Suppose we have a zero-coupon bond that pays $1 after one year if the issuing firm is not in default.If the firm is in default the recovery rate is 40%.The one-year risk free interest rate in simple terms is 5% and the risk-neutral probability that the firm defaults is 10%.What is the fair credit spread on the bond (again,in simple terms)?
A)5.0%
B)6.7%
C)10.5%
D)11.7%

Question

Quizplus · Accepted Answer

The expected payoff of the bond is 0.9 * $1 + 0.1 * $0.4 = $0.94. The present value of this expected payoff at the risk-free rate is $0.94 / 1.05 = $0.8952. The fair credit spread is the difference between the risk-free rate and the yield that equates the present value of the expected payoff to the bond's face value. Solving for the yield: $1 / (1 + yield) = $0.8952 gives a yield of approximately 11.7%. The credit spread is 11.7% - 5% = 6.7%.

Suppose We Have a Zero-Coupon Bond That Pays $1 After