Keeping each present value separate, multiply the present value by the period in which the payment is made. For instance, with a two-year bond paying annual interest payments, you’ll multiply the present value of the first payment by 1 and the second payment by 2. Then add those numbers together and divide by the present value of all the bond’s payments. By using modified duration, investors can gauge a bond’s sensitivity to interest rates. While the formula has limitations, it can be helpful since bonds generally are more complicated than stocks.

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Lastly, we want to think about the relationship between Macaulay duration and yield to maturity. If we look at coupon payments of a fixed-rate bond, we can also see how two similar bonds with different coupon rates can have different duration measures. As such, modified duration is a formula that expresses the measurable change in a security’s reaction to an interest rate change.

If two bonds are identical except for their coupon rates, the bond with the higher coupon rate will pay back its original costs faster than the bond with a lower yield. The higher the coupon rate, the lower the duration, and the lower the interest rate risk. In general, the higher the duration, the more a bond’s price will drop as interest rates rise. For example, if rates were to rise 1%, a bond or bond fund with a five-year average duration would likely lose about 5% of its value.

Macaulay Duration as a Measure of Bond’s Interest Rate Risk

Using the formula above, let’s calculate the Macaulay duration for a hypothetical three-year bond. We begin by calculating the present values of the cash flows from each of the three years. Modified duration works out to 1.83 which means the bond prices increases (decreases) by 1.83% given a 1% decrease (increase) in bond price. Where PV1, PV2 and PVn refer to the present value of cash flows that occur T1, T2 and Tn years in future and PV is the price of the bond i.e. the sum of present value of all the bond cash flows at time 0.

How Investment Professionals Use Macaulay Duration

Any historical returns, expected returns, or probability projections may not reflect actual future performance. The key to successful portfolio immunization is understanding and applying the Macaulay Duration concept effectively. For information pertaining to the registration status of 11 Financial, please contact the state securities regulators for those states in which 11 Financial maintains a registration filing. When continuously compounded, the modified duration is equal to the Macaulay duration. By that, it means that the duration of individual securities in a portfolio can be combined into a duration for that entire portfolio.

Of course, like traditional investments, it is important to remember that alternatives also entail a degree of risk. A mix of portfolio assets also serves to diversify portfolio holdings, which can mitigate overall risk and help protect against inflation. In fact, over the long term, financial planners widely agree that diversification is necessary to investment success. Regarding bond portfolios, the computation of Macaulay Duration necessitates an extra step. A weighted average of the Macaulay Durations of the individual bonds is taken, with each bond’s weight being determined by its proportion of the portfolio’s overall value. Effective Duration takes into consideration the potential changes in cash flows that result from changes in interest rates.

1. This makes intuitive sense using our see-saw as a longer bond would require moving the fulcrum further to the right, increasing the Macaulay duration.
2. In the image below, the calculation of the curved line represents the change in prices, given a change in yields.
3. To understand modified duration, keep in mind that bond prices generally have an inverse relationship with interest rates.
4. Yes, modified duration can be used in some private markets such as income-producing real estate, since these kinds of properties are generally subject to interest rate risk.
5. One such formula is called modified duration, which can help investors judge risk based on changing interest rates.

When interest rates change, the modified duration can tell investors approximately how much the price of a bond will change. Thus, it can be used as a risk management tool, for example, telling investors how much the price of a bond will decrease if interest rates go up by X. As such, unlike the modified duration and Macaulay duration, effective duration looks at the actual change in duration for an upwards and downwards change in yield to maturity for an instrument.

The longer the maturity, the higher the duration, and the greater the interest rate risk. Consider two bonds that each yield 5% and cost $1,000, but have different maturities. A bond that matures in what is modified duration one year would repay its true cost faster than a bond that matures in 10 years. Therefore, the shorter-maturity bond would have a lower duration and less risk.

Understanding modified duration and other duration measures is essential for effective risk management in bond investing. Modified duration is an essential metric in bond investing, as it helps investors assess interest rate risk and manage their bond portfolios effectively. Understanding this measure is crucial for making informed investment decisions and evaluating bond performance.