top of page
Search

MS Excel: DURATION function for Macaulay duration

  • Writer: Fakhriddinbek
    Fakhriddinbek
  • Apr 27
  • 3 min read

The DURATION function in Excel calculates the Macaulay duration of a bond, which is the weighted average time until a bond's cash flows are received. It represents the bond’s interest rate sensitivity or how much the bond price will change with changes in interest rates.


An Excel spreadsheet with a "Function Arguments" window open, showing fields for Settlement, Maturity, Coupon, Yld, and Frequency.

A longer duration typically means the bond is more sensitive to interest rate changes, while a shorter duration means less sensitivity.

The DURATION function is commonly used in fixed income analysis to determine the interest rate risk of a bond.


Syntax


DURATION(settlement, maturity, coupon, yld, frequency, [basis])


Argument

Description

settlement

The bond’s settlement date, which is the date after issuance when the bond is traded to the buyer.

maturity

The bond’s maturity date, i.e., the date the bond will mature and the face value is paid back.

coupon

The bond’s annual coupon rate expressed as a percentage (e.g., 5% would be entered as 0.05).

yld

The bond’s annual yield expressed as a percentage.

frequency

The number of coupon payments per year:


  • 1 = annual

  • 2 = semiannual

  • 4 = quarterly | | basis (Optional) | The day count basis to use for the calculation:

  • 0 = US (NASD) 30/360

  • 1 = Actual/actual

  • 2 = Actual/360

  • 3 = Actual/365

  • 4 = European 30/360 |


Key Points


  • The DURATION function calculates the Macaulay duration of a bond, which measures the weighted average time to receive the bond’s cash flows.

  • A higher duration indicates a greater price sensitivity to interest rate changes, making the bond riskier.

  • The DURATION function is often used by bond investors and portfolio managers to assess the interest rate risk and the overall stability of bond investments.


Practical Example


Scenario:


You are evaluating a bond with the following details:


  • Settlement Date: January 1, 2025

  • Maturity Date: January 1, 2035

  • Coupon Rate: 5% (annual coupon)

  • Yield: 4%

  • Frequency: 2 (semiannual payments)

  • Day Count Basis: Actual/actual


You want to calculate the duration of this bond.


Formula:


=DURATION("2025-01-01", "2035-01-01", 0.05, 0.04, 2, 1)


Explanation:


  • settlement: The bond’s settlement date is January 1, 2025.

  • maturity: The bond matures on January 1, 2035.

  • coupon: The coupon rate is 5% (entered as 0.05).

  • yld: The bond’s annual yield is 4% (entered as 0.04).

  • frequency: The bond pays interest semiannually, so the frequency is 2.

  • basis: The day count basis is 1, which means Actual/actual.


Result: 8.963 years


Explanation:The Macaulay duration for this bond is 8.963 years, meaning the weighted average time it takes to receive the bond’s cash flows is approximately 8.96 years.


Another Example:


Now let’s calculate the duration of a different bond with a higher coupon rate. Assume the following:


  • Settlement Date: March 15, 2025

  • Maturity Date: March 15, 2030

  • Coupon Rate: 6%

  • Yield: 5%

  • Frequency: 4 (quarterly payments)

  • Day Count Basis: Actual/actual


Formula:


=DURATION("2025-03-15", "2030-03-15", 0.06, 0.05, 4, 1)


Result: 4.768 years


Explanation:The Macaulay duration for this bond is 4.768 years, which is shorter than the previous bond. This is because the bond has a higher coupon rate, meaning more of the bond's cash flows are received earlier.


Summary


Item

Value

Bond's Coupon Rate

5% (0.05)

Yield

4% (0.04)

Frequency

2 (Semiannual)

Maturity Date

January 1, 2035

Settlement Date

January 1, 2025

Day Count Basis

Actual/Actual

Duration

8.963 years


Important Notes


  • The DURATION function calculates the weighted average time for the bond’s cash flows based on the yield, coupon rate, and payment frequency.

  • The frequency argument is critical in determining how often interest is paid. For bonds with different payment frequencies (annual, semiannual, or quarterly), the duration will vary.

  • The basis argument can be adjusted depending on the day count convention used by the bond issuer (e.g., Actual/Actual or 30/360).

  • Duration is a useful measure for understanding the interest rate risk of a bond. Bonds with longer durations are more sensitive to changes in interest rates.


When to Use DURATION?


  • To calculate the interest rate sensitivity of a bond and understand the impact of yield changes on its price.

  • In fixed income analysis, especially when managing a portfolio of bonds.

  • To assess interest rate risk in investment strategies, particularly for bond investors.

  • For pricing bonds and determining their duration-based risk for risk management purposes.


Conclusion


The DURATION function in Excel is a powerful tool for calculating the Macaulay duration of a bond, which measures the weighted average time to receive the bond’s cash flows.This calculation is essential for understanding a bond’s interest rate sensitivity and helps investors assess interest rate risk when investing in bonds.

Comments

bottom of page