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Modified duration measures how much a bond's price will change in response to a 1% change in interest rates. It is expressed as a percentage, and the relationship is inverse: when rates rise, bond prices fall, and when rates fall, bond prices rise. A bond with a modified duration of 5 will lose approximately 5% of its value if interest rates increase by 1%, and gain approximately 5% if rates fall by 1%. Think of modified duration as a speedometer for interest rate risk: the higher the number, the faster the bond's price moves in response to rate changes.
Raymond James describes modified duration as "the percentage change in price for each given percent change in interest rates" and notes that it is what most market participants mean when they simply say a bond has a "duration" of a certain number of years.
Modified duration builds on Macaulay duration, which measures the weighted average time to receive all of a bond's cash flows. The formula for converting Macaulay duration to modified duration is straightforward:
Modified Duration = Macaulay Duration ÷ (1 + Yield to Maturity / Number of Coupon Periods per Year)
For a five-year zero-coupon bond with a 7% annual yield, the Macaulay duration equals five years (since there are no intermediate cash flows). Modified duration would be approximately 4.83 years: 5 ÷ (1 + 0.07 ÷ 2) = 5 ÷ 1.035 ≈ 4.83. That means a 1% rise in rates would produce roughly a 4.83% price decline.
Three factors drive a bond's modified duration, and understanding them helps you select bonds that match your interest rate outlook.
Modified duration is a practical portfolio management tool, not just an academic measure. Portfolio managers use it to express and control interest rate risk. A portfolio with an average modified duration of 1 has minimal rate sensitivity, suitable for short horizons or capital preservation objectives. A portfolio with average modified duration above 7 has high sensitivity, appropriate for investors with long horizons who are positioned for falling rates and can absorb price volatility along the way.
Bond portfolio managers targeting a specific duration exposure can construct their holdings to achieve that target. If you expect rates to rise, you shorten duration by shifting toward shorter-maturity bonds. If you expect rates to fall, you extend duration to capture larger price appreciation as yields decline.
Modified duration is an approximation that assumes a linear relationship between price changes and yield changes. In reality, that relationship is curved, a characteristic called convexity. For small changes in yield, modified duration provides a good estimate. For large rate moves, convexity becomes significant and the modified duration approximation understates price gains when rates fall and overstates price losses when rates rise.
Modified duration also assumes that underlying cash flows are fixed. For bonds with embedded options, such as callable bonds or mortgage-backed securities where prepayment speeds vary with rate levels, effective duration is the more appropriate measure. Effective duration accounts for the possibility that cash flows themselves will change when rates change, which modified duration cannot capture.
With deep roots in traditional finance and the digital asset industry, Acquire.Fi operates as a specialist M&A advisory firm. Coverage spans M&A, secondaries, OTC, and capital markets advisory across digital assets and frontier tech. Decades of combined experience across every stage of the deal lifecycle.
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