected return and standard deviation respectively?
3In the context of the Capital Allocation Line (CAL), if the risk-free rate is 5% and a risky asset has an expected return of 16% with a standard deviation of 15%, what is the slope of the CAL?
4Using the Index Model, if Stock A has a beta of 0.8, Stock B has a beta of 1.2, and the market standard deviation (sigma_M) is 0.20, what is the covariance between returns A and B?
5Consider an index model regression for Stock A: R_A = 0.01 + 0.8 * R_M + e_A (where variables are excess returns). If the market standard deviation is 0.20 and the residual standard deviation of A is 0.20, which of the following statements are correct?
6A stock is currently priced at 40 units. It is expected to pay a 3 unit dividend and sell for 41 units in one year. If the risk-free rate is 5%, the market return is 12%, and the stock's beta is 0.5, identify the correct assessment under CAPM.
7If the 1-year zero-coupon bond YTM is 7% and the 2-year zero-coupon bond YTM is 8%, what is the market price of a 2-year bond with a 9% annual coupon rate and a face value of 100?
8Under the expectations theory of the yield curve, if the 1-year YTM is 7% and the 2-year YTM is 8%, what is the expected 1-year forward rate starting one year from now?
9In an index model regression, if we switch from excess returns to raw returns (where r_f = 2%, alpha = 0.01, and beta = 0.8), what would be the new intercept of the regression?
10If you believe in the liquidity preference theory and assume a liquidity premium of 1%, how does the expected one-year yield to maturity (starting one year from now) compare to the forward rate?
