Question

You own a $1,000-par zero-coupon bond that has 5 years of remaining maturity. You plan on selling the bond in one year, and believe that the yield to maturity next year will have the following probability distribution:

Probability, Yield %
A. 0.1, 6.6%
B. 0.2, 6.75%
C. 0.4, 7%
D. 0.2, 7.2%
E. 0.1, 7.45%
a. What is your expected price when you sell the bond?
b. What is the standard deviation of the bond price?

Answer 1

To calculate the expected price when you sell the bond, you need to calculate the present value of the bond's future cash flows based on the probability distributions of the yield to maturity. To calculate the standard deviation of the bond price, you need to calculate the variance of the bond price and then take the square root to find the standard deviation.

Step-by-step explanation:

To calculate the expected price when you sell the bond, you need to calculate the present value of the bond's future cash flows based on the probability distributions of the yield to maturity. Given the probability distribution provided, you can calculate the expected price as follows:

1. Calculate the present value of the bond's future cash flows for each yield to maturity using the formula PV = FV / (1 + r)^t, where PV is the present value, FV is the future value (face value of the bond), r is the yield to maturity, and t is the time to maturity.
2. Multiply each present value by its respective probability.
3. Add up all the weighted present values to find the expected price.

To calculate the standard deviation of the bond price, you need to calculate the variance of the bond price and then take the square root to find the standard deviation. The variance can be calculated as the weighted sum of squared differences between each bond price and the expected price, using the respective probabilities. Finally, take the square root of the variance to find the standard deviation.