Macaulay Duration vs Modified Duration
Duration is the single most important number for understanding how a bond reacts to interest rate movements. Macaulay duration, introduced by Frederick Macaulay in 1938, is the weighted-average time until a bond's cash flows are received, measured in years. For a 5-year bond paying a 2% annual coupon with a yield to maturity of 3%, the Macaulay duration is approximately 4.7 years, because the small coupon payments pull the weighted average slightly forward from the 5-year maturity. A zero-coupon bond's Macaulay duration equals its maturity exactly, since there is only one cash flow at the end.
Modified duration converts Macaulay duration into a direct measure of price sensitivity: it equals Macaulay duration divided by (1 + yield/n), where n is the number of coupon periods per year. For the bond above, modified duration is roughly 4.7 / 1.03 = 4.56. This means a 1 percentage point rise in interest rates causes the bond's price to fall approximately 4.56%. The distinction matters because Macaulay duration tells you when you get your money back, while modified duration tells you how much you lose when rates move.
Duration in Portfolio Management
Institutional investors use duration matching to align the interest rate sensitivity of their assets with their liabilities. A pension fund that owes payments averaging 15 years into the future will target a bond portfolio with a duration near 15 years, so that rate changes affect both sides of the balance sheet equally. When this alignment breaks, the consequences can be severe: in September 2022, UK pension funds using liability-driven investment (LDI) strategies faced a crisis when gilt yields spiked roughly 1.5 percentage points in days. Funds with leveraged long-duration positions faced margin calls exceeding 100 billion pounds, forcing the Bank of England to intervene with emergency bond purchases.
How Individual Investors Should Think About Duration
For individual investors choosing bond funds, duration is the primary risk dial. A short-duration fund (duration of 1-3 years) will lose roughly 1-3% if rates rise by 1 percentage point, while a long-duration fund (duration of 10-20 years) could lose 10-20%. During the 2022 rate hiking cycle, the Bloomberg U.S. Aggregate Bond Index, with a duration of about 6.2 years, fell roughly 13%, its worst annual loss on record. Investors who assumed bonds were 'safe' were caught off guard because they did not understand duration.
Practical Tips and Limitations
Duration is a linear approximation that works well for small rate changes but becomes less accurate for large moves. Convexity, the second-order effect, captures the curvature in the price-yield relationship. For most individual investors, checking the duration figure on a bond fund's fact sheet is sufficient: match it to your investment horizon. If you plan to hold for 3 years, a fund with a duration near 3 minimizes your interest rate risk over that period. Also remember that duration changes as rates move and time passes, so a fund's duration today may differ from its duration a year from now. Books on fixed-income investing cover duration and convexity in depth