 # How to use the MDURATION function in Excel In this article, we will learn How to use the MDURATION function in Excel.

Scenario :

What is Macauley duration? Macauley duration is the weighted average time recorded to the maturity of cash flows for par value of \$100. Learn more mathematical formulas about macaulay duration here. We calculate the weighted average using the DURATION function in Excel. In contrast to Macaulay duration, modified duration (commonly known as MD) is a price sensitivity measure, defined as the percentage derivative of price with respect to yield for par value of \$100. In excel we can calculate the modified duration using the MDURATION function. The mathematical relation between the two can be shown as shown below.

Modified duration = macaulay duration / ( 1 + market yield/coupon payments per year)

MDURATION function in Excel

MDURATION function returns the modified duration in years for a security for assumed \$100 par value with some required terms. These required terms are given as argument to the function. Let's learn more about the argument in the syntax stated below.

MDURATION function syntax:

 =MDURATION( settlement, maturity , rate , yld , redemption , frequency, [basis])

Settlement : Settlement date of the security

Maturity : Maturity date of the security. The maturity date is the date when the security expires.

rate : The security's annual coupon rate

yld : The security's annual yield rate

frequency - payments per year (1 = annual, 2 = semi, 4= quarterly)

basis - [optional] Day count basis. Default is 0 and for see  the table below.

 Basis Day count basis 0 US (NASD) 30 / 360 1 actual / actual 2 actual / 360 3 actual / 365 4 European 30 / 360

Example :

All of these might be confusing to understand. Let's take an example and apply the function on the given terms on security. Here we have some terms which will be used as arguments in the function.

Use the MDURATION formula:

 =MDURATION( B3 , B4 , B5 , B6 , 2 , 0 ) Here the function returns the 4.09 years for the stated terms on security \$100 assumed par value which is roughly 49 months.

Giving the same arguments to the duration function is stated below.

Use the DURATION formula:

 =DURATION( B3 , B4 , B5 , B6 , 2 , 0 ) Here the function returns the 4.09 years for the stated terms on security \$100 assumed par value which is roughly 52 months.

You must be thinking what could these results be used for. MDURATION function returns the number of years

For example, assume bank A and bank B enter into an interest rate swap. The modified duration of the receiving leg of a swap is calculated as nine years and the modified duration of the paying leg is calculated as five years. The resulting modified duration of the interest rate swap is four years (9 years – 5 years).

Here are all the observational notes regarding using the formula.
Notes :

1. Excel stores dates as serial numbers and is used in calculation by the function. So it’s recommended to use dates as cell reference instead of giving direct argument to the function. Check the date values if the function returns #VALUE! Error.
2. The security settlement date is the date after the issue date when the security is traded to the buyer.
3. Arguments like settlement date, maturity date, frequency & basis are truncated to integers.
4. The function returns the #VALUE! Error if the settlement date & maturity date is not a valid date format.
5. The function returns the #NUM! Error if:
1. Payment Frequency argument is not one of the three (1, 2 or 4)
2. If the basis argument is either < 0 or  > 4.
3. If maturity date settlement value.
4. If coupon rate or yield rate argument is < 0
6. The function generates #VALUE! Error if arguments to the function is non - numeric.

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