Modified Duration Formula, Calculation, and How to Use It

The bond price is simply the amount that the issuing entity is asking for the bond. In contrast, the bond value is based on more criteria than simply the asking price. This example shows how knowing the modified duration allows us to make a simple calculation to determine the (approximate) price of the bond. Of course, we could recalculate the price of the bond by accounting for the yield changes, but that is more complicated then the above approach.

• The modified duration provides a good measurement of a bond’s sensitivity to changes in interest rates.
• A higher reading indicates higher sensitivity to interest rate changes, which on the other hand leads to greater price volatility.
• For example if we enter the time period in months, we get the monthly duration, which can be annualized by simple multiplication with 12.
• As the modified duration of a bond increases, so does its interest rate risk.

Taxes on Investments: Understanding the Basics

Divide the present value of each coupon payment by the calculated market value of the bond. For each result, multiply the result by the number of years that have elapsed; multiply that result by -1. Remember, while the modified duration can provide a meaningful snapshot of interest rate risk, it should certainly not be the only factor considered when purchasing bonds. Other aspects such as credit risk of the issuer, the liquidity of the bond, tax considerations, among others, should also be taken into account. Duration is a measure of the average (cash-weighted) term-to-maturity of a bond.

Modified Duration: Understanding its Role in Bond Price Fluctuations

The formula to calculate the percentage change in the price of the bond is the change in yield multiplied by the negative value of the modified duration multiplied by 100%. This resulting percentage change in the bond, for an interest rate increase from 8% to 9%, is calculated to be -2.71%. Therefore, if interest rates rise 1% overnight, the price of the bond is expected to drop 2.71%.

Impact on Modified Duration and Bond Prices in a Falling Interest Rate Environment

In truth, the relationship between bond prices and interest rates isn’t strictly linear, especially for large changes in yield. The concept of convexity was introduced to handle this non-linearity which modified duration overlooks. The modified duration hence acts as a measure of the sensitivity of bond prices to changes in interest rates. When it comes to bond portfolio management, the concept of modified duration plays a pivotal part. It quantifies the sensitivity of the price of a bond to changes in interest rates.

By using convexity in the yield change calculation, a much closer approximation is achieved (an exact calculation would require many more terms and is not useful). Modified duration is a measure of a bond price sensitivity to changes in its yield to maturity. It is calculated by dividing the Macaulay’s duration of the bond by a factor of (1 + y/m) where y is the annual yield to maturity and m is the total number of coupon payments per period. Conversely, if interest rates were to decrease, bonds with higher modified durations would increase in price more than those with lower durations. Modified Duration is a key metric in fixed income portfolio management that measures the sensitivity of a bond’s price to changes in interest rates.

To calculate Macauley duration, you have to figure out the timing of all cash flows from the bond. Most bonds make relatively small interest payments and then make a big principal repayment at maturity. The fund invests in the investment grade spectrum of the market, which is considered to be the least likely to default, with the typical maturity being somewhere between one and five years.

Generally, bonds with a higher modified duration tend to have more volatile prices. Depending on the yield movement, they can offer higher returns or higher losses. The effective duration is another key metric in analysing the sensitivity of a bond’s price to changes in interest rates, but it is however applied to different portfolios. It is used for bonds that have embedded options and factors in that expected cash flows will vary as interest rates change. 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.

• The bottom line is that you don’t have to shy away from using modified duration because of its complexity.
• Then, the resulting value is added to the total number of periods multiplied by the par value, divided by 1, plus the periodic yield raised to the total number of periods.
• For example, it is a linear approximation for small changes in yield and it assumes that duration stays the same along the yield curve (which is often not the case).
• Understanding this measure is valuable, particularly for longer-term investors who are considering an extensive timeline before the bond’s maturity.
• Then, add those numbers together and divide the result by the present value of all the bond’s payments.

Using Modified Duration in Strategy Formulation

Recall that modified duration illustrates the effect of a 100-basis point (1%) change in interest rates on the price of a bond. Modified duration illustrates the concept that bond prices and interest rates move in opposite directions – higher interest rates lower bond prices, and lower interest rates raise bond prices. This result shows that it takes 2.753 years to recoup the true cost of the bond. First, as maturity increases, duration increases and the bond becomes more volatile.

Macaulay Duration vs. Modified Duration: What’s the Difference?

In plain-terms – think of it as an approximation of how long it will take to recoup your initial investment in the bond. Yield to Maturity (ytm) is the internal rate of return of a bond, incorporating all coupon payments and the redemption at maturity. Modified duration is an unfamiliar term for many investors, but the underlying idea probably isn’t. The valuation of securities, particularly bonds, changes as interest rates change.

Macaulay’s duration measures the weighted average time till the bond cash flows. Modified duration adjusts Macaulay’s duration so that it can be used to estimate the price movement given a change in yield. Modified duration doesn’t just provide a measure to anticipate potential changes in bond prices. Its importance lies beyond the realm of calculating potential volatility, to be seen as a tool for risk management. As the modified duration of a bond increases, so does its interest rate risk. Essentially, bonds with a higher modified duration will experience a significant percentile decrease in price for a 1% rise in interest rates, all else being constant.

The formula for the modified duration of the interest rate swap is the modified duration of the receiving leg minus the modified duration of the paying leg. Modified duration could be extended to calculate the number of years it would take an interest rate swap to repay the price paid for the swap. An interest rate swap is the exchange of one set of cash flows for another and is based on interest rate specifications between the parties.

For this reason, Modified Duration is seen as a more practical tool for investors who aim to predict the impacts of interest rate fluctuations on a bond’s price. The numeric value of the modified duration is a direct indicator of the degree of bond price volatility. Simply put, the higher the value of modified duration, the more sensitive the bond is to adjustments in interest rate. In other words, a bond with a high modified duration what is modified duration will experience a more significant drop in price when interest rates rise than a bond with a lower modified duration. This is the interest rate or yield the bond is currently offering for each period (normally semi-annually).

As bond prices and interest rates move in opposite directions, the effective duration estimates the expected decline of a bond’s price when interest rates rise by 1%. The value of the effective duration should always be lower than the maturity of the bond. In summary, Macauley duration is a weighted average maturity of cash flows (measured in units of time) and is useful in portfolio immunization where a portfolio of bonds is used to fund a known liability. Modified duration is a price sensitivity measure and is the percentage change in price for a unit change in yield. Modified duration is more commonly used than Macauley duration and is a tool that provides an approximate measure of how a bond price will change given a modest change in yield.

This helps investors make smart investment decisions and manage investment risk. The modified duration tells you how much the price of a bond will change for a given change in its yield. So, in the example above, investors can expect to see a 1.859% move in price when the bond’s yield to maturity changes by one percentage point. Once you know how much and when all payments will be made, you have to time-weight their discounted values.

This offers us a way to approximate the modified duration when we have a list of the price of the bond at different yields. 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.