Last updated on Dec 11, 2023
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What is bond duration?
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How to calculate Macaulay duration?
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How to calculate modified duration?
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How to use bond duration?
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How to compare bond duration?
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Here’s what else to consider
Bond duration is a measure of how sensitive a bond's price is to changes in interest rates. It can help you assess the risk and return of investing in bonds, as well as compare different bonds with different characteristics. In this article, you will learn how to calculate bond duration using two common methods: Macaulay duration and modified duration.
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- David Semmens, CFA Chief Investment Officer. ESG Portfolio Manager. Lecturer. Non Executive Director.
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- 'JB' Beckett
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1 What is bond duration?
Bond duration is the weighted average of the time it takes to receive the cash flows from a bond. It reflects how long you have to wait to recover your initial investment and earn interest. The longer the duration, the more sensitive the bond's price is to changes in interest rates. For example, a bond with a duration of 10 years means that its price will change by 10% for every 1% change in interest rates.
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- Esther Jordan Experienced SEO Writer | Seasoned Editor with Team Management Expertise | Content Strategist | Social Media Moderator
Bond duration measures a bond's sensitivity to interest rate changes, indicating its price volatility. To calculate: Multiply each cash flow by the time until receipt, then divide the sum of these products by the bond's current price. Divide Macaulay Duration by 1 plus the periodic yield-to-maturity rate (expressed as a decimal) divided by the number of payment periods per year. Measures a bond's sensitivity to changes in yield, considering potential changes in the bond's cash flows due to embedded options or features. It's calculated as the percentage change in price for a 1% change in yield. Using these methods, investors assess how bond prices might change with fluctuations in interest rates, aiding in investment decisions.
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2 How to calculate Macaulay duration?
Macaulay duration is the most basic form of bond duration. It is calculated by summing up the present value of each cash flow multiplied by the time until it is received, and then dividing by the total present value of the bond. The formula is: Macaulay duration = (C1/(1+r) * 1 + C2/(1+r)^2 * 2 + ... + Cn/(1+r)^n * n) / (C1/(1+r) + C2/(1+r)^2 + ... + Cn/(1+r)^n) where C1, C2, ..., Cn are the cash flows from the bond, r is the interest rate, and n is the number of periods.
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3 How to calculate modified duration?
Modified duration is a more useful form of bond duration for investors. It measures how much the bond's price will change for a given change in the yield to maturity (YTM), which is the interest rate that makes the present value of the bond's cash flows equal to its price. Modified duration is calculated by dividing the Macaulay duration by 1 plus the YTM per period. The formula is: Modified duration = Macaulay duration / (1 + YTM / m) where m is the number of periods per year.
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4 How to use bond duration?
Bond duration can help you evaluate the risk and return of investing in bonds. Generally, the higher the duration, the higher the potential return, but also the higher the risk. This is because a bond with a high duration will have a larger price change for a given change in interest rates, which can create capital gains or losses for investors. Therefore, you should consider your risk tolerance, investment horizon, and interest rate expectations when choosing bonds with different durations.
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Duration can be interpreted and can be useful solely in comparison to the durations of other bonds or financial instruments. Such comparisons are regularly made in various scenarios. For instance, a bond portfolio manager, under specific economic conditions, decides to increase or decrease holdings in bonds with longer durations.In macroeconomic analysis, consider the instance when a yield curve characteristic to the current economy is formed. The yield curve is constructed using bond durations.Another financial example arises when a company prepares for a bond issuance. Comparing the duration of the intended bond to the yield curve provides a benchmark for anticipating the yield during the issuance.
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5 How to compare bond duration?
Bond duration can be used to compare different bonds with various characteristics, such as coupon rate, maturity, and frequency of payments. Rules of thumb suggest that, all else being equal, a bond with a lower coupon rate will have a higher duration than one with a higher coupon rate because there is less cash flow in the early periods. Similarly, a bond with a longer maturity will have a higher duration than one with a shorter maturity due to more cash flow in the later periods. Additionally, a bond with a lower frequency of payments will have a higher duration than one with a higher frequency of payments as there is less cash flow in the early periods.
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6 Here’s what else to consider
This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?
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- David Semmens, CFA Chief Investment Officer. ESG Portfolio Manager. Lecturer. Non Executive Director.
Given it is a simple number taken in isolation, taking duration and not considering its construction and form is a signficant oversimplification. Reflect on how a 30 year bond and a zero coupon bond could have the same durations but very different appearances beyond their identifical durations.
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With Modified Duration, it’s providing a linear estimate and, in terms of absolute value, the change is the same whether it’s an increase or decrease in yield-to-maturity.But the thing is, for a given coupon rate and time-to-maturity, % price change is greater in absolute value when rate goes down vs when it goes up.So you need to do Convexity Adjustment, as this accounts for the convex curve relationship between bond price and yield-to-maturity.Without getting too technical, an example could show that, for a bond, if the yield jumped by 100bps or fell by 100bps then you would have:Jumps 100bps: loss in value of bond = X%Drops 100bps: gain in value of bond = gain in value of bond >X%
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- 'JB' Beckett
One of the enduring challenges of duration is the trajectory of the yield curve and relationship between short and long term rates. This can give a misleading comparison between bonds at different coupon rates and different maturities on and off run. Not a major consideration in an extended disinflationary period since 2012 but has very much been the case since 2022. In some ways we can step back if we take a hold to maturity perspective. Some may suggest using convexity to adjust the price change estimate and that helps but I would suggest far more practical measures are DTS *since we can consider ‘spread’ a dirty indicator of rate surprises and market volatility, plus estimating the duration of a bond for different maturities and Refi.
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How to buy bonds and create a portfolio?Its not simple and straightforward, esp if the awareness and understanding is low.This is a specialized subject and needs technical expertise.Hence I trust Debt Mutual Funds.But even there...i have a slightly diversified investment strategy- across short and long duration bonds.
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