Q1 You have ?500,000 available to invest. The risk-free rate (which is also the rate at which you could borrow) is 8%, and there is a (risky) fund in which you could invest that has an expected return of 16%. What would you have to do to produce a portfolio with an expected return of 22%?
Q2 In a world in which your investment choices consist of a risky portfolio and a risk-free asset, the expected return on the former is 15%, and the return on the latter is 10% (which is also your borrowing rate). The standard deviation of the return on the risky portfolio is 20%. If your complete portfolio has a standard deviation of 25%, what are the proportions in which you have allocated your wealth between the risky portfolio and the risk-free asset?
Q3. The risk-free rate is 4%. The expected market rate of return is 11%. If you expect stock X with a beta of 0.8 to offer a rate of return of 12 percent, would you buy this stock or sell it short? Why?
Q4 Assume that both X and Y are two well-diversified portfolios, and that the risk-free rate is 8%. Portfolio X has an expected return of 14% and a beta of 1.00. Portfolio Y has an expected return of 9.5% and a beta of 0.25. According to the arbitrage pricing theory, would these portfolios appear to be fairly priced? Explain your answer.
Q5 Consider the following two situations:
a) Portfolios A and B both have expected returns of 15%, but portfolio A has a beta of 1.2, while portfolio B has a beta of 1.0.
b) Portfolio A has an expected return of 20% with a standard deviation of 30%, while portfolio B has an expected return of 15% but a standard deviation of 35%.
In a world in which CAPM is valid, could either or both of these situations occur? Explain your answer.
Q6. All other things being equal, which of the following bonds has the longest duration?
a) A 15-year bond with a 10% coupon
b) A 20-year bond with a 9% coupon
c) A 20-year bond with a 7% coupon
d) A 10-year zero-coupon bond
Q7 How could you create an investment position involving a put, a call, and riskless lending or borrowing that would have the same payoff structure at expiration as a long position in the common stock?