Modified Duration
February 25, 2025
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. Based on the concept that interest rates and bond prices have an inverse relationship (i.e. move in opposite directions), it estimates the percentage impact that a 100-basis-point (or 1%) change in interest rates will have on the price of a 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.
Key Learning Points
- Modified duration is a measure of the bond’s sensitivity to changes in interest rates and is directly used to assess risk and bond valuations
- It is an extension of the Macaulay duration, which measures the number of years a bond must be held to recover the initial investment
- Modified duration estimates the percentage change in the price of a bond as a result of a 1% (or 100 basis points) change in interest rates
- The formula does not take into account any flexibility around repayments making it suitable for traditional bonds only
Modified Duration Formula
To calculate the modified duration of a bond, investors would need to first calculate its Macaulay duration, which estimates the time required to recover their initial investment – we have a dedicated blog on Macaulay duration, where you can find more about its formula and application.
Then modified duration can be calculated using the below formula:
Where:
- Macaulay Duration – measures the time it would take for an investor to recover the money initially invested in the bond
- YTM – Yield to Maturity, which measures the total return on a bond if held until maturity
- n – the number of coupon periods per year
For example, if a bond has modified duration of 2%, it would fall by 2% if there was 100 basis points (or 1%) rise in the interest rates. Conversely, it would go up by 2% if there was a 100 basis points fall in the interest rates.
Example of Modified Duration
Theoretical Example of Modified Duration
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.
| Modified Duration | Change in Interest Rates | Change in Bond’s Price |
| 3 Years | Down by 100 Basis Points | Up by 3% |
| 3 Years | Up by 100 Basis Points | Down by 3% |
Real-Life Example of Modified Duration
Let’s look into the AXA Sterling Credit Short Duration Bond Fund, which aims to provide income combined with any capital growth over the short-term (defined as three years or less). Below is some information from the most recent factsheet for the fund.
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. 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.
Effective Duration vs. Modified Duration
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.
For example, with callable bonds the issuer can “call” the bond before its maturity date, which effectively means repaying the principal to the bondholder earlier than expected.
This would typically happen when interest rates are declining, and bond issuers are able to call bonds with higher coupons and reissue debt at lower rates. Since it is hard to estimate the rate of return for a bond with fluctuating cash flows, the effective duration effective duration helps investors to assess the expected cash flows from the bond by calculating the volatility of interest rates in relation to the yield curve. 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.
Being an essential risk measure for bonds with optionality, the effective duration is applicable to a number of investments such as callable municipal bonds or mortgage-backed securities (MBS), where the timing of principal repayment is highly dependent on the prevailing interest rate environment.
However, despite being a more complete measure of bond’s risk, it also has some drawbacks. 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). Therefore, effective duration may be less accurate for larges interest rate changes.
On the other hand, modified duration assumes stable cash flows when measuring the percentage change in a bond’s price for a given change in yield. It is best suited for traditional option-free bonds and it is a simpler measure as it does not consider changes in cash flow timing.
Conclusion
Overall, modified duration is a key measure that provides insights about the bond’s level of risk and valuation. When interest rates change, it offers investors an estimate of what the expected change in the bond’s price would be. Being an extension of the Macaulay duration measure, modified duration is a relatively straight-forward calculation but also has its limitations in that it doesn’t account for flexible cash flows.