This duration measure is less commonly used but essentially indicates how much a 0.01% price move in a bond will impact the yield of that instrument. There are other variations of dollar duration that market participants tend to use. Practically, a longer Macaulay duration shows at a glance (and relative to another bond) a bond’s interest rate risk. Longer duration bonds are more volatile – they are more sensitive to interest rate changes. If you have all of the details of the bond and know the market yield or the bond’s yield to maturity, use the “You Know Yield to Maturity” option. The limitation of duration-matching is that the method only immunizes the portfolio from small changes in interest rate.

- Macaulay duration also demonstrates an inverse relationship with yield to maturity.
- By balancing the duration of assets and liabilities, investors can protect their portfolios from significant losses when interest rates change.
- A modified duration of 1.89 means that for every 1% change in yield, the price of the bond changes by -1.89%.
- A bond’s price is calculated by multiplying the cash flow by 1, minus 1, divided by 1, plus the yield to maturity, raised to the number of periods divided by the required yield.
- Effective duration is a useful measure of the duration for bonds with embedded options (e.g., callable bonds).

On the other hand, if the market Interest Rate increases by 1%, the price of the same Bond will decrease by 5%. The Yield to Maturity (YTM) of a Debt Fund indicates the potential returns of a Debt Fund and the quality of the Bonds that the scheme invested in. A higher YTM typically indicates that the scheme is invested in low-quality Bonds that can potentially give higher returns but carry a higher degree of risk investments as compared to Debt Funds with a lower YTM.

Now that we understand and know how to calculate the Macaulay duration, we can determine the modified duration. In order to arrive at the modified duration of a bond, it is important to understand the numerator component – the Macaulay duration – in the modified duration formula. A full analysis of the fixed income asset must be done using all available characteristics.

This occurs when there is an inverse relationship between the yield and the duration. The yield curve for a bond with a negative convexity usually follows a downward movement. Using the formula above, let’s calculate the Macaulay duration for a hypothetical three-year bond. We begin by calculating the present values of the cash flows from each of the three years.

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Personal Finance & Money Stack Exchange is a question and answer site for people who want to be financially literate. Therefore, if interest rates rise 1% overnight, the price of the bond is expected to drop 4.62%. Amanda Bellucco-Chatham is an editor, writer, and fact-checker with years of experience researching personal finance topics. Specialties include general financial planning, career development, lending, retirement, tax preparation, and credit. Over 1.8 million professionals use CFI to learn accounting, financial analysis, modeling and more.

## How to Calculate Average Maturity?

The Macaulay duration and the modified duration are chiefly used to calculate the duration of bonds. Conversely, the modified duration measures the price sensitivity of a bond when there is a change in the yield to maturity. The previous percentage price change calculation was inaccurate because it failed to account for the convexity of the bond (the curvature in the above picture).

The BPV will make sense for the interest rate swap (for which modified duration is not defined) as well as the three bonds. A bond’s price, maturity, coupon and yield to maturity all factor into the calculation of duration. As interest rates increase, duration decreases and the bond’s sensitivity to further interest rate increases goes down. Also, a sinking fund in place, a scheduled prepayment before maturity, and call provisions all lower a bond’s duration. In Macaulay duration, the time is weighted by the percentage of the present value of each cash flow to the market price of a bond. Therefore, it 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.

A bond with a higher trading price will have a higher dollar duration than a bond with the same modified duration that trades at a lower price. This bond duration tool can calculate the macaulay duration and modified duration based on either the market price of the bond or the yield to maturity (or the market interest rate) of the bond. Key rate durations require that we value an instrument off a yield curve and requires building a yield curve. In terms of standard bonds (for which cash flows are fixed and positive), this means the Macaulay duration will equal the bond maturity only for a zero-coupon bond.

This bond’s price sensitivity to interest rate changes is different from a non-puttable bond with otherwise identical cash flows. Modified duration can be extended to instruments with non-fixed cash flows, while Macaulay duration applies only to fixed cash flow instruments. Modified duration is defined as the logarithmic derivative of price with respect to yield, and such a definition will apply to instruments that depend on yields, whether or not the cash flows are fixed. Another difference between Macaulay duration and Modified duration is that the former can only be applied to the fixed income instruments that will generate fixed cash flows. For bonds with non-fixed cash flows or timing of cash flows, such as bonds with a call or put option, the time period itself and also the weight of it are uncertain. The Macaulay duration of a bond can be impacted by the bond’s coupon rate, term to maturity, and yield to maturity.

## What is Macaulay Duration?

Start with a free account to explore 20+ always-free courses and hundreds of finance templates and cheat sheets. Average Maturity, Macaulay Duration, and Modified Duration can provide valuable insight into a Debt Fund’s Interest Rate sensitivity. A clear understanding of these aspects of Debt Mutual Funds can help you make informed choices regarding your Debt Investments so that you can optimize your returns while minimizing the overall risk to your portfolio.

However, Modified duration can still be calculated since it only takes into account the effect of changing yield, regardless of the structure of cash flows, whether they are fixed or not. 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. Regarding bond portfolios, the computation of Macaulay Duration necessitates an extra step.

## Types of Duration Measures

This is the point of time represented by the orange triangle above measured in years. A bond with positive convexity will not have any call features – i.e. the issuer must redeem the bond at maturity – which means that as rates fall, both its duration and price will rise. To price such bonds, one must use option pricing to determine the value of the bond, and then one can compute its delta (and hence its lambda), which is the duration.

Because of the shape of the price yield curve, for a given change in yield down or up, the gain in price for a drop in yield will be greater than the fall in price due to an equal rise in yields. This slight “upside capture, downside protection” is what convexity accounts for. Mathematically ‘Dmod’ is the first derivative of price with respect to yield and convexity is the second derivative of price with respect to yield. Another https://1investing.in/ way to view it is, convexity is the first derivative of modified duration. 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 DV01 is analogous to the delta in derivative pricing (one of the “Greeks”) – it is the ratio of a price change in output (dollars) to unit change in input (a basis point of yield).

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. It also means that Macaulay duration decreases as time passes (term to maturity shrinks). For example, a 2-year bond with a $1,000 par pays a 6% coupon semi-annually, and the annual interest rate is 5%. Thus, the bond’s market price is $1,018.81, summing the present values of all cash flows. 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 calculated by dividing the dollar value of a one basis point change of an interest rate swap leg, or series of cash flows, by the present value of the series of cash flows.