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Duration, commonly known as Macaulay duration, determines the weighted average time to receive a bond’s cash flow. Modified duration measures a bond’s price sensitivity to changes in interest rates. Our discussion on “pure” or Macaulay duration measures is very much a theoretical construct. Macaulay Duration serves as a link between bond prices and interest rates, as it measures how sensitive a bond’s price is to changes in interest rates.

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For example, a pension fund with obligations due in 15 years may choose to invest in bonds with a Macaulay Duration of 15 years to match the fund’s liabilities. Investing in stocks and bonds can help to build wealth for anyone with disposable income. The articles and research support materials available on this site are educational and are not intended to be investment or tax advice. All such information is provided solely for convenience purposes only and all users thereof should be guided accordingly. However, long and short mean something different when used to describe trading strategies based on duration. A Roth conversion ladder moves money from traditional IRAs to Roth accounts over time.

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Convexity, another measure of bond price sensitivity, accounts for this nonlinearity and provides a more accurate estimate of bond price changes for larger yield fluctuations. Modified duration is used to evaluate bond performance by comparing it against benchmarks and conducting attribution analysis. This measure helps investors understand the sources of their portfolio’s performance, including the impact of interest rate changes. Investors employ modified duration in designing bond portfolio strategies, such as active and passive management, duration matching, and convexity optimization.

Macaulay Duration plays a pivotal role in ALM, as institutions often seek to match the durations of their assets and liabilities to minimize interest rate risk. Ultimately, it guides strategic investment decisions, contributing to risk management and the potential for higher returns. Founded in 1993, The Motley Fool is a financial services company dedicated to making the world smarter, happier, and richer. Recall that modified duration illustrates the effect of a 100-basis point (1%) change in interest rates on the price of a bond. In order to arrive at the modified duration of a bond, it is important to understand the numerator component – the Macaulay duration – in the modified duration formula. Modified duration is used to manage interest rate risk through strategies like portfolio immunization and asset-liability management.

1. These organizations often hold bonds in their fixed-income portfolios with prices that can fluctuate based on interest rate changes.
2. As interest rates fluctuate, so do the value of the assets held by the fund and the rate at which those assets generate income.
3. Unlike conventional mortgages, ARMs don’t decline in value when market rates increase, because the rates they pay are tied to the current interest rate.
4. As a rule of thumb, the longer the Macaulay Duration, the higher the interest rate risk for a bond.
5. The valuation of securities, particularly bonds, changes as interest rates change.

How is modified duration calculated?

This is the point of time represented by the orange triangle above measured in years. The unit of Macaulay’s duration and the modified duration is the same as the units in which maturities are entered. For example if we enter the time period in months, we get the monthly duration, which can be annualized by simple multiplication with 12. Graphically, Macaulay Duration is the point of balance (in years) what is modified duration for the cash flows from the bond (see below). A 5-year annual payment of $11,000 bond has a Macaulay duration of 1.5 years. A 4-year annual payment of $12,000 bond has a Macaulay duration of 5.87 years.

Yes, modified duration can be negative for bonds with cash flows that increase as interest rates rise. In this case, the bond’s price would actually increase as interest rates rise, and the modified duration would be negative. For example, a bond with a modified duration of 5 years would be expected to experience a 5% change in price for a 1% change in yield. If interest rates were to rise by 1%, the price of the bond would be expected to decline by approximately 5%. Modified duration is important because it provides critical valuation insight to bond investors.

Modified duration is better than maturity because the Modified duration facilitates a clear plan with a prospective effect on a bond price due to a change in the interest rate. The opposite is true of low convexity bonds, whose prices don’t fluctuate as much when interest rates change. When graphed on a two-dimensional plot, this relationship should generate a long-sloping U shape (hence, the term “convex”). This relationship is more pronounced for bonds with longer Macaulay Durations. Hence, if interest rates are expected to rise, an investor may prefer bonds with shorter Macaulay Durations to limit price volatility. Asset-Liability Management (ALM) is an essential practice in financial institutions, where the objective is to manage the use of assets and cash flows to meet company obligations.