# Expected return, Standard Deviation, Forward Contract

1. Suppose the expected returns and standard deviations of stocks A and B are E(RA) = 0.17, E(RB) = 0.27, StdDevA = 0.12, and StdDevB = 0.21, respectively.

a. Calculate the expected return and standard deviation of a portfolio that is composed of 35 percent A and 65 percent B when the correlation between the returns on A and B is 0.6.

b. Calculate the standard deviation of a portfolio that is composed of 35 percent A and 65 percent B when the correlation coefficient between the returns on A and B is -0.6.

c. How does the correlation between the returns on A and B affect the standard deviation of the portfolio?

2. Suppose the expected return on the market portfolio is 14.7 percent and the risk-free rate is 4.9 percent.Solomon Inc.stock has a beta of 1.3.Assume the capital-asset-pricing model holds.

a. What is the expected return on Solomon's stock?

b. If the risk-free rate decreases to 3.7 percent, what is the expected return on Solomon's stock?

3. A portfolio that combines the risk-free asset and the market portfolio has an expected return of 22 percent and a standard deviation of 5 percent.The risk-free rate is 4.9 percent, and the expected return on the market portfolio is 19 percent.Assume the capital-asset-pricing model holds.What expected rate of return would a security earn if it had a 0.6 correlation with the market portfolio and a standard deviation of 3 percent?

4. Suppose you have invested $50,000 in the following four stocks:

Security Amount Invested Beta

Stock A $ 10,000 0.7

Stock B 15,000 1.2

Stock C 12,000 1.4

Stock D 13,000 1.9

The risk-free rate is 5 percent and the expected return on the market portfolio is 18 percent. Based on the capital-asset-pricing model, what is the expected return on the above portfolio?

5. 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 4 percent per annum and 9 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 1 percent. What is the price of a forward contract otherwise identical to yours?

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.

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#### Solution Summary

The following are answered:

1) Expected return and standard deviation of a portfolio given return, standard deviation and corelation of stocks

2) Expected return on a portfolio using CAPM

3) The price of a forward contract for different spot interest rates.