How to Calculate Bond Duration

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The bond duration refers to the weighted average of the cash flows of the bonds maturity. The duration is important to measure because of the sensitivity of the price of the bond created by the movement of the interest rate. Often, the bond duration is proportional to the percentage change in the price of the yield. To cite as an example, if the interest rate of the bond increases by 2 percent and the bond matures in 15 years and the bond duration is equal to 5 then it means that the value of the bond will fall by 5 percent if there is an increase in the interest rate of 2 percent. This is referred to as the Modified Duration but there are still many more ways to calculate the bond duration. The following five options are different methods available that can be used to suit different calculation outcomes. These methods provide for different outputs in terms of accuracy and suitability….

Option 1

The Macaulay Duration method to calculate bond duration - This method was developed by Frederick Macaulay which uses the weighted average maturity of the bonds where the relative discounted cash flows for every period are used. This is used in order to predict the interest rate risk. You can utilize the available software on the Internet or just key in the formula in your spreadsheets. You can find the calculator here.

Option 2

The Modified Duration method to calculate bond duration - The method is useful in case the yield is compounded n times since the previous method would no longer give you a valid data result. The calculator can be found here.

Option 3

The embedded options and effective duration - If you purchased bonds that have embedded options or are callable and puttable, to use the Macaulay and the Modified duration methods would no longer give you accurate data. For you to be able to price these kinds of bonds, you need to use option pricing methods. An effective duration method on the other hand is more of an approximate value of the embedded options method.

Option 4

The average duration method to calculate the bond duration - In this method, what is taken into consideration is the average duration of the bonds in a portfolio which is determined by the weighted average of all the cash flows in the portfolio. I wasn’t able to find an online calculator but the formula can be found here.

Option 5

The dollar duration method and the VaR applications to calculate the bond duration- The dollar duration is simply the product of the duration and the price which determines the variation of the bond value for simple variations in the interest. This kind of method is used to calculate the value at risk or the VaR.

These calculations often use complex formulas so it is advisable to get someone who is adept in bond calculation to perform it for you or to have the data required in your hands and use a software application of these duration formulas. There are also online tools that can be utilized to key in the data and the program will do the calculation for you.

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