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.

(a) Suppose Mr. Weiss holds the bond to maturity. What will be his holding period return if Risky Corp. does not default? What will be his holding period return if the firm defaults?

(b) What is the expected return of the Risky Corp. bond? Is the bond risky or riskfree? Explain.

(c) What is the YTM of the government bond? Is this YTM the riskfree rate? Explain.

(d) Compare the expected return of the Risky Corp. bond with the riskfree rate. Would a risk-averse investor buy the Risky Corp. bond at $930? Explain.

(e) 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?

(f) 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.

Answer 1

Thank you for your question. below are the answers.

(a) Holding Period Return Formula= (ending value - initial value)/(initial value) HPR no default = 7.53% HPR with default = -100.00%

(b) Expected return is the weighted average of returns in the expansion and recession. ER = 2.15%

(c) Bond Cash Flows Date 1 $ (970.87) Yield to Maturity formula for one period bond : YTM= (Price/Face Value)-1 Date 2 $ 1,000.00 YTM = 3.00%

(d)To calculate standard deviation of the return of Risky Corp. Bond: SD=Variance^.5 and Var=p1(X1-E(X))^2+p2(X2-E(X))^2 Values from above calculations: Expected Return default: -100.00% P(default): 0.05 Expected Return no default: 7.53% P(no default): 0.95 Expected Return overall: 2.15% Variance: 5.49% Standard Deviation: 23.43%

(e) Beta of the Risky Corp. formula : Beta=(covariance btwn bond and market porfolio*standard deviation of the bond) / (standard deviation of the market portfolio) standard deviation of the market portfolio: 40% Covariance btwn bond and market portfolio: 0.75 standard deviation of the bond: 23.43% Beta for Risky Corp bond: 0.4394 According to the CAPM model Er = riskfree rate + Beta1(E[rtrn market] - riskfree rate) : CAPM expected return = 6.08% Mr. Weiss undervalued the bond relative to CAPM. According to Mr. Weiss the bond's expected return is 2.15% while it is 6.08% according to CAPM.