Modified Duration-Definition, Formula, Calculation, Examples

This yield is utilized as the desired rate of return in finding the present value of future cash flows. 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. The modified duration provides a good measurement of a bond’s sensitivity to changes in interest rates. The higher the Macaulay duration of a bond, the higher the resulting modified duration and volatility to interest rate changes.

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. Duration is a measure of interest rate risk of a bond, the risk of decrease in bond price due to increase in market interest rates. In general, the degree to which bond price moves due to a change in yield i.e. interest rate is directly proportional to the time to maturity. It means the longer the bond cash flows are stretched the more pronounced the price movement is.

Incorporating Modified Duration into a Bond Ladder

Insurance companies and pension funds can use modified duration to manage their risk related to interest rates, as well. These organizations often hold bonds in their fixed-income portfolios with prices that can fluctuate based on interest rate changes. Modified duration is a formula that measures the sensitivity of the valuation change of a security to changes in interest rates. The result is the modified duration, which represents the approximate change in bond value for a 100 basis point change in interest rates. A major potential limitation of modified duration is that it only provides accurate estimates of the price change due to a small or infinitesimal change in interest rates.

Modified Duration Formula, Calculation, and How to Use It

Should the interest rate drop, the bond becomes less attractive to investors and the value to investors is likely to decrease accordingly. Once the comparison is made, it is possible to determine what a shift in interest rate would do to the bond value between the time the change occurs and the maturity date of the bond. Unlike the Macaulay duration, which helps investors assess the time aspect of cash flow recovery, modified duration is directly used in risk management and bond pricing. A higher reading indicates higher sensitivity to interest rate changes, which on the other hand leads to greater price volatility. Investors can use modified duration to assess the price volatility of individual bonds or an overall portfolio. Frederic Macaulay developed the Macaulay duration in 1938 what is modified duration to measure the number of years required to recover the true value of a bond.

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. The calculated modified duration can help investors understand how the bond’s price will move with interest rate changes.

Convexity is a measure of the amount of “whip” in the bond’s price yield curve (see above) and is so named because of the convex shape of the curve. Because of the shape of the price yield curve, for a given change in yield down or up, the gain in price for a drop in yield will be greater than the fall in price due to an equal rise in yields. This slight “upside capture, downside protection” is what convexity accounts for. Mathematically ‘Dmod’ is the first derivative of price with respect to yield and convexity is the second derivative of price with respect to yield. Another way to view it is, convexity is the first derivative of modified duration.

Impact on Portfolio Stability

Looking at the modified duration of the portfolio, it is 2.44 years, which makes its sensitivity to changes in interest rate expectations relatively low compared to funds invested in longer-term bonds. We first need to calculate the Macaulay’s duration, which is the average maturity of the bond cash flows weighted based on their relevant contribution to the present value of the bond. However, this does not mean that bonds with shorter modified durations are definitively ‘better’ for sustainable investing. Returns and risk levels may well be offset by the eco-friendly nature of the projects funded by these securities. The Modified Duration builds upon Macaulay Duration and adjusts the measure to reflect changes in yield. It allows investors to accurately predict how much the price of a bond would change in response to a one percent change in interest rates.

In actual practice, this means that the modified duration uses a formula with a one plus the yield to maturity to determine the impact of the interest rate change on the bond value. While this may appear to be somewhat convoluted, this process is not unlike the formulas used to predict the change that occurs with a mortgage carrying a floating or variable rate. By identifying the change in the interest rate, the investor can determine what type of return can be reasonably expected over the life of the bond if that change should actually occur. 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: Understanding its Role in Bond Price Fluctuations

Modified Duration is a critical financial metric used to assess the sensitivity of a bond’s price to interest rate changes. It builds upon the concept of Macaulay Duration, adjusting it to directly relate to changes in yield to maturity. In essence, it measures how much the price of a bond is expected to change for a 1% change in interest rates.

