Bond duration Wikipedia

Duration and convexity are two tools used to manage the risk exposure of fixed-income investments. Convexity relates to the interaction between a bond’s price and its yield as it experiences changes in interest rates. Macaulay duration can be viewed as the economic balance point of a group of cash flows.

• Also of note is the error when using duration-derived estimates of present value compared to direct calculation of present value.
• By using convexity in the yield change calculation, a much closer approximation is achieved (an exact calculation would require many more terms and is not useful).
• The Macaulay duration of a bond is the weighted average payout of the bond, measured in years.
• Banks employ gap management to equate the durations of assets and liabilities, effectively immunizing their overall position from interest rate movements.

Duration is one of the fundamental characteristics of a fixed-income security (e.g., a bond) alongside maturity, yield, coupon, and call features. It is a tool used in the assessment of the price volatility of a fixed-income security. If you’re a regular investor in mutual funds, you may now need to understand a new term to navigate the maze of debt mutual funds. SEBI’s new norms on categorisation of mutual funds require fund houses to classify their debt schemes into clearly defined buckets based on their Macaulay Duration.

Non-fixed cash flows

Institutions with future fixed obligations, such as pension funds and insurance companies, differ from banks in that they operate with an eye towards future commitments. For example, pension funds are obligated to maintain sufficient funds to provide workers with a flow of income upon retirement. As interest rates fluctuate, so do the value of the assets held by the fund and the rate at which those assets generate income. Therefore, portfolio managers may wish to protect (immunize) the future accumulated value of the fund at some target date, against interest rate movements. In other words, immunization safeguards duration-matched assets and liabilities, so a bank can meet its obligations, regardless of interest rate movements.

Well, the key parameters of Average Maturity, Macaulay Duration, and Modified Duration can give valuable insight into how a scheme’s performance will be impacted by future changes in Interest Rates. In our example, changes in the present value due to an interest rate change can be calculated directly without much effort. Regardless of the amount of effort, when changes in present value are calculated directly, the imperfections of the duration estimates can be observed.

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It is generally the case that, when the number of active employees accruing benefits increases, the further out in time are benefits expected to be received, which increases the duration. The limitation of duration-matching is that the method only immunizes the portfolio from small changes in interest rate. Where the division by 100 is because modified duration is the percentage change.

A bond with a higher Macaulay duration will be more sensitive to changes in interest rates. The Macaulay duration of a bond can be impacted by the bond’s coupon rate, term to maturity, and yield to maturity. With all the other factors constant, a bond with a longer term to maturity assumes a greater Macaulay duration, as it takes a longer period to receive the principal payment at the maturity.

Deconstructing actuarial liability

That is why its quoted in years and it gives an indication of when, on a weighted basis, cash flows are paid out (mature). For example, in the image of phi, the pv of cash flow at t1 (9.61) is paid out/matures at t1. In his example MD is 1.78 meaning the bulk of the maturity of cash flows occurs close to t2, simply because the last coupon is paid at t2 plus the par value is returned to the investor. Duration is a concept from interest theory used to describe how the present value of a cash flow series changes when small changes are made to the underlying interest rates.

For example, assume liability interest rates are linked to market bond yields, and further assume a retirement plan has a liability duration of 15 with a bond asset portfolio of duration 8. When the bond yield drops, for example 0.25%, the value of the bonds increases and with lower interest rates to discount cash flows, liabilities also increase. Using what we know about duration, we can estimate that the liability will increase by 3.75% and assets will macaulay duration meaning increase by 2.00%. As a result, the funding level of the plan decreases and opportunity presents itself to fix this mismatched response. Using duration, we have opened the door to understanding more about LDI and managing retirement risk. This only scratches the surface of LDI strategies, but it is encouraging to know that next time duration is mentioned, you will have the requisite information to further explore the context in which it is found.

Factors that Affect Macaulay Duration

Duration helps you understand, at a glance, how sensitive your bond portfolio is to interest rate changes. You can see how the small payments sum up to the invested amount, and why the Macaulay Duration is always shorter than the period of payments of the bond. It is not surprising that the largest duration belongs to the ongoing traditional DB plan. An annuity-based plan with a typical distribution of active employees of varying ages who are all eligible for benefits will have higher durations because the younger cohort won’t receive their benefits until later. Plans that pay annuities but don’t have younger active employees eligible for benefits, or plans that only pay lump sums, will have shorter durations.

Instead, the change function has curvature, and using convexity one can improve on the estimates provided by Macaulay duration and Modified duration. In practice, none of these assumptions will be entirely true, and when using duration to approximate changes in present value, each assumption should be considered in the context of the work being performed. The validity of conclusions drawn from duration should be understood as based on an estimate containing imperfect assumptions. The effects of imperfections in the first two assumptions have been studied but are beyond the scope of this article. The third assumption, while recognized as a significant factor for specific asset classes, is usually a nonissue in the context of payments to retirees in a retirement plan.

Duration

Typically, retirement plan payments to retirees do not change when the interest rate varies. However, for retirement income plans where retiree payments do change as interest rates vary, proceed with caution when using duration. The modified duration of the receiving leg of a swap is calculated as nine years and the modified duration of the paying leg is calculated as five years. The resulting modified duration of the interest rate swap is four years (9 years – 5 years). Duration is a measure of the average (cash-weighted) term-to-maturity of a bond. In plain-terms – think of it as an approximation of how long it will take to recoup your initial investment in the bond.

The time to receive each cash flow is then weighted by the present value of that cash flow to the market price. The modified duration is an adjusted version of the Macaulay duration, which accounts for changing yield to maturities. The formula for the modified duration is the value of the Macaulay duration divided by 1, plus the yield to maturity, divided by the number of coupon periods per year. The modified duration determines the changes in a bond’s duration and price for each percentage change in the yield to maturity.