Question

A newly issued bond with 1 year to maturity has a price of $1,000, which equals its face value. The coupon rate is 15% and the probability of default in 1 year is 35%. The bond’s payoff in default will be 65% of its face value.

a. Calculate the bond’s expected return.
b. Use a data table to show the expected return as a function of the recovery percentage and the price of the bond.

Answer 1

The bond's expected return is the sum of the expected payments weighted by their respective probabilities. With a coupon rate of 15%, a default probability of 35%, and a recovery rate of 65%, the expected return is negative. A data table can show the expected return for varying recovery percentages and bond prices.

Step-by-step explanation:

Calculation of the Bond's Expected Return

To calculate the bond's expected return, we must consider both the scenario where the bond does not default and the scenario where it defaults. Given the bond has a coupon rate of 15% on its $1,000 face value, it will pay $150 in interest ($1,000 * 0.15). If the bond does not default, the total payment will be the face value plus the interest payment, which amounts to $1,150 ($1,000 + $150).

In the event of default, the bond's payoff is 65% of its face value, which equates to $650 ($1,000 * 0.65). The probability of default is given as 35%, so the expected payoff in the event of default is $227.50 ($650 * 0.35).

The bond's expected return, considering the probabilities of both scenarios, is calculated as follows:

1. Expected payoff if the bond does not default: 65% probability * $1,150 = $747.50
2. Expected payoff if the bond defaults: 35% probability * $227.50 = $79.63
3. Total expected payoff = $747.50 + $79.63 = $827.13

The bond's expected return is then the expected payoff ($827.13) minus the bond price ($1,000), which equals a negative return of -$172.87.

Expected Return as a Function of Recovery Percentage and Bond Price

The expected return can be displayed as a function of the recovery percentage and the bond price by creating a data table where the rows represent different potential recovery percentages and the columns represent different bond prices. Each cell in the table would show the expected return calculated by adjusting the recovery rate in the formula above.

Assuming we want to use a fixed bond price of $1,000 for illustration:

• If recovery percentage is 65%, as mentioned in the question, the expected return has already been calculated as -$172.87.
• For different recovery percentages, the calculation would adjust the $650 figure in the 'expected payoff if the bond defaults' step to match the respective recovery percentage.