The earlier in the lifecycle of a bond that interest rates change, the greater the impact on the bond’s price and modified duration. A skillful balancing of higher and lower duration bonds can help you achieve a desirable risk/return profile for your bond portfolio. Bonds with higher modified durations are riskier due to their increased sensitivity to changes in interest rates, but they also typically offer higher yields as compensation for the increased risk. The Macaulay Duration, named after Frederick Macaulay who introduced it in 1938, is the classic measure of bond duration. Essentially, it gauges the weighted average time to receive the bond’s cash flows. Otherwise stated, it reflects a bond’s time sensitivity relative to changes in interest rates.

• This is the interest rate or yield the bond is currently offering for each period (normally semi-annually).
• 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.
• Just as importantly – it’s not only a tool for individual investors, but also an invaluable resource for portfolio managers.
• The modified duration determines the changes in a bond’s duration and price for each percentage change in the yield to maturity.

A two-step process to calculate modified duration

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. Duration and modified duration look at different aspects of bond analysis. 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.

The easiest way to come up with the modified duration for a bond is to start by calculating another type of duration called Macauley duration. This type of duration produces the weighted average time in which the investor will receive cash flows from the bond. One of the critical assumptions that modified duration makes is that there is a linear relationship between bond price changes and interest rate changes. This presupposes that for a small change in yield, the change in bond price will be proportional and predictably so.

• 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.
• The result is the modified duration, which represents the approximate change in bond value for a 100 basis point change in interest rates.
• 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.
• Conversely, it would go up by 2% if there was a 100 basis points fall in the interest rates.
• However, in practical scenarios, the impact can also be influenced by additional factors such as the bond’s coupon rate, yield, term to maturity, and the overall condition of the bond market.

Therefore, effective duration may be less accurate for larges interest rate changes. In the below table, we look at a bond with a modified duration of three years and how 1% change in interest rate would impact its 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. The modified duration of both legs must be calculated to compute the modified duration of the interest rate swap. The difference between the two modified durations is the modified duration of the interest rate swap.

As such, it gives us a (first order) approximation for the change in price of a bond, as the yield changes. The modified duration is calculated by dividing the dollar value of a one basis point change of an interest rate swap leg, or series of cash flows, by the present value of the series of cash flows. The modified duration for each series of cash flows can also be calculated by dividing the dollar value of a basis point change of the series of cash flows by the notional value plus the market value. Modified duration helps investors understand this relationship by measuring the sensitivity of a bond’s price to changes in interest rates.

This metric is invaluable for portfolio managers and investors in gauging interest rate risk. Generally, a higher modified duration indicates greater sensitivity to interest rate changes, implying higher risk and potential return. Consequently, green bonds with higher modified durations will experience more considerable price changes. This presents a risk for sustainable investors, who may not necessarily prioritize high returns over their environmental objectives. The previous percentage price change calculation was inaccurate because it failed to account for the convexity of the bond (the curvature in the above picture). Similarly, as the yield increases, the slope of the curve will decrease, as will the duration.

Moreover, modified duration becomes a handy tool for investors as they formulate their investment strategies. For example, if an investor believes that interest rates will decline in the future, they might opt to purchase bonds with high modified durations to maximize their price increases. On the other hand, if the investor foresees an uptick in rates, they may choose bonds with lower durations to limit potential price decreases. Interest rates and the bond market share an inverse relationship — when interest rates rise, bond prices fall, and conversely, when interest rates fall, bond prices rise. This interplay of interest rates and bond prices is crucial to understanding the concept of modified duration. Modified duration, in effect, measures the possible percentage change in the price of a bond for a 1% change in yield.

There are many types of duration, and all components of a bond, such as its price, coupon, maturity date, and interest rates, are used to calculate duration. Calculate the current price of the bond, known as its market value, by summing the present values computed in step 4. From the definition of Modified duration, we can use it to estimate the change in price of a bond as interest rate changes. The Macaulay duration is named after economist and mathematician Frederick Macaulay, who developed the concept of bond duration in the 1930s.