Bond Duration

The Bond Duration calculation lets you calculate the Macaulay duration and the modified duration of a bond.

The Macaulay duration is the weighted average maturity of a bond's cash flows where the weight of each cash flow is determined by its present value.
It is a measure of "how long" it will take to recover the price of the bond. It is also a measure of sensitivity of the bond's price to changes in its yield.

The modified duration is a measurement of the change in value of a bond in response to a change in interest basis (rate and payment frequency).
It is a measure of sensitivity of the bond's price to changes in its yield. It is also inversely proportional to the approximate percentage change in price for a given change in yield.

Input

• required yield
• settlement date
• redemption date
• annual, semiannual or quarterly coupon rate
• face value
• redemption value

Results

• Macaulay duration

• Modified duration

Note: the price of a bond can be determined by looking at the total of the present value of its cash flows as indicated in the Details.

Examples

•

Example 1

A $1,000 bond, bought on January 1, 2003 and redeemable at par on January 1, 2006, pays semiannual coupons at 9 % compounded semiannually. The required yield is 8 % compounded semiannually.

What are the bond's Macaulay and modified duration?

Input	Required yield:	8 %
	Settlement date [mm/dd/yyyy]:	1/01/2003
	Redemption date [mm/dd/yyyy]:	1/01/2006
	Semiannual coupon rate:	9 %
	Face value:	1,000
	Redemption value:	1,000

Result	Macaulay duration:	2.7
	Modified duration:	2.596

Answer: Macaulay duration is 2.7 years, modified duration is 2.596.

Note: if this were a zero-coupon bond its Macaulay duration would be exactly 3 years.

•

Example 2

The modified duration - altough expressed in years - can also be viewed as the percentage change of a bond's price with respect to a 1 % change in yield.

In the above example, the bond's modified duration is 2.596.

Now switch to Bond Price calculation and note that its purchase price $1,026.21.

If the required yield drops to 7 % this would result in a price of (100 % + 2.596 %) x $1,026.21 or $1,052.85.

If the required yield rises to 9 % this would result in a price of (100 % - 2.596 %) x $1,026.21 or $999.57.

By entering 7 % and 9 % as the required yield, we obtain $1,053.70 and $1,000.00 respectively. As you can see the values that were estimated using the modified duration are pretty close but should still be regarded as an approximation.

Related topics

Zero-Coupon Bond Price