Please answer all questions in details. Thanks. (15pts) Mr. Weiss just bought a

Question

Please answer all questions in details. Thanks.

(15pts) Mr. Weiss just bought a zero-coupon bond issued by Risky Corp. for $870, with $1000 face value and one year to mature. He believes that the market will be in expansion with probability 0.9 and in recession with probability 0.1. 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 $952.38. Assume that the government never defaults. The expected value and the standard deviation of the return of the market portfolio are 15% and 30%, respectively. Risky Corp's bond return has a correlation of 0.67 with the market portfolio return. Assume that interest is compounded annually.* (a) Suppose Mr. Weiss holds the bond to maturity. What wil 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? xplain. (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 $870? Explain. (e) The standard deviation of the return of the Risky Corp. bond is 34.48% 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 50% of the money on the market portfolio, and the other 50% on the government bond. What are the expected value and the standard deviation of his portfolio return? Is his portfolio efficient? Explain.

Explanation / Answer

Expansion Probability = 0.9

Recession Probability = 0.1

Expected Value from Bond = 0.9*1000 + 0.1*0 = $900

Holding Period Return (HPY) = (P1 - P0 + D1)/P0

P1 - End Period Price

P0 - Beginning Period Price

D1 - Expected Cash inflow

(a) HPY = (100 - 870)/870 = 14.9%

In case of default, HPY = (0 - 870)/870 = -100%. Complete loss of investment

Approx. Bond's YTM = [C + (Face Value - Bond Price)/Period]/(Face Value + Bond Price)/2

= [(1000 - 870)/1]/(1000+870)/2 = 13.9%

(b)

Expected HPY = (900 - 870)/870 = 3.45%

The bond is risky as it tend of default during recession, but the default probability is less.

(c)

Approx. Govt Bond's YTM = [C + (Face Value - Bond Price)/Period]/(Face Value + Bond Price)/2

= [(1000 - 952.38)/1]/(1000+952.38)/2 = 4.82%

4.82% YTM is risk free rate from today till the end of bond tenure

(d)

The YTM for corp bond is 13.9% in case no default and govt bond is 4.82% with no default. The risk averse investor would prefer to buy govt bond rather than corp bond with a probability of default. The investor has chance to lose 100% of the investment in case of economic recession, but investing in govt bond has 4.82% return with sovereign guarantee.

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