This presents a risk for sustainable investors, who may not necessarily prioritize high returns over their environmental objectives. Conversely, if interest rates were to decrease, bonds with higher modified durations would increase in price more than those with lower durations. In contrast, the modified duration identifies how much the duration changes for each percentage change in the yield while measuring how much a change in the interest rates impacts the price of a bond. Thus, the modified duration can provide a risk measure to bond investors by approximating how much the price of a bond could decline with an increase in interest rates. It’s important to note that bond prices and interest rates have an inverse relationship with each other.

## Understanding Macaulay Duration, Modified Duration and Convexity

This presupposes that for a small change in yield, the change in bond price will be proportional and predictably so. 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. This explanation provides an overview of the theoretical impact of changing interest rates on the modified duration.

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. For larger changes in yield, both the modified duration and convexity are used to better approximate how a bond price will change for a given change in yield. The Macaulay duration and the modified duration are chiefly used to calculate the duration of bonds. The Macaulay duration calculates the weighted average time before a bondholder would receive the bond’s cash flows. Conversely, the modified duration measures the price sensitivity of a bond when there is a change in the yield to maturity.

The coupon rate of a bond is another factor that can affect its modified duration. Bonds with higher coupon rates typically have lower modified durations than bonds with lower coupon rates. 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.

By employing strategies such as duration-matching or immunization, investors can what is modified duration balance their portfolios to align with their risk tolerance and investment objectives. 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.

- If the YTM rises, the value of a bond with 20 years to maturity will fall further than the value of a bond with five years to maturity.
- To sum up, both Macaulay and Modified Duration serve crucial roles in deciding investment strategies.
- 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.
- The longer the duration of a bond is, the more sensitive it will be to changes in interest rates.
- A bond’s coupon rate, or yield that it pays, is a key factor in the calculation of duration.
- Below, we’ll explain in more detail exactly what modified duration is, how to calculate it, and provide an example of how to use it.

First, as maturity increases, duration increases and the bond becomes more volatile. Second, as a bond’s coupon increases, its duration decreases and the bond becomes less volatile. Third, as interest rates increase, duration decreases, and the bond’s sensitivity to further interest rate increases goes down. 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.

## The Macaulay Duration

It’s also key to equally recognize established financial concepts such as modified duration, optimizing returns in line with risk appetite. One common strategy to manage interest rate risk is building a ‘bond ladder’, which is a portfolio of bonds with varying maturities. This strategy can provide a steady income stream, and part of the portfolio matures at regular intervals.

## Nonlinear Relationship between Bond Prices and Yields

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. A vital detail to remember throughout these scenarios is the timing of interest rates changes. Any sudden or swift movement in rates can bring about equally swift changes in bond prices, thereby affecting the bond’s modified duration. The earlier in the lifecycle of a bond that interest rates change, the greater the impact on the bond’s price and modified duration. Modified duration, in effect, measures the possible percentage change in the price of a bond for a 1% change in yield. Generally, bonds with a higher modified duration tend to have more volatile prices.

All other things being equal, a bond with a longer time to maturity will have a higher modified duration than a bond with a shorter time to maturity. By selecting bonds with different durations, investors can create a portfolio that is more or less sensitive to changes in interest rates, depending on their individual preferences. This means that the modified duration of a bond can help investors predict how the bond’s price will change as interest rates fluctuate.

Modified duration, a formula commonly used in bond valuations, expresses the change in the value of a security due to a change in interest rates. In other words, it illustrates the effect of a 100-basis point (1%) change in interest rates on the price of a bond. Modified duration is used to manage interest rate risk through strategies like portfolio immunization and asset-liability management. This is because longer-term bonds are more sensitive to changes in interest rates than shorter-term bonds. This result shows that it takes 2.753 years to recoup the true cost of the bond. While the underlying idea behind modified duration is simple, the calculation of the measure isn’t as straightforward as you might like.

Modified duration plays a crucial role in allowing investors to assess the potential impact of interest rate changes on the price of a bond. Specifically, it measures the sensitivity of a bond’s price to variations in interest rates. Bond traders also use key rate duration to see how the value of the portfolio would change at a specific maturity point along the entirety of the yield curve. When keeping other maturities constant, the key rate duration is used to measure the sensitivity of price to a 1% change in yield for a specific maturity. Because Macaulay duration is a partial function of the time to maturity, the greater the duration, the greater the interest rate risk or reward for bond prices. Different factors can affect a bond’s duration, including the time to maturity and the coupon rate.

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master’s in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology.

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

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