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# Yield to Maturity and Risk Free Rate

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Problem One:
(a). The yield to maturity on ACL bonds maturing in 2008 is 8.75 percent. The yield to maturity on a similar maturity U.S. Government Treasury bond in 7.06 percent and the yield on Treasury bills is 6.51 percent. What is the default risk premium on the ACL bond?
(b) AKA is considering expanding into a new product area. AKA's current beta is 1.2 and its beta is expected to increase to 1.45 after the expansion. The long-term growth rate of the firm's earnings is expected to increase from 6.5 percent to 10 percent. AKA's current dividend is \$1.70 per share, the current risk-free rate is 9.1 percent, and the expected market return is 12.9 percent. Should AKA undertake the planned expansion?

Problem Two:
John has a portfolio of 8 securities, each with a market value of \$5,000. The current beta of the portfolio is 1.28 and the beta of the riskiest security is 1.75. John wishes to reduce his portfolio beta to 1.15 by selling the riskiest security and replacing it with another security with a lower beta. What must be the beta of the replacement security?

Problem Three:
Christy is considering investing in the common stock of One Liberty and Heico. The following data are available for these two securities:
One Liberty Heico
Expected return................................................ 12% 16%
Standard deviation of return................................. 8% 20%

If she invests 30% of her funds in Heico and 70% in One Liberty, and if the correlation of returns between these securities is +0.65, what is the portfolio's expected return and standard deviation?
(a). Determine the expected rate of return on Christy's portfolio.
(b). Determine the standard deviation of possible rates of return on Christy's portfolio (to the nearest tenth of a percent).
(c). Determine the coefficient of variation for the rate of return on Christy's portfolio.

Problem Four:
Currently the risk-free rate equals 6% and the expected return on the market portfolio equals 12%. An investment analysis provides you with the following information:
Stock Beta Expected Return
A 1.50 15%
B 0.85 13%
C 1.62 18%
D 0.72 10%
a. Indicate whether each stock is over-priced, under-priced, or correctly priced.
b. For each stock, subtract the risk-free rate from the stock's expected return and divide the result by the stock's beta. Provide an interpretation for these ratios. Which stock has the highest ratio and which has the lowest?
c. Show how a smart investor could construct a portfolio of stocks C and D that would outperform stock A.
d. Construct a portfolio consisting of some combination of the market portfolio and the risk-free asset such that the portfolio's expected return equals 10%. What is the beta of this portfolio? What does this say about stock D?
e. Divide the risk premium on stock C by the risk premium on stock D. Next, divide the beta of stock C by the beta of stock D. Comment on what you find.