### Macauley Duration

Often abbreviated to just **Duration**

This is not used much in the real world.

To provide a somewhat better measure than maturity, we can compute the macaulay duration of a set of cash flows.

The weighted average number of years that the bond holder receives interest and principal payments

This type of duration only makes sense for instruments with fixed cash flows.

This is a very simple measure that uses the weighted-average term to maturity of the cash flows.

The weight of each cash flow is determined by dividing the present value of the cash flow by the price.

This is the percentage change in the bond price with respect to interest rates.

Has the unit of years

This is the weighted average term to payment of the cash flows.

This value is always less than or equal to the overall life of the bond.

Only a zero coupon bond will have a duration equal to the maturity.

This can be calculated in Excel using the __DURATION__ function.

DURATION (settlement, maturity, coupon, yield, frequency, basis)

The DURATION function calculates a Macauley duration given the settlement date, maturity date, coupon rate, yield, frequency, and basis. It uses the following syntax:

For example, suppose you want to calculate the duration of a bond you purchased on April 23, 2000, and that will mature on November 30, 2020. Further suppose that the coupon rate is 8%, which is paid in four quarterly payments, but that the bond yield is 7%. If you want to use the US (NASD) day count basis of 30 days in a month and 360 days in a year, you would use the following formula to calculate this bond's yield:

=DURATION ("4/23/2000","11/30/2020",.08,.07,4,0)

The formula returns the value 10.6496.

Example - Lets consider a 3yr 7% coupon on a £100 bond

First calculate the present value of the cash flows

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