Macaulay Duration is the weighted average time until a bondholder receives the bond's cash flows. Each cash flow is weighted by its present value as a proportion of the bond's total price. The formula sums (t × PV(CF_t)) / Price across all periods, where t is measured in years. A higher Macaulay Duration means a longer effective maturity and greater sensitivity to rate changes.

Modified Duration builds on Macaulay Duration to directly estimate price sensitivity: Modified Duration = Macaulay Duration / (1 + y/freq). It approximates the percentage price change for a 1% change in yield. For example, a Modified Duration of 7.5 means the bond price will drop approximately 7.5% if yields rise by 1 percentage point, assuming a linear approximation.

Duration is a first-order approximation. For large yield changes, convexity (a second-order measure) becomes important because the price-yield relationship is curved, not linear. Portfolio managers use duration to match assets and liabilities, hedge interest rate risk, and construct immunized portfolios that are protected against small yield movements.