Problem
You have priced two pure discount bonds, each with 5 years to maturity and with a face value of $1000. They pay no coupons. The first bond sells for $780.58, and the second sells for $667.43.
A. What are their yields to maturity?
B. Why does the second bond sell for less than the first?
C. If their default risk is uncorrelated with the rest of the economy, then their expected cash flows can be discounted at the riskless rate, which is 5 percent. If they have the same expected yield, what is the probability of default for the second bond? (Assume that if the bond defaults, you receive nothing, but if it does not default, you receive the full face value.)