Question

Given maturities of 1,2- and 20-year bonds with respective yields of 4, 5 and 11 percent. These bonds have rated yields at 7, 9, and 16 percent.What is the implied probability of repayment on one-year B-rated debt? What is B-rated debt bonds and implied probability represent here? Show work and discuss the importance of implied probability.

MUST SHOW WORK. PLEASE AND THANK YOU!

Answer 1

There is a formula for calculating the implied probability of default. From there we can calculate the implied probability of repayment.

The formula,

S = p (1 - R)

where , S = credit spread

p = probability of default

R = annualised default rates

In this case, we will first calculate, p the probability of default than do (1 - p) for probability of repayment. See the table below for the value of R, annualised default rates.

So, p = S / (1 - R)

For 1 year bond, p = (0.07 - 0.04) / (1 - 0.0368) = 0.0311

Probability of repayment = 1 - p = 1 - 0.0311 = 0.9688 = 96.88 %

For 2 year bond, p = (0.09 - 0.05) / (1 - 0.0368) = 0.0415

Probability of repayment = 1 - p = 1 - 0.0415 = 0.9584 = 95.84 %

  For 20 year bond, p = (0.16 - 0.11) / (1 - 0.0368) = 0.0519  

Probability of repayment = 1 - p = 1 - 0.0519 = 0.948 = 94.80 %

Different rating are given to different bonds depending on the depending on the creditworthiness of the issuer. The bond with the highest rating would be given a AAA (government securities for example) while google or apple will get a AA rating because they are very sure that these companies will pay back but definately not better than the government hence a AA. As the credit worthiness falls so does the rating from AAA to AA to A to BBB to BB and finally to B and C. As company with lower credit rating like B will have a higher probability of default hence people will be unwilling to lend them money but what if the issuer increase the interest rate on the bond. Than there will be some investors who will be willing to take that risk. Hence, you can also see that from the credit spread above. One the 1 year bond there is a 3% difference between the risk free bond of 4% and this B-reted bond of 7%.