what are different types of duration 
the duration of a bond in practice can refer to two different things the macaulay duration is the weighted average time until all the bond s cash flows are paid by accounting for the present value of future bond payments the macaulay duration helps an investor evaluate and compare bonds independent of their term or time to maturity the second type of duration is called modified duration unlike macaulay duration modified duration is not measured in years modified duration measures the expected change in a bond s price to a 1 change in interest rates to understand modified duration keep in mind that bond prices are said to have an inverse relationship with interest rates therefore rising interest rates indicate that bond prices are likely to fall while declining interest rates indicate that bond prices are likely to rise macaulay duration finds the present value of a bond s future coupon payments and maturity value fortunately for investors this measure is a standard data point in most bond searching and analysis software tools because macaulay duration is a partial function of the time to maturity the greater the duration the greater the interest rate risk or reward for bond prices macaulay duration can be calculated manually as follows the previous formula is divided into two sections the first part is used to find the present value of all future bond cash flows the second part finds the weighted average time until those cash flows are paid when these sections are put together they tell an investor the weighted average amount of time to receive the bond s cash flows imagine a three year bond with a face value of 100 that pays a 10 coupon semiannually 5 every six months and has a yield to maturity ytm of 6 to find the macaulay duration the first step will be to use this information to find the present value of all the future cash flows as shown in the following table this part of the calculation is important to understand however it is not necessary if you already know the ytm for the bond and its current price this is true because by definition the current price of a bond is the present value of all its cash flows to complete the calculation an investor needs to take the present value of each cash flow divide it by the total present value of all the bond s cash flows and then multiply the result by the time to maturity in years this calculation is easier to understand in the following table the total row of the table tells an investor that this three year bond has a macaulay duration of 2 684 years traders know that the longer the duration is the more sensitive the bond will be to changes in interest rates if the ytm rises the value of a bond with 20 years to maturity will fall further than the value of a bond with five years to maturity how much the bond s price will change for each 1 the ytm rises or falls is called modified duration the modified duration of a bond helps investors understand how much a bond s price will rise or fall if the ytm rises or falls by 1 this is an important number if an investor is worried that interest rates will change in the short term the modified duration of a bond with semiannual coupon payments can be found with the following formula using the numbers from the previous example you can use the modified duration formula to find how much the bond s value will change for a 1 shift in interest rates as shown below in this case if the ytm increases from 6 to 7 because interest rates are rising the bond s value should fall by 2 61 similarly the bond s price should rise by 2 61 if the ytm falls from 6 to 5 unfortunately as the ytm changes the rate of change in the price will also increase or decrease the acceleration of a bond s price change as interest rates rise and fall is called convexity 