Evaluating a bond’s performance would be relatively easy if the market never changed over the course of its maturity period. Because that’s impossible, evaluating a stock can be a difficult process. Modified duration is a measure investors use to determine a security’s ability to withstand changes in common interest rates in the market. It is also based on another duration measurement, Macauley duration, which measures the time needed for a bond investment to recoup its principal and interest payments. Modified duration measures are more accurate when interest rates change less than 1 percent, but become less reliable with larger changes.

## Calculating Macauley Duration

Set the bond’s expected yield price as variable BEY. In our example, a bond has an expected yield of $100, so BEY = 100 and matures in two years, or four coupon periods.

Determine the coupon rate, represented by C. If the bond pays semiannually, C is equal to half the annual rate. Our example bond pays 6 percent biannually, so C = 3.

Determine the expected yield rate per payment period by dividing the BEY rate by the number of payments. Then convert the rate to a basis of 100 percentage points as variable R. The advertised BEY rate for the investment is 8 percent, and paying semiannually, which yields 4 percent return each coupon period. This can be represented at 1.04 for the example.

Calculate the Macauley duration, d, by plugging terms into the equation: D = 1/BEY + SUM (1 * [C/r^1) + 2 * [C/r^2] + 3 * [C/r^3] … n * [C/r^n]

In the example, D = 1/100 + ( 1 * [3/1.04^1] + 2 * [3/1.04^2] + 3 * [3/1.04^3] +4 * [3/1.04^4]) D = 1.91.

## Calculating Modified Duration

Define D as the Macauley’s duration for the bond. In this example, D = 1.91, as calculated in the previous section.

Establish variable R as the interest rate paid each period. Continuing the example of the previous step, with a 8-percent yield paid biannually, R = 4. Express this figure in terms of percentage yield, so R = 1.04.

Compute modified duration using the formula: MD = D/(1+R)

In the example, MD = 1.91/(1 + 1.04) Or MD = 0.94.

#### Tips

Many spreadsheets and financial software compute Macauley duration and modified duration automatically for their users. Consult your spreadsheet's documentation to determine how to activate the automatic calculation feature.

References

- Western Washington University: Valuation of Bonds
- San Francisco State University: Duration, Convexity and Interest Rate Risk
- Metro State College of Denver: Valuation of Bonds
- Milken Institute. "An Introduction to Duration." Accessed Sept. 25, 2020.
- New York University. "Duration and Convexity." Accessed Sept. 25, 2020.

Tips

- Many spreadsheets and financial software compute Macauley duration and modified duration automatically for their users. Consult your spreadsheet's documentation to determine how to activate the automatic calculation feature.

Writer Bio

Wilhelm Schnotz has worked as a freelance writer since 1998, covering arts and entertainment, culture and financial stories for a variety of consumer publications. His work has appeared in dozens of print titles, including "TV Guide" and "The Dallas Observer." Schnotz holds a Bachelor of Arts in journalism from Colorado State University.