Default risk) You buy a very risky bond that promises a 9.5% coupon and return of the

$1,000 principal in 10 years. You pay only $500 for the bond.
a. You receive the coupon payments for three years and the bond defaults. After liquidating
the firm, the bondholders receive a distribution of $150 per bond at the end of 3.5
years. What is the realized return on your investment?
b. The firm does far better than expected and bondholders receive all of the promised
interest and principal payments. What is the realized return on your investment?

To calculate the realized return on your investment, you need to consider the cash flows you receive and the amount you initially invested. Let's analyze both scenarios:

a. In this scenario, you buy the bond for $500 and receive coupon payments for three years. Given that the bond promises a 9.5% coupon, the annual coupon payment would be $1,000 * 9.5% = $95. Therefore, you receive a total of 3 * $95 = $285 in coupon payments.

However, the bond defaults after three years, and the bondholders receive a distribution of only $150 per bond at the end of 3.5 years. Since you initially invested $500 for the bond, you effectively lose $500 - $150 = $350.

To calculate the realized return, you need to sum up all the cash flows you received and deduct the initial investment:

Realized return = (Coupon payments received + Distribution at bond liquidation - Initial investment) / Initial investment

In this case, the realized return would be ($285 + $150 - $500) / $500 = -33%. This negative return means that you incurred a loss on your investment.

b. In this scenario, the bond performs well, and you receive all the promised interest and principal payments. This means you receive $95 annually for ten years as coupon payments and an additional $1,000 at the end of the ten-year period as the principal payment.

Since you initially invested $500 for the bond, your total cash flows received would be $95 * 10 + $1,000 = $1,900.

To calculate the realized return, you use the same formula as before:

Realized return = (Coupon payments received + Principal payment - Initial investment) / Initial investment

In this case, the realized return would be ($95 * 10 + $1,000 - $500) / $500 = 290%. This positive return indicates that you made a substantial profit on your investment.

Note: These calculations assume that there are no additional costs involved, such as transaction fees or taxes.