12th letter to friends of Brunei (Bond's valuation: Duration)

Bond's price and yield are highly sensitive to interest rate movement. We uses the concept of "duration" to express this sensitivity. For example, what would be the expected bond price if interest move up by 2%?

Duration is a measure on how long does it take to recover your invested capital in a bond. The calculation is a bit complex, but let me illustrate with 2 examples.

If Mr. A invests $1000 into a zero coupon bond (par value $1000)with 3 years to maturity. At the end of 3rd year, Mr. A will receive $1000, and the duration is 3 years. If Mr. A invests the same amount in to an 8% coupon bond, the duration could be shorter, say 2.78 years (a rough figure). Because Mr. A has begun to receive the coupons.

The duration (D) information is used to estimate changes in bond price.

% bond price change = - D x changes in interest rates

(the -ve sign denotes the inverse relationship between bond price and interest rate movement)

Example 1: Bond A is an 8% coupon bond, par value $1000, 3 years to maturity and current price is $950.25. The duration is 2.53 years. Estimate the bond price when interest rate falls 1.5%.

% bond price change = -2.53 x -1.5% = 3.795%

Therefore, the new bond price is $950.25 x (1+ .03795) = $986.31

Example 2: Using above information, estimate the bond price if interest rate rises 0.5%.

% bond price change = -2.53 x 0.5% = -1.265%

Therefore, the new bond price is $950.25 x (1- 0.01265) = $938.23