The modified duration is often considered as an extension of the Macaulay duration. Unlike the Macaulay duration, modified duration is measured in percentages. The modified duration figure indicates the percentage change in the bond’s value given an X% interest rate change. It is primarily applied to bonds, but it can also be used with other types of securities that can be considered as a function of yield. Relative to the Macaulay duration, the modified duration metric is a more precise measure of price sensitivity. V – The present value of all cash flows from the asset.PV i – The present value of the ith cash flow from the asset.t i– The time until the ith cash flow from the asset will be received.The formula for the calculation of Macaulay duration is expressed in the following way: For zero-coupon bonds, the duration equals the time to maturity. The Macaulay duration for coupon-paying bonds is always lower than the bond’s time to maturity. The Macaulay duration is measured in units of time (e.g., years). It is a measure of the time required for an investor to be repaid the bond’s price by the bond’s total cash flows. The concept was introduced by Canadian economist Frederick Macaulay. Macaulay duration is a weighted average of the times until the cash flows of a fixed-income instrument are received. The most common are the Macaulay duration, modified duration, and effective duration. The duration metric comes in several modifications. A full analysis of the fixed-income asset must be done using all available characteristics.ĬFI’s Fixed Income Fundamentals Coursecovers the essential topics for fixed-income valuation. However, duration only reveals one side of a fixed-income security. Using interest rate forecasts, a portfolio manager can change a portfolio’s composition to align its duration with the expected level of interest rates. The general rule states that a longer duration indicates a greater likelihood that the value of a bond will fall as interest rates increase.ĭuration is commonly used in the portfolio and risk management of fixed-income instruments. Since the interest rate is one of the most significant drivers of a bond’s value, duration measures the sensitivity of the value fluctuations to changes in interest rates. It is a tool used in the assessment of the price volatility of a fixed-income security. Duration is one of the fundamental characteristics of a fixed-income security (e.g., a bond) alongside maturity, yield, coupon, and call features.
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