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# Investment Decision Questions

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?

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?

#### Solution Summary

The solution examines different investment opportunities in order to determine which is the best decision.

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