Question

Suppose you are trying to determine the interest rate sensitivity of two bonds. Bond 1 is a 12% coupon bond with a 7-year maturity and a $1000 principal. Bond 2 is a ‘zero-coupon’ bond that pays $1120 after 7 year. The current interest rate is 12%.

- Determine the duration of each bond.

- If the interest rate increases 100 basis points (100 basis points = 1%), what will be the capital loss on each bond?

Answer 1

Solution

Part A ) Determining the duration of the bond

Bond 1 : Face value = 1000, Coupon = 12% ,Yield = 12% , Time = 7 years

Duration for this bond is calculated in excel and given below

Macaulay duration is 5.11, Modified Duration = Macaulay / (1+ yield) = 4.56

BOND 2

For zero coupon bond, Macaulay duration is same as the time to maturity  

So, Macaulay duration = 7

Modified Duration = Macaulay / (1 + yield ) = 7 / 1.12 = 6.25

Part B ) Determining the change in price with the help of modified duration

Change in price / Price = - Duration * change in yield

For Bond 1: Change in price = -4.56 * 0.01 *1000 = -45.60

So capital loss due to change in price = -45.60

For Bond 2 .

Zero coupon bond Price = Maturity value / (1+yield )^year = 1120 / 1.12^7 = 506.63 (Where interest rate = 12%)

Zero coupon bond Price = Maturity value / (1+yield )^year = 1120 / 1.13^7 = 476.07 (Where interest rate = 13%)

Capital loss due to change in interest = 506.63 - 476.07 = 30.56