The current 1-year spot rate on a treasury bill is 4.25% and the current 1-year spot...

The current 1-year spot rate on a treasury bill is 4.25% and the current 1-year spot rate on a BB-rated bond of equivalent risk to a prospective loan is 11.55%. The bond has a marginal probability of default in year 2 of 8.5% 11. What is the marginal probability of default in year 1? (3 points) 12. What is the cumulative probability of default over the 2 years? (4 points)

Solutions

Expert Solution

The formula to calculate marginal probability of default is given as:

$p_{default}=1-\left [ \frac{1+r_{f}}{1+r_{r}} \right ]$

Where $r_f$ is the risk free rate or spot rate on treasury bill and $r_r$ is the spot rate on risky asset. This formula is derived by assuming that an investor would be indifferent between return on a risky asset multiplied by its probability of repayment (which is equal to 1 - probability of default) and return on a risk less asset.

Substituting values given in the question, we get:

$p_{default}=1-\left [ \frac{1+0.0425}{1+0.1155} \right ]$

which is equal to 0.0654 or 6.54%

The formula to calculate cumulative probability of default is:

$C=1-\left [ (1-p_1)(1-p_2) \right ]$

Where $p_1$ and $p_2$ are marginal probabilities of default in years 1 and 2 respectively. The intuitive sense of the formula is that we are trying to calculate the cumulative probability of repayment by multiplying probabilities of repayment in both years 1 and 2 and then we are subtracting that from 1 to calculate cumulative probability of default.

plugging in the values we get

$C=1-\left [ (1-0.0654)(1-0.085) \right ]=0.1448$

or 14.48%

jeff jeffy answered 1 year ago

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