The limitation of duration-matching is that the method only immunizes the portfolio from small changes in interest rate. 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. For instance, the modified duration of a 5-year, 8% annual payment bond is 3.786. Modified Duration (ModDur) is an extension of Macaulay Duration and helps to measure the sensitivity of a bond to changes in interest rates. Duration helps you understand, at a glance, how sensitive your bond portfolio is to interest rate changes. Practically, a longer Macaulay duration shows at a glance (and relative to another bond) a bond’s interest rate risk.
An investor must hold the bond for 1.915 years for the present value of cash flows received to exactly offset the price paid. 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.
This way, using the relationship between Average Maturity and Interest Rate Sensitivity, you can determine the best way to actively manage your Debt Investments to balance the overall risk and return in your portfolio. 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.
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. By understanding the concept of Macaulay Duration, investors can better manage the risk and return profile of their bond investments. For example, if investors expect interest rates to decrease, they may want to invest in bonds with longer durations to maximize price appreciation. This is particularly relevant for bonds with embedded options, such as callable or puttable bonds. In contrast, Macaulay Duration assumes that cash flows do not change with interest rates, making it less appropriate for bonds with embedded options.
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. In the case of an individual bond, Maturity refers to the time period after which the initial investment, i.e., the Principal, is repaid by the Bond Issuer to the Bond Holder. So to calculate the Average Maturity of a Debt Fund, you have to use the weighted average method to determine how much time it will take for all the bonds in the fund’s portfolio to mature. Bond duration is a linear estimate of a bond’s price sensitivity to changes in market yield. 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).
- 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.
- 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).
- It calculates the weighted average time it takes to receive the bond’s cash flows, factoring in present value.
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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. 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).
What is Average Maturity?
It is also used in Asset-Liability Management (ALM) to match the durations of assets and liabilities, thereby reducing interest rate risk. 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. Regarding bond portfolios, the computation of Macaulay Duration necessitates an extra step. A weighted average of the Macaulay Durations of the individual bonds is taken, with each bond’s weight being determined by its proportion of the portfolio’s overall value.
Inverse Relationship Between Bond Prices and Interest Rates
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. The modified duration for each series of cash flows can also be calculated by dividing the dollar value of a basis point change of the series of cash flows by the notional value plus the market value. Macaulay Duration, named after economist Frederick Macaulay, is a measure of a bond’s sensitivity to interest rate changes.
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. Effective Duration is the best duration measure of interest rate risk when valuing bonds with embedded options because such bonds do not have well-defined internal rates of return (yield-to-maturity). Therefore, yield durations statistics such as Modified and Macaulay Durations do not apply. Bond duration estimates changes in bond price assuming that variables other than yield-to-maturity or benchmark rates are held constant.
Comparison of Macaulay Duration With Other Duration Measures
There are other variations of dollar duration that market participants tend to use. If you imagine this entire cash flow diagram being put on a see-saw, duration https://1investing.in/ is the point where the cash flow balances, also known as a fulcrum. This is the point of time represented by the orange triangle above measured in years.
Conceptual Understanding of Macaulay Duration
This is useful for market practitioners to get an idea of a change in bond price for movements in yield in 1 basis point increments. On trading floors, you will also hear DV01 called PVBP (the Price Value of a Basis Point). This means that yield to maturity and Macaulay duration have an inverse relationship. 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.
Embedded options and effective duration
This definition of “pure” duration was introduced by Canadian economist Frederick Macaulay. 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. In the figure above, we have a simplified diagram of a five-year fixed-rate, annual-pay coupon bond. Each of the bars represents interest cash flows, or coupons, and a final cash flow consisting of the principal and the final interest payment. A fixed income security with a greater duration indicates a higher sensitivity to interest rates and thus, the greater the interest rate risk it has.
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. As you can see in the figure above, the duration of a bond is not the same as its maturity. As a matter of fact, for coupon-paying bonds, the duration of that bond will always be shorter than the term to maturity of that bond.
Then, the resulting value is added to the total number of periods multiplied by the par value, divided by 1, plus the periodic yield raised to the total number of periods. 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. 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.
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 macaulay duration and modified duration and interest rates move in opposite directions. It considers the time value of money and the present value of future cash flows, helping investors manage risk-return trade-offs effectively.
In the above table, you can see that both of these schemes have posted significantly high returns during periods when RBI has decreased Interest Rates. This strategy can deliver significantly high returns for the investor if a fall in Interest Rates is predicted accurately. You might also have noticed that the opposite happened when RBI increased Interest Rates i.e. both the schemes underperformed. This is due to their higher Interest Rate Sensitivity and the inverse relationship between Bond Prices and Interest Rates, i.e., an increase in Interest Rates leading to lower Bond Prices. So, one way in which you can minimize the impact of rising Interest Rates on Your Debt Portfolio is to increase your investments in Debt Funds with low Average Maturity.