Wall Street bond expert Michael Brandes, in his book “Naked Guide to Bonds,” defines duration as “the percentage change in a bond's price given each 1 percent rise or fall in interest rates.” A bond with 6.5 years' duration would rise or fall by approximately 6.5 percent, while a 30-year bond with a 13-year duration would rise or fall by approximately 13 percent for every 1 percent change in rates. Effective duration is used with callable bonds, which give issuers the right to redeem (“call”) their bonds before maturity. For straight or ordinary bonds, use Macaulay's or modified duration formulas.
Calculating Effective Duration for a Single Bond
Get the bond's current price from your broker or from the Yahoo! Finance Bonds Center (see Resources).
Calculate the bond's Option Adjusted Spread (OAS) with a free OAS calculator available on the web or manually, if you are a math whiz.
Take the Treasury yield curve and shift it up by a hypothetical increase in the interest rate to generate a new interest rate path. F ind the current Treasury yield curve on Bloomberg, Yahoo!Finance and other financial websites.
Calculate a present value PVup for the bond's cash flows under the new interest rate scenario, using the OAS derived in Step 2.
Repeat the Treasury yield curve exercise, but this time shift the curve down by the same amount as in Step 3.
Calculate a present value PVdown for the bond's cash flows under this interest rate scenario, again using the derived OAS.
Plug the found values into the following formula to find effective duration stated in years: Deffective = - [(PVup – PVdown)/2 x Delta “i” x P], where Delta “i” is the hypothetical change in the interest rate and P is the price of the bond.
Calculating Weighted Average Effective Duration for a Portfolio
Calculate the effective duration for each bond in the portfolio.
Find the portfolio weight of each bond in the portfolio. Example: Bond A for $100,000 divided by the portfolio's total $1,000,000 value gives it a weight of 0.10
Multiply each bond's portfolio weight by its effective duration.
Add up the results from Step 3 to arrive at the the portfolio's weighted average duration.
Lower duration results in less bond price volatility. Manage your portfolio's exposure to expected interest rate changes by either lengthening or shortening its weighted average duration. Lengthen it when you expect interest rates to drop (bond prices increase) to maximize gains; shorten it if rates will rise (bond prices decrease) to minimize losses.
Automate duration, OAS and present value calculations for individual bonds or entire portfolios by using bond calculators embedded in financial management software or in Microsoft Excel. If you have a brokerage account, use your brokerage's online tools or lean on your broker to supply duration statistics.
Duration, while useful, is an imperfect tool. A bond’s price is dependent on many variables apart from the duration calculation. Seek reliable professional investment advice for more highly refined approaches to investing in and managing bonds.
- Duke University: Duration Measures
- California Debt and Investment Advisory Commission: Duration Basics
- "Naked Guide to Bonds"; Michael V. Brandes; 2003