Macaulay Duration Overview, How To Calculate, Factors

To capture the sensitivity of bonds to changes in interest rates, while also factoring in a bond’s call structure, market participants thus developed Effective Duration,5 or option-adjusted duration. The difference between the Modified and Effective Duration for option-free (i.e., non-callable) bonds is very small. However, for some bonds with optionality, the difference can be substantial.

The modified duration determines the changes in a bond’s duration and price for each percentage change in the yield to maturity. In summary, modified duration is an important concept for fixed-income securities analysis and portfolio management. It provides a more accurate estimate of interest rate risk than Macaulay duration and can help investors and portfolio managers make more informed decisions about bond investments. It is a measure of a bond’s sensitivity to changes in interest rates and is critical in determining the bond’s price sensitivity. Modified duration and Macaulay duration are two measures commonly used to calculate a bond’s duration and provide different insights into the bond’s price sensitivity to interest rate changes. 5 Effective Duration is calculated by summing up all the multiples of the present values of cash flows and corresponding time periods and then dividing the sum by the market bond price.

Sometimes we can be misled into thinking that it measures which part of the yield curve the instrument is sensitive to. After all, the modified duration (% change in price) is almost the same number as the Macaulay duration (a kind of weighted average years to maturity). For example, the annuity above has a Macaulay duration of 4.8 years, and we might think that it is sensitive to the 5-year yield.

The Macaulay duration is named after economist and mathematician Frederick Macaulay, who developed the concept of bond duration in the 1930s. Calculating the Macaulay duration is the most difficult part of calculating the modified duration of an asset. For example, assume bank A and bank B enter into an interest rate swap. 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.

At a glance, one may think that it’s easier to understand bonds than stocks. If you are interested in a further discussion of the difference between Macaulay, modified and effective duration, here is a little quiz I wrote in our forum. Breckinridge makes no assurances, warranties or representations that any strategies described herein will meet their investment objectives or incur any profits.

Factors that Affect Macaulay Duration

But it has cash flows out to 10 years and thus will be sensitive to 10-year yields. If we want to measure sensitivity to parts of the yield curve, we need to consider key rate durations. The Macaulay duration and the modified duration are chiefly used to calculate the duration of bonds. The Macaulay duration calculates the weighted average time before a bondholder would receive the bond’s cash flows. Conversely, the modified duration measures the price sensitivity of a bond when there is a change in the yield to maturity.

1. The BPV in the table is the dollar change in price for $100 notional for 100bp change in yields.
2. It is the time it takes for an investor to receive the present value of the bond’s future cash flows, including both interest payments and principal repayment.
3. Now that we understand and know how to calculate the Macaulay duration, we can determine the modified duration.
4. This bond has an annual coupon rate (the yield paid through maturity) of 5%.
5. By that, it means that the duration of individual securities in a portfolio can be combined into a duration for that entire portfolio.

How yields impact Macaulay Duration

It is a measure of the time required for an investor to be repaid the bond’s present value by the bond’s total cash flows. The Macaulay duration is measured in units of time (e.g., years). However, in the markets, duration can also be understood to be a measure of how much a bond price will move given changes in the yield-to-maturity. This interpretation is more correctly called “dollar duration” but market participants stubbornly tend to use this duration definition the most. Modified duration and DV01 as measures of interest rate sensitivity are also useful because they can be applied to instruments and securities with varying or contingent cash flows, such as options. Formally, modified duration is a semi-elasticity, the percent change in price for a unit change in yield, rather than an elasticity, which is a percentage change in output for a percentage change in input.

Calculation of Modified and Macaulay Durations

Modified duration takes into account the fact that as interest rates change, the expected cash flows from the bond may also change. This measure measures the percentage change in bond price for a 1% change in yield, assuming all other factors remain constant. On the other hand, Macaulay duration measures the weighted average time to receive all the bond’s cash what is modified duration flows, taking into account the present value of each cash flow and the bond’s maturity. Modified duration measures the size of the interest rate sensitivity.

Additionally, effective duration may also be useful when looking at option-free bonds in instances of large yield moves, as duration is not a constant figure due to the concept of convexity. Comparing this with the bond on the top with smaller coupon payments, you will see that the fulcrum is further out to the right hand side, meaning a longer duration. Duration is commonly used in the portfolio and risk management of fixed income instruments.

What is it, how to calculate it, formula, why it’s important

1. Breckinridge makes no assurances, warranties or representations that any strategies described herein will meet their investment objectives or incur any profits.
2. Modified duration could be extended to calculate the number of years it would take an interest rate swap to repay the price paid for the swap.
3. Relative to the Macaulay duration, the modified duration metric is a slightly more precise measure of price sensitivity.
4. Several websites offer these online calculators that can be used for free.
5. Modified duration takes into account the fact that as interest rates change, the expected cash flows from the bond may also change.
6. It’s important to note that bond prices and interest rates have an inverse relationship with each other.

It assumes that interest rates and bond prices move in opposite directions, which may not always be the case. It also assumes that interest rates change uniformly across all maturities, which is not always true. 3 A bond’s yield to maturity is the discount rate that equates a bond’s price with the present value of the bond’s future payments. The drawback of Modified Duration is that it does not consider that interest rate movements can change a bond’s cash flows. For example, the cash flows of bonds with optionality4 can change with the rise or fall of interest rates.

While both measures are used to assess how a bond’s price will react to changes in interest rates, they are not interchangeable. Investors must understand the key differences between the two and how to use them effectively in their decision-making process. Macaulay duration is the weighted average of the time to receive the cash flows from a bond. Macaulay duration tells the weighted average time that a bond needs to be held so that the total present value of the cash flows received is equal to the current market price paid for the bond. In contrast, the modified duration identifies how much the duration changes for each percentage change in the yield while measuring how much a change in the interest rates impacts the price of a bond.

More simply put, it measures how much the bond’s price will change if interest rates shift. Modified duration takes into account the bond’s yield and coupon payments, while Macaulay duration does not. The issuer of a callable bond can “call” the bond prior to maturity, thereby returning principal to the bondholder earlier than expected. This typically occurs when interest rates are falling and issuers are able to call bonds with higher coupons and reissue debt at the new, lower prevailing market interest rates. Therefore, market participants came up with a more practical duration measure, called modified duration.