The Macaulay Duration of a bond is directly related to the bond’s price sensitivity to changes in interest rates. A bond with a longer Macaulay Duration will have a greater price change for a given change in interest rates than a bond with a shorter Macaulay Duration. Consequently, this approach respects the diverse values and durations of individual bonds within a comprehensive portfolio, providing a more accurate duration measure for the entire portfolio. Investment professionals frequently use Macaulay Duration to manage interest rate risk and align bond portfolio durations with investment horizons. As a rule of thumb, the longer the Macaulay Duration, the higher the interest rate risk for a bond.
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.
For example, if the Fund Manager is anticipating an increase in Interest Rates, he/she might decide to reduce the Modified Duration of the portfolio by investing in short-maturity Debt Instruments. This will help reduce the adverse impact of the Interest Rate increase on the Debt Fund. On the other hand, when the Fund Manager anticipates a decrease in Interest Rates, he/she might decide to maintain a high Modified Duration in the portfolio by investing in long-maturity Bonds. This will help the Debt Fund generate high returns when Bond Prices increase due to the decrease in Interest Rates.
Macaulay Duration plays a pivotal role in ALM, as institutions often seek to match the durations of their assets and liabilities to minimize interest rate risk. 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. By adding up the present values of each of the three years, we get to a sum of $102.78, which is the bond’s price.
It will compute the mean bond duration measured in years (the Macaulay duration), and the bond’s price sensitivity to interest rate changes (the modified duration). The modified Duration of a bond is a measure of how much the price of a Bond changes because of a change in its Yield To Maturity (YTM) or interest rate. In the simplest terms, if the Modified Duration of a Bond is 5 years and the market Interest Rate decreases by 1%, then the Bond’s price will increase by 5%.
The effective duration is a discrete approximation to this latter, and will require an option pricing model. 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. One of the reasons why returns of Debt Funds can be volatile in the short run is the change in Interest Rates. The impact of Interest Rate changes is not uniform across Debt Fund categories or even funds within a category.
Modified duration equals Macaulay duration divided by 1 + required yield per period. It gives us the estimated change in the price of a bond in response to a 1% change in yield. Macaulay Duration serves as a link between bond prices and interest rates, measuring how sensitive a bond’s price is to changes in interest rates. It’s based on the principle that bond prices and interest rates move in opposite directions. Macaulay Duration can change with market conditions, especially for bonds with embedded options. If interest rates change significantly, the issuer or bondholders may choose to exercise their options, changing the bond’s cash flows and thus its Macaulay Duration.
- Macaulay duration is the weighted average of the time to receive the cash flows from a bond.
- If we look at coupon payments of a fixed-rate bond, we can also see how two similar bonds with different coupon rates can have different duration measures.
- Macaulay duration and modified duration are chiefly used to calculate the durations of bonds.
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- Therefore, if interest rates rise 1% overnight, the price of the bond is expected to drop 2.71%.
Shorter duration bonds will be relatively price stable; they will pay out most of their promised cash flow in the near future. Longer duration bonds are less stable; long duration bonds have all the risk of taking longer to pay out their funds, including a shift in the market’s demanded yield. For a one percent increase in interest rates, the bond’s market price will decrease by the percentage shown by the modified duration. For a one percentage point decrease in interest rates, the bond price will increase by the percentage shown by the modified duration.
Low-Interest Rate Environment
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.
What Modified Duration Can Tell You
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 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).
This measure is meant to simplify the understanding of the impact to a bond’s yield for a 1/32nd (or a “tick”) move in the price of the bond. Therefore, market participants came up with a more practical duration measure, called modified duration. Relative to the Macaulay duration, the modified duration metric is a slightly more precise measure of price sensitivity.
Example: Compute the Macaulay Duration for a Bond
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.
Interpreting the Modified Duration
It is a crucial tool for investors and portfolio managers who need to manage the interest rate risk of their bond investments effectively. In plain-terms – think of it as an approximation of how long it will take to recoup your initial investment in the bond. In our example above, using our analogy, you may be able to see that the bond on the bottom with the higher coupon rate will have a shorter duration as more of the weight sits on the left hand side of the see-saw. 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. Therefore, for a given interest rate increase, it can be expected that the bond with the longer term to maturity will have a larger interest rate risk than a shorter bond with the same coupon. From the series, you can see that a zero coupon bond has a duration equal to it’s time to maturity – it only pays out at maturity.
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.
Example: Compute the Modified Duration for a Bond
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.
A bond with a higher Macaulay duration will be more sensitive to changes in interest rates. 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 impact the price of a bond. Thus, the modified duration can provide a risk measure to bond investors by approximating how much the price of a bond could decline with an increase https://1investing.in/ in interest rates. It’s important to note that bond prices and interest rates have an inverse relationship with each other. The term duration is mathematically defined as the sum of the weighted average time of each of the cash flows that make up a bond. In other words, “pure” duration (denoted in years) is how long it will take for an investor to receive the bond’s present value based on the expected future cash flows of the bonds.
The Macaulay duration is calculated by multiplying the time period by the periodic coupon payment and dividing the resulting value by 1 plus the periodic yield raised to the time to maturity. Then, the resulting value is added to the total number of periods multiplied by the par value, divided by 1, macaulay duration and modified duration plus the periodic yield raised to the total number of periods. The yield-price relationship is inverse, and the modified duration provides a very useful measure of the price sensitivity to yields. For large yield changes, convexity can be added to provide a quadratic or second-order approximation.
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