Question

The yield on 3-month T bill is 1%.

The yield on 3-month commercial paper is 1.88%.

Assume that investors get 60% of the face value when commercial paper defaults.

What is the probability of default of the commercial paper?

Answer 1

3-month T-bill yield or Risk-free rate = 1%

Yield on 3-month commercial paper = 1.88%

The extra yield over risk-free rate for commercial paper is the Credit Spread.

Credit Spread = Yield on Commercial Paper - Yield on T-bill

Credit Spread = 1.88% - 1% = 0.88%

Recovery Rate = 60%

Formula for Credit Spread with respect to Recovery rate and Probability of Default:

Credit Spread = (1 - Recovery Rate)*(Probability of Default)

The formula above is essentially the expected loss in case of default as (1 - Recovery rate) is the lost amount and multiplied by Probability of default means the expected loss.

We know the Credit Spread which we just calculated and the Recovery rate.

=> 0.88% = (1 - 60%) * Probability of Default

=> Probability of Default = 0.88% / 40%

Probability of default = 0.022 or 2.20%

Hence, the probability of default of the commercial paper is 2.20%.