Question

A bond portfolio is estimated to have a 12% probability of default per dollar invested. In case a default occurs, the average recovery rate is estimated to be 0.31 on the dollar. What is the expected loss per dollar invested? Enter answer accurate to three decimal places. The answer has to be .083. Please show all the steps.

Answer 1

Step 1:

Expected loss per dollar invested = Loss incurred on default x Probability of default

Step 2:

There is 12% probability of default per dollar invested. So, Probability of default = 12% = 0.12

Step 3:

If the bond portfolio defaults, there is an average recovery of 0.31 on the dollar. Therefore, Loss incurred on default = 1 - 0.31 = 0.69

Step 4:

Expected loss per dollar invested = Loss incurred on default x Probability of default

= 0.69 x 0.12

= 0.0828 = 0.083 (rounded off)