For the three problems below answer the following questions:
a. What financial concept or principle is the problem asking you to solve?
b. In the context of the problem scenario, what are some business decisions that a manager would be able to make after solving the problem?
c. Is there any additional information missing from the problem that would enhance the decision-making process?
d. Without showing mathematical calculations, explain in writing how you would solve the problem.
Question 1: A portfolio that combines the risk-free asset and the market portfolio has an expected return of 25 percent and a standard deviation of 4 percent.The risk-free rate is 5 percent, and the expected return on the market portfolio is 20 percent.Assume the capital-asset-pricing model holds. What expected rate of return would a security earn if it had a 0.5 correlation with the market portfolio and a standard deviation of 2 percent?
Question 2: Suppose you have invested $30,000 in the following four stocks:
Security Amount Invested Beta
Stock A $ 5,000 0.75
Stock B 10,000 1.1
Stock C 8,000 1.36
Stock D 7,000 1.88
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The risk-free rate is 4 percent and the expected return on the market portfolio is 15 percent.
Based on the capital-asset-pricing model, what is the expected return on the above portfolio?
Question 3: You enter into a forward contract to buy a 10-year, zero-coupon bond that will be issued in one year. The face value of the bond is $1,000, and the 1-year and 11-year spot interest rates are 3 percent per annum and 8 percent per annum, respectively. Both of these interest rates are expressed as effective annual yields (EAYs).
a. What is the forward price of your contract?
b. Suppose both the 1-year and 11-year spot rates unexpectedly shift downward by 2 percent. What is the price of a forward contract otherwise identical to yours?