< Return to Fixed Income

Fixed Income Volatility: Macaulay Duration

The Macaulay Duration estimates when you'll recoup your investment in bonds taking into account interest payments and shifting rates.

Education Hero Image

Excel User Guide for Calculating Macaulay Duration

Introduction

This guide will help you use Microsoft Excel to calculate the Macaulay Duration of a bond. Macaulay Duration is a measure that helps assess the sensitivity of a bond's price to changes in interest rates. It's a valuable tool for bond investors to estimate the average time it takes to receive the bond's cash flows.

Step 1: Gather Bond Information

Before starting, gather the necessary information about the bond:

  • Face value 
  • Coupon rate
  • Coupon payment
  • Time to maturity 
  • Yield to maturity

Step 2: Set Up Excel Sheet

Open a new Excel spreadsheet and organize your data into columns. Label the columns as follows:

  • Column A: Period
  • Column B: Cash Flow 
  • Column C: Time
  • Column D: Present Value
  • Column E: Weighted Contribution

Step 3: Fill in Periods and Cash Flows

In Column A, list the periods from 1 to n (the time to maturity). In Column B, enter the cash flow for each period. For a bond with annual payments, this is the annual coupon payment.

Step 4: Calculate Time

In Column C, calculate the time until receipt of cash flow for each period. For example, in cell C2, enter the formula: =A2.

Step 5: Calculate Present Value

In Column D, calculate the present value for each cash flow. Use the formula: =B2 / (1 + YTM)^C2. Drag this formula down for all periods.

Step 6: Calculate Weighted Contribution

In Column E, calculate the weighted contribution for each period. Use the formula: =D2 * C2. Drag this formula down for all periods.

Step 7: Calculate Bond Price

In a new cell, sum the present values from Column D to get the total bond price. Use the formula: =SUM(D2:Dn).

Step 8: Calculate Macaulay Duration

In another cell, calculate the Macaulay Duration using the formula: =SUM(E2:En) / Bond Price.

Conclusion

You've now successfully calculated the Macaulay Duration of a bond using Excel. This measure provides insights into how the bond's price is expected to react to changes in interest rates. You can use this information for better decision-making in your bond investments.

This article takes inspiration from a lesson found in FIN 4243 at the University of Florida.