Question

Bond Sam has 6% coupons, makes semi-annual payments and is priced at par value. Bond sam has 6 years to maturity. If interest rates suddenly rise by 2% what is the percentage change in the price of bond Sam?

Answer 1

Assuming face value to be $1000

Since bond is priced at par, price = $1,000

When price of the bond is equal to face value, coupon rate will be equal to YTM.

Therefore, YTM = 6%

Price after rise in interest rate:

Semi annual interest rate = (6% + 2%) / = 4%

Coupon = (6% of 1000) / 2 = 30

Number of periods = 6 * 2 = 12

New price = Coupon * [1 - 1 / (1 + r)^n] / r +FV / (1 + r)^n

New price = 30 * [1 - 1 / (1 + 0.04)^12] / 0.04 + 1000 / (1 + 0.04)^12

New price = 30 * [1 - 0.624597] / 0.04 + 624.59705

New price = 30 * 9.385074 + 624.59705

New price = $906.14926

Percentage change in price = [(Ending value - beginning value) / beginning value] * 100

Percentage change in price = [(906.1426 - 1000) / 1000] *

Percentage change in price = -9.39%