Modified duration is used by a variety of different people in the financial industry. It can be used by individual investors to help them make more informed decisions about their portfolios, and by portfolio managers to help them make better choices about what investments to make. Modified duration is also used by analysts to help them understand the potential risks and rewards of certain investments, and by rating agencies to help them assign credit ratings to different debt instruments. In general, modified duration is a widely-used tool that can provide a lot of useful information about a particular investment. Key rate durations require that we value an instrument off a yield curve and requires building a yield curve. This represents the bond discussed in the example below – two year maturity with a coupon of 20% and continuously compounded yield of 3.9605%.

Modified duration is used to evaluate bond performance by comparing it against benchmarks and conducting attribution analysis. This measure helps investors understand the sources of their portfolio’s performance, including the impact of interest rate changes. The frequency of coupon payments is another factor that can affect a bond’s modified duration. Bonds that pay coupons more frequently have lower modified durations than bonds that pay coupons less frequently. 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. A bond with positive convexity will not have any call features – i.e. the issuer must redeem the bond at maturity – which means that as rates fall, both its duration and price will rise.

A short-duration strategy is one where a fixed-income or bond investor is focused on buying bonds with a small duration. This usually means that the investor is focused on bonds with a small amount of time to maturity. A strategy like this would be employed when investors think interest rates will rise or when they are very uncertain about interest rates and want to reduce their risk. In the financial press, you may have heard investors and analysts discuss long-duration or short-duration strategies, which can be confusing. In a trading and investing context, the term “long” would be used to describe a position where the investor owns the underlying asset or an interest in the asset that will appreciate in value if the price rises.

## Bond investing in today’s market

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. 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.

- MD is important for investors because it can help them understand how their bond holdings will react to changes in interest rates.
- Fixed-income traders will use duration, along with convexity, to manage the riskiness of their portfolio and to make adjustments to it.
- Whether you are in retirement or investing to build a better future, consistent performance and low fees are critical to achieve your goals.
- Effective duration is a duration calculation for bonds that have embedded options.

Modified Duration tells us how much a bond’s price will change with respect to a change in yield. Thus, a bond trading at par with a modified duration of 4.33 years tells us that the bond’s price will rise by 4.33% if interest rates fall by 100bp (1%). It also indicates that the bond’s price will fall by 4.33% if interest rates rise by 100bp.

## A Detailed Understanding of Duration

The calculation of Modified Duration is an offshoot of Macaulay’s Duration. Here, we divide Macaulay’s Duration by (1 + yield to maturity) due to differentiation formulas in calculus. Duration can measure how long it takes, in years, for an investor to be repaid a bond’s price by the bond’s total cash flows. Duration can also measure the sensitivity of a bond’s or fixed income portfolio’s price to changes in interest rates. Modified duration measures the average cash-weighted term to maturity of a bond.

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It is the time taken by the issuer of the bond to repay the principal from the bond’s internal cash flows. In this case the BPV or DV01 (dollar value of modified duration meaning an 01 or dollar duration) is the more natural measure. The BPV in the table is the dollar change in price for $100 notional for 100bp change in yields.

## Modified Duration Formula, Calculation, and How to Use It

Understanding duration is particularly important for those who are planning on selling their bonds prior to maturity. If you purchase a 10-year bond that yields 4% for $1,000, you will still receive $40 dollars each year and will get back your $1,000 principal after 10 years regardless of what happens with interest rates. If, however, you sell that bond before maturity (or if you are invested in a fund that buys and sells bonds while you own it) then the price of your bonds will be affected by changes in rates. In such cases, investors should rely on effective duration, which accounts for the potential impact of these options on a bond’s price sensitivity.

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. However, a long-duration strategy describes an investing approach where a bond investor focuses on bonds with a high duration value.

## Modified Duration

Credit risk refers to the possibility that the bond issuer will not be able to make principal and interest payments. For example, if a bond has a duration of five years and interest rates increase by 1%, the bond’s price will decline by approximately 5%. Conversely, if a bond has a duration of five years and interest rates fall by 1%, the bond’s price will increase by approximately 5%.

In this situation, an investor is likely buying bonds with a long time before maturity and greater exposure to interest rate risks. A long-duration strategy works well when interest rates are falling, which usually happens during recessions. Every bond and every bond fund has a duration that can be used to compare individual bonds and bond funds. During times when interest rates are rising, rising durations may point the way toward shorter-duration bonds that have less interest rate risk. Dollar Duration is calculated as the change in the price of a bond for a unit change in the interest rate measured in basis points. Dollar duration measures the change in the price of a bond for every 100 bps (basis points) of change in interest rates.

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. Bond duration is calculated according to several different formulas which we’ll describe below, however, we can get the easiest duration calculation out of the way first. It is for zero-coupon bonds which do not pay a coupon payment, meaning that they pay no interest over the lifetime of the bond.

A bond with a longer time to maturity will have a price that is more sensitive to interest rates, and thus a larger duration than a short-term bond. To complete the calculation, an investor needs to take the present value of each cash flow, divide it by the total present value of all the bond’s cash flows and then multiply the result by the time to maturity in years. The first part is used to find the present value of all future bond cash flows. The second part finds the weighted average time until those cash flows are paid.

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. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.

We also sell both admissions and sponsorship packages for our investment conferences and advertising on our websites and newsletters. Investors employ modified duration in designing bond portfolio strategies, such as active and passive management, duration matching, and convexity optimization. These strategies aim to maximize returns while managing interest rate risk. This is because as yields rise, the price of the bond falls, and the sensitivity of the bond’s price to further changes in yield decreases. The time to maturity of a bond is one of the key factors that affect its modified duration.

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