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

Answer 1

Bonds are given ratings based on the credit worthiness of the bonds. These ratings assign a letter grade to Bonds that indicates their credit quality. Private independent rating services evaluate a bond issuer's financial strength to pay the bonds principal and interest in a timely fashion and base the rating of the bonds on this evaluation. The ratings vary from AAA to D in descending order of credit quality. B rated bonds are somewhere in the middle of the range which are termed speculative. This type of bonds are considered more vulnerable to adverse business, financial and economic conditions but currently has the capacity to meet financial commitments.

If the particular bond did not have any default risk then the yield to maturity of the 1 year bond would have been 4%.at the treasury yield level However since this is a B rated bond with some expected probability of default the rated yield is 7% which is higher by 3% So the credit spread for this bond is 3% and the spread is an indicator of the probability of default . The probability of default as implied by the credit spread for the bond is the implied probability of default for the bond. The credit spread is higher for lower rated bonds and lower for higher rated bonds. So implied probability is important when deciding on the rated yields and bond ratings.

There is a relationship between the implied probability of default , credit spread in percentage terms , year to maturity of the bond and the recovery rate in percentage terms which is called the Hulls equation.

P = 1 - e ^ (- S / (t - R) ) where S is the flat CDS spread and R is the recovery rate.

In this case the credit spread in percentages is .03 , t = time to maturity = 1

R = Recovery rate in percentage terms for a B rated bond with one year to maturit

Putting these values into the formula

P = 1 - e ^ ( -3/ ( 1 - 35.9)) = 1 - e ^ -.08596 = 1 - .917 = .082 which is 8.2 %

So the calculated implied probability of the B rated bond is 8.2%.