Question

A 20-yr bond making annual payments with a coupon rate of 4% has duration of 13.681, and convexity of 225.94. The bond currently sells at a yield to maturity of 48 IV. 5%.

a. Find the price of the bond if rates increase to 6%
b. what price would be predicted by the duration rule?
c. what price would be predicted by the duration+convexity rule?
d. what do you conclude about the accuracy of the two rules?

Answer 1

To find the price of the bond given a change in interest rates, you can use the duration rule or duration+convexity rule. By comparing the predicted prices with the actual price, you can determine the accuracy of these rules.

Step-by-step explanation:

a. To find the price of the bond if rates increase to 6%, you can use the formula:

Price = Coupon Payment x (1 - (1 + Yield)^(-Duration)) / Yield + Face Value x (1 + Yield)^(-Duration)

Using the given information and substituting the values, the price of the bond will be calculated.

b. The price predicted by the duration rule can be calculated using the formula:

Price = Price at current yield x (1 + Duration x (Change in yield))

c. The price predicted by the duration+convexity rule can be calculated by using the formula:

Price = Price at current yield + (1/2) x (Convexity x (Change in yield)^2)

d. By comparing the calculated prices with the actual price, you can conclude the accuracy of the duration and duration+convexity rules.