Modified Duration: Meaning, Formula, Examples The Motley Fool

This bond has an annual coupon rate (the yield paid through maturity) of 5%. Modified duration can be calculated by dividing the Macaulay duration of the bond by 1 plus the periodic interest rate, which means a bond’s Modified duration is generally lower than its Macaulay duration. If a bond is continuously compounded, the Modified duration of the bond equals the Macaulay duration.

1. The Macaulay duration is calculated by multiplying the time period by the periodic coupon payment and dividing the resulting value by 1 plus the periodic yield raised to the time to maturity.
2. This measure measures the percentage change in bond price for a 1% change in yield, assuming all other factors remain constant.
3. The Macaulay duration and the modified duration are both essential measures of bond duration that provide valuable information to investors.
4. This means that the price of the bond will increase by 2.54% for every 1% decrease in the interest rate.
5. If you are interested in a further discussion of the difference between Macaulay, modified and effective duration, here is a little quiz I wrote in our forum.
6. Another difference between Macaulay duration and Modified duration is that the former can only be applied to the fixed income instruments that will generate fixed cash flows.
7. This means that the price change for a given change in yield is not constant.

Formula to calculate modified duration

It is a weighted average of the time until each payment is received, with the weights being the present value of each payment divided by the total present value. This means that yield to maturity and Macaulay duration have an inverse relationship. You can also find online calculators that can help you calculate both Macaulay and modified durations. Several websites offer these online calculators that can be used for free.

Modified duration is another frequently used type of duration for bonds. The Macaulay duration is the weighted average of time until the cash flows of a bond are received. In layman’s term, the Macaulay duration measures, in years, the amount of time required for an investor to be repaid his initial investment in a bond. A bond with a higher Macaulay duration will be more sensitive to changes in interest rates.

1. In other words, it illustrates the effect of a 100-basis point (1%) change in interest rates on the price of a bond.
2. Alternatively, and often more usefully, convexity can be used to measure how the modified duration changes as yields change.
3. Macaulay Duration is a financial concept that is used to measure the sensitivity of a bond’s price to interest rate changes.
4. Second, as a bond’s coupon increases, its duration decreases and the bond becomes less volatile.
5. Hence, if we picture the see-saw, the duration for a zero-coupon bond would be equal to its term to maturity, as we see in the illustration below.
6. Similar risk measures (first and second order) used in the options markets are the delta and gamma.

Does a Zero-Coupon Bond Pay Interest?

For example, if a bond has a modified duration of 5, it means that for every 1% increase in interest rates, the bond’s price will decrease by 5%. Macaulay Duration is a financial concept that is used to measure the sensitivity of a bond’s price to interest rate changes. It is named after Frederick Macaulay, who introduced the concept in 1938.

Periodically compounded

Unlike the Macaulay duration, modified duration is measured in percentages. Lastly, we want to think about the relationship between Macaulay duration and yield to maturity. In the figure above, we have a simplified diagram of a five-year fixed-rate, annual-pay coupon bond. Each of the bars represents interest cash flows, or coupons, and a final cash flow consisting of the principal and the final interest payment.

Thus, the modified duration can provide a risk measure to bond investors by approximating how much the price of a bond could decline what is modified duration with an increase in interest rates. It’s important to note that bond prices and interest rates have an inverse relationship with each other. Modified duration measures the average cash-weighted term to maturity of a bond. The concept of duration is fundamental in bond investing as it helps investors determine how much the price of a bond will change in response to changes in interest rates.

A fixed income security with a greater duration indicates a higher sensitivity to interest rates and thus, the greater the interest rate risk it has. And as the price of most fixed income securities have an inverse relationship with yields, a security with a greater duration will have more interest rate risk than a security with a shorter duration. With the inequalities being strict unless it has a single cash flow. In terms of standard bonds (for which cash flows are fixed and positive), this means the Macaulay duration will equal the bond maturity only for a zero-coupon bond. The Macaulay duration is the sum of these weighted-average time periods, which is 1.915 years. An investor must hold the bond for 1.915 years for the present value of cash flows received to exactly offset the price paid.

Duration is not the same as maturity

Modified duration can help investors and portfolio managers make more informed decisions about bond investments. For example, if an investor expects interest rates to rise, they may consider investing in bonds with shorter modified durations to reduce their exposure to interest rate risk. Both modified and dollar duration, therefore, are metrics for how sensitive a bond’s price is to movements in its yield. The price of a longer modified or dollar duration fixed-income instrument will move more significantly to a change in yield as compared to the price of a shorter modified or dollar duration instrument. The modified duration measure takes duration one step further and gives the percentage change in the bond’s price per basis point.

Dollar duration measures the dollar change in a bond’s value to a change in the market interest rate, providing a straightforward dollar-amount computation given a 1% change in rates. A bond’s price is calculated by multiplying the cash flow by 1, minus 1, divided by 1, plus the yield to maturity, raised to the number of periods divided by the required yield. The resulting value is added to the par value, or maturity value, of the bond divided by 1, plus the yield to maturity raised to the total number of periods. Modified duration helps investors understand this relationship by measuring the sensitivity of a bond’s price to changes in interest rates.

Dollar duration or DV01 is the change in price in dollars, not in percentage. It gives the dollar variation in a bond’s value per unit change in the yield. It is often measured per 1 basis point – DV01 is short for “dollar value of an 01” (or 1 basis point). The name BPV (basis point value) or Bloomberg “Risk” is also used, often applied to the dollar change for a $100 notional for 100bp change in yields – giving the same units as duration. PV01 (present value of an 01) is sometimes used, although PV01 more accurately refers to the value of a one dollar or one basis point annuity.

Modified duration follows the concept that interest rates and bond prices move in opposite directions. This formula is used to determine the effect that a 100-basis-point (1%) change in interest rates will have on the price of a bond. Modified duration is not a perfect measure of interest rate risk.

When the commodity is money, spot prices are called spot rates (a.k.a., spot interest rate). A spot price is simply the market’s current price to buy or sell a commodity for immediate delivery… For example, if an investor owns a bond with a Macaulay Duration of 5 years, it means that if interest rates rise by 1%, the bond’s price will fall by approximately 5%.

These organizations often hold bonds in their fixed-income portfolios with prices that can fluctuate based on interest rate changes. In asset-liability portfolio management, duration-matching is a method of interest rate immunization. A change in the interest rate affects the present value of cash flows, and thus affects the value of a fixed-income portfolio. Modified duration is important because it allows us to assess the risk of investing in bonds. If you’re investing in bonds, you want to know how much the bond’s price will fluctuate in response to changes in interest rates. Modified duration gives you a sense of the bond’s price sensitivity, which can help you make a more informed investment decision.