The resulting modified duration of the interest rate swap is four years (9 years – 5 years). Now that we understand and know how to calculate the Macaulay duration, we can determine the modified duration. 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. This is because longer-term bonds are more sensitive to changes in interest rates than shorter-term bonds.

1. This slight “upside capture, downside protection” is what convexity accounts for.
2. While the risk is still there, the company offers help in capitalizing on areas such as real estate, legal finance, art finance and structured notes — as well as a wide range of other unique alternative investments.
3. 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.
4. Second, as a bond’s coupon increases, its duration decreases and the bond becomes less volatile.

To understand modified duration, keep in mind that bond prices generally have an inverse relationship with interest rates. Therefore, rising interest rates indicate that bond prices are likely to fall while declining interest rates indicate that bond prices are likely to rise. Both modified and dollar duration, therefore, are metrics for how sensitive a bond’s price is to movements in its yield.

Is the Modified Duration Always Less than Macaulay Duration?

As such, investors often avail themselves of formulas aimed at helping them do just that. One such formula is called modified duration, which can help investors judge risk based on changing interest rates. Modified duration calculation divides the dollar value of a basis point change of a series of cash flows or an interest swap leg by the present value of the cash flow series.

In periods when interest rates spike unexpectedly, banks may suffer drastic decreases in net worth, if their assets drop further in value than their liabilities. Although Macaulay Duration is a valuable indicator for simple bonds, modified or effective durations are more suited to complex bond features and non-parallel shifts in the yield curve. This tool plays a pivotal role in asset-liability management, portfolio immunization, and aligning investment horizons with bond durations. Its versatility extends to comparing bonds with varied maturities, coupons, and face values.

What is the difference between Macaulay Duration, Modified Duration, and Effective Duration?

Unfortunately, duration has limitations when used as a measure of interest rate sensitivity. While the statistic calculates a linear relationship between price and yield changes in bonds, in reality, the relationship between the changes in price and yield is convex. 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 what is modified duration the fund at some target date, against interest rate movements.

Relationship Between Macaulay Duration and Bond Prices

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. Duration is a measure of the sensitivity of the price of a bond or other debt instrument to a change in interest rates. While the first approach is the more theoretically correct approach, it is harder to implement in practice. Therefore, the second approach below is the more commonly method used by fixed income portfolio managers.

Conversely, if interest rates decrease by 1%, the price of the bond will increase by 2.67%. Let’s suppose you have a bond with a face value of $1,000 that matures in three years. First, as maturity increases, duration increases and the bond becomes more volatile.

When these sections are put together, they tell an investor the weighted average amount of time to receive the bond’s cash flows. Duration measures how long it takes, in years, for an investor to be repaid a bond’s price through its total cash flows. Duration can also be used to measure how sensitive the price of a bond or fixed-income portfolio is to changes in interest rates.

Higher-interest bonds tend to have smaller modified durations because more of their cash flow comes from interest payments that come sooner in the bond’s lifespan. Then, add those numbers together and divide the result by the present value of all the bond’s payments. Dollar duration measures the dollar change in a bond’s value to a change in the market interest rate, providing a straightforward dollar-amount computation given a 1% change in rates.