Duration analysis is a basic measure of how much the price of a bond will change if there is an alteration in interest rates, and it’s generally composed of Macaulay duration and modified duration. Macaulay duration reflects the weighted average maturity time of the cash flows from a bond, while modified duration is an adjusted version derived to gauge price sensitivity with respect to interest rate changes. A 10-year bond with a coupon rate of 5% and a yield to maturity of 4% will have a Macaulay duration slightly higher than its modified duration (7.9 years vs. Macaulay duration). This means that if the interest rate increases by 1%, then the bond price may fall by around 7.9%.
Definition of duration
Duration is the measure of a bond’s future cash flows, given as a weighted average, used to derive the price sensitivity of that bond with respect to interest rate changes. With longer durations, the bond is more sensitive to changes in interest rates—a higher percentage price decline (or gain) from a given absolute change in rates. Duration is basically split into two distinct types: Macaulay duration and modified duration. “Duration” and “convexity” are the two key concepts that help investors quantify their exposure to interest rate risk in terms of their investment portfolios, thus enabling them to position themselves better as far as investing goes.
The Macaulay duration is measured in years and sets out to estimate the weighted average time or maturity for bond cash flows. It is normally used to assess the interest rate risk and term structure of a bond. A 5-year treasury bond with a YTM of 3% usually has a Macaulay duration of around 4.7 years. Modified duration is actually the Macaulay duration adjusted to a yield change, and it directly shows how sensitive the bond price will be in response to changes in interest rates. If this 5-year treasury bond has a yield to maturity of 3%, its modified duration could be pared down to, say, around 4.6 years, scaling back how far the price would move relative to interest rates by roughly even less than two percentage points.
Duration calculation and examples
Macaulay duration and modified duration are not actually computed through specific formulas but are derived using real data. So let us take an example: say a bond with a face value of $1000, paying 5% annually for 10 years, and the current market interest rate is also at 4%. The bond’s Macaulay duration will be approximately 8.2 years, and its modified duration will be approximately 7.9 years. This means that for a 1% rise in the market interest rate, the value of this bond will drop by somewhere around 7.9%. This estimate offers investors a data-based calculation of interest rate risk so that they can gauge the impact on prospective market volatility.
If a bond has a $500 par value and a 6% yield to maturity while the present market interest rate is 5%, its Macaulay duration would be about 9 years; long-term bonds tend to have greater durations than short-term bonds. Its modified duration will work out to be approximately 8.5 years. This means that when interest rates go up by 1%, it is logical to assume a decline in bond price of around 8.5%. This method of calculation is used in practice across various types of fixed-income products, from corporate to government bonds.
Application of duration
As bond prices change with interest rates, another aspect to consider is if one has invested a large sum or, by one’s own standard, a small amount to invest. Now, with long duration, it shall be that much more responsive as compared to short-term—put simply, when rates rise, the fall would be greater for longer-term bonds, and less erosion could be experienced over shorter time frames. Thus, if interest rates are expected to rise, investors can limit their exposure with a shorter-duration bond. If interest rates go up by 0.5% and the duration of a bond is 10 years, then its market price will tend to fall by about 5%. On the other hand, if the duration is only 3 years, then that price would only drop by 1.5%.
Managers may also reduce or extend the duration of their portfolios to align with projected market interest rate movements. Investors may add duration to their bonds to appreciate and gain more capital when interest rates are coming down. A Bloomberg poll found that in 2023, bonds with a duration of 15 years saw their returns climb by around 15% when interest rates were cut by one percentage point, while those with just five years had merely risen by approximately 5%.
Limitations of duration
Duration assumes a linear relationship between bond prices and interest rate changes, assuming that marginal changes are equally proportionate until a simple rebuild from scratch when all maturities behave similarly. A 5-year duration bond may lose 11%, rather than the expected drop of only 10%, in response to an abrupt increase in interest rates by, say, 2%. The insight into this non-linear mechanism is that duration may be incomplete when we study the behavior of prices in extreme market turbulence.
Duration is the measure that calculates how long it will take for your bond to pay for itself and its value fluctuation, with a focus on the idea that interest rates go up all alike when in reality, changes happen at different moments: market yields are non-parallel. Portfolio risk management through durations alone was tested this year, with almost 20% of interest rate changes divergent from the parallel, and CD rates even turned signs in some cases, as per a JP Morgan study. Duration analysis pays a lot of attention to interest rate risk but can miss out on the credit and other market-based risks inherent in fixed income. Duration matching minimizes gap exposure, or duration mismatch. Even credit bonds that have short durations moved more based on their own borrowing costs right there as Q3 2022 began, so surely shorter-maturity high-yield corporates navigated price volatility in early Q1 2023 due to credit issues rather than interest rate changes.
