Question

The duration of an 11-year, $1,000 Treasury bond paying a 12% semi-annual coupon and selling at par (yield = coupon rate) has been estimated at 6.5 years. What will be the estimated price change on the bond if interest rates increase 0.20 percent? ΔR=0.002

Answer 1

Duration: The term duration refers to a measure which indicates the extent to which price of bonds changes as the yields or interest rate changes. In other words the duration is the approximate changes in the price of bond given 100 basis points change in interest.

Following formula is used to compute approximate percentage price change:

= Duration × ∆y∗ × 100

Where,

∆y is change in yield (in decimal) for which we are required to compute the percentage price changes.

Lets compute the approximate percentage price change given the duration and change in yield.

Given,

Duration = 6.5

∆y = .002

Applying the above formula, we have the following equation:

= -6.5 × (+0.002) × 100 = - 1.3%

Applying the approximate percentage price change to the face value we can compute the price change as below

@1,000 × -1.3% = ($1,000 - $13) = $987.

Please note the bonds price and yield have inverse relationship. As the rate of yield increases the price of the bonds decreases and vice versa.