What is the probability of default for the corporate bond assuming the recovery rate is zero?

A corporate bond maturing in 1 year yields 8.5% per year,while a similar treasury bond yields 4% .

What is the probability of default for the corporate bond assuming the recovery rate is zero?
A . 4.15%
B . 4.50%
C . 8.50%
D . Cannot be determined from the given information

View Answer

Answer: A

Explanation:

The probability of default would make the future cash flows from both the bonds identical. If p be the probability of default, the cash flows from the risky corporate bond would be = (cash flows in the event of default x probability of default) + (cash flows without default x (1 – probability of default)) => p*0 + (1 – p)*(1 + 8.5%) = (1 – p)*1.085.

The cash flows from the treasury bond would be 1.04. These two should be equal, ie, 1.04 = (1-p)*1.085, implying p = 4.15%.

(Note: The above is a simplification intended for the exam. In reality investors would demand a ‘credit risk premium’ for the corporate bond over and above the expected default loss rate. They are unlikely to be happy with just being compensated with exactly the expected default loss rate plus the risk-fre rate because the expected default loss rate itself is uncertain. They would demand some premium over and above what the default rate alone might mathematically imply above the risk free rate. In this question, this credit risk premium is ignored.)