Question

A bond has par=$1000, coupon rate of 3% and matures in 4 years. The bond pays semi-annual coupons. On the market, you see that the current YTM is 9%, however, a trader told you that his expected yield on the bond is only 3.6%. What default probability on the par is the trader's expectation consistent with? (Provide your answer as percent rounded to two decimals, omitting the % sign.)

Answer 1

Calculate the bond price using current YTM

N = 4 x 2 = 8, I/Y = 9%/2 = 4.5%, FV = 1000, PMT = 3% x 1000 / 2 = 15

=> Compute PV = $802.12

Now, let's calculate the future value using the current price and expected yield

N = 8, I/Y = 3.6%/2 = 1.8%, PV = -802.12, PMT = 15

=> Compute FV = $797.34

% Default Probability = 1 - 797.34/1000 = 20.27%