Question

Mr. Weiss just bought a zero-coupon bond issued by Risky Corp. for $930, with $1000 face value and one year to mature. He believes that the market will be in expansion with probability 0.95 and in recession with probability 0.05. In the event of expansion, Risky Corp. can always repay the debt. In the event of recession, the company would fail to meet its debt obligation. The bondholders would recover nothing and completely lose their investment, should the firm default. A zero-coupon government bond with the same maturity and face value is selling at $970.87. Assume that the government never defaults. The expected value and the standard deviation of the return of the market portfolio are 10% and 40%, respectively. Risky Corps bond return has a correlation of 0.75 with the market portfolio return. Assume that interest is compounded annually.

(1) What is the standard deviation of the return of the Risky Corp. bond? What is the beta of the bond? What would be the equilibrium expected return of the Risky Corp. bond if the CAPM holds? Does Mr. Weiss overvalue or undervalue the bond relative to the CAPM?

(2) Suppose Mr. Weiss changes his mind and sells his Risky Corp. bond. He invests in a portfolio that allocates 60% of the money on the market portfolio, and the other 40% on the government bond. What are the expected value and the standard deviation of his portfolio return? Is his portfolio efficient? Explain.

Please answer both parts with detail. Thank you!

Answer 1

A)

Risk free return 1000/970.87 - 1 = 3.0068% or 3%

Standard deviation of the bond= = 217.95 or 22.45%

Beta of the bond= correlation*(std deviation of bond)/std deviation of market = 0.75*.2245/.4 = 0.42

Expected return = Risk Free rate + Beta * Market risk premium = 3%+ 0.42*(10%-3%) = 5.9

Current return of the bond = 1000/930 - 1 = 7.5%

Since the rate of return is higher then CAPM derived rate therefore the bond is underpriced

2) Expected return = 0.6*10+0.4*3 = 7.2%

Expected Standard deviation = = 24%

Yes the portfolio is efficient because for the given amount of risk the return generated will lie on the efficient frontier.