Macaulay = Sum(t x PV_CF) / Bond Price
Modified = Macaulay / (1 + YTM/n)
Modified duration estimates the percentage price change for a 1% change in yield to maturity.
Bond duration is a measure of the sensitivity of a bond's price to changes in interest rates. It represents the weighted average time until a bondholder receives the bond's cash flows. Duration is expressed in years and is one of the most important concepts in fixed-income investing, helping investors understand and manage interest rate risk in their portfolios.
There are two primary types of duration: Macaulay duration, which measures the weighted average time to receive cash flows, and Modified duration, which estimates the percentage change in bond price for a 1% change in yield. Both measures are essential tools for bond portfolio management and risk assessment.
Macaulay duration calculates the weighted average number of years an investor must hold a bond until the present value of cash flows equals the amount paid for the bond. It is particularly useful for immunization strategies where the goal is to match the duration of assets and liabilities. A bond with a higher Macaulay duration will take longer to recoup its cost through cash flows.
Modified duration, derived from Macaulay duration, directly measures price sensitivity to yield changes. If a bond has a modified duration of 5 years, a 1% increase in interest rates would cause approximately a 5% decrease in the bond's price. This makes modified duration the preferred measure for assessing interest rate risk and constructing hedging strategies.
Several factors influence a bond's duration. Time to maturity is the most significant -- longer-maturity bonds have higher durations because cash flows are received further in the future. Coupon rate also plays a role; higher coupon bonds have lower durations because a greater proportion of total cash flows are received earlier. Additionally, yield to maturity affects duration inversely; as yields rise, duration decreases.
Payment frequency impacts duration as well -- bonds paying coupons more frequently (e.g., quarterly vs. semi-annually) will have slightly lower durations. Zero-coupon bonds represent the extreme case where Macaulay duration equals time to maturity, as all cash flows are received at the end. Understanding these relationships helps investors make informed decisions about portfolio construction and interest rate risk management.