what is the macaulay duration 
the macaulay duration is the weighted average term to maturity of the cash flows from a bond the weight of each cash flow is determined by dividing the present value of the cash flow by the price macaulay duration is frequently used by portfolio managers who use an immunization strategy macaulay duration can be calculated as follows macaulay duration t 1 n t c 1 y t n m 1 y n current bond price where t respective time period c periodic coupon payment y periodic yield n total number of periods m maturity value begin aligned text macaulay duration frac sum t 1 n frac t times c 1 y t frac n times m 1 y n text current bond price textbf where t text respective time period c text periodic coupon payment y text periodic yield n text total number of periods m text maturity value end aligned macaulay duration current bond price t 1n 1 y tt c 1 y nn m where t respective time periodc periodic coupon paymenty periodic yieldn total number of periodsm maturity value investopedia julie bangunderstanding the macaulay durationthe metric is named after its creator frederick macaulay macaulay duration can be viewed as the economic balance point of a group of cash flows another way to interpret the statistic is that it is the weighted average number of years that an investor must maintain a position in the bond until the present value of the bond s cash flows equals the amount paid for the bond factors affecting durationa bond s price maturity coupon and yield to maturity all factor into the calculation of duration all else being equal duration increases as maturity increases as a bond s coupon increases its duration decreases as interest rates increase duration decreases and the bond s sensitivity to further interest rate increases goes down also a sinking fund in place a scheduled prepayment before maturity and call provisions all lower a bond s duration calculation examplethe calculation of macaulay duration is straightforward let s assume that a 1 000 face value bond pays a 6 coupon and matures in three years interest rates are 6 per annum with semiannual compounding the bond pays the coupon twice a year and pays the principal on the final payment given this the following cash flows are expected over the next three years period 1 30 period 2 30 period 3 30 period 4 30 period 5 30 period 6 1 030 begin aligned text period 1 30 text period 2 30 text period 3 30 text period 4 30 text period 5 30 text period 6 1 030 end aligned period 1 30period 2 30period 3 30period 4 30period 5 30period 6 1 030 with the periods and the cash flows known a discount factor must be calculated for each period this is calculated as 1 1 r n where r is the interest rate and n is the period number in question the interest rate r compounded semiannually is 6 2 3 therefore the discount factors would be period 1 discount factor 1 1 03 1 0 9709 period 2 discount factor 1 1 03 2 0 9426 period 3 discount factor 1 1 03 3 0 9151 period 4 discount factor 1 1 03 4 0 8885 period 5 discount factor 1 1 03 5 0 8626 period 6 discount factor 1 1 03 6 0 8375 begin aligned text period 1 discount factor 1 div 1 03 1 0 9709 text period 2 discount factor 1 div 1 03 2 0 9426 text period 3 discount factor 1 div 1 03 3 0 9151 text period 4 discount factor 1 div 1 03 4 0 8885 text period 5 discount factor 1 div 1 03 5 0 8626 text period 6 discount factor 1 div 1 03 6 0 8375 end aligned period 1 discount factor 1 1 03 1 0 9709period 2 discount factor 1 1 03 2 0 9426period 3 discount factor 1 1 03 3 0 9151period 4 discount factor 1 1 03 4 0 8885period 5 discount factor 1 1 03 5 0 8626period 6 discount factor 1 1 03 6 0 8375 next multiply the period s cash flow by the period number and by its corresponding discount factor to find the present value of the cash flow period 1 1 30 0 9709 29 13 period 2 2 30 0 9426 56 56 period 3 3 30 0 9151 82 36 period 4 4 30 0 8885 106 62 period 5 5 30 0 8626 129 39 period 6 6 1 030 0 8375 5 175 65 period 1 6 5 579 71 numerator begin aligned text period 1 1 times 30 times 0 9709 29 13 text period 2 2 times 30 times 0 9426 56 56 text period 3 3 times 30 times 0 9151 82 36 text period 4 4 times 30 times 0 8885 106 62 text period 5 5 times 30 times 0 8626 129 39 text period 6 6 times 1 030 times 0 8375 5 175 65 sum text period 1 6 5 579 71 text numerator end aligned period 1 1 30 0 9709 29 13period 2 2 30 0 9426 56 56period 3 3 30 0 9151 82 36period 4 4 30 0 8885 106 62period 5 5 30 0 8626 129 39period 6 6 1 030 0 8375 5 175 65 period 1 6 5 579 71 numerator current bond price pv cash flows 1 6 current bond price 30 1 03 1 30 1 03 2 current bond price 1030 1 03 6 current bond price 1 000 current bond price denominator begin aligned text current bond price sum text pv cash flows 1 6 phantom text current bond price 30 div 1 03 1 30 div 1 03 2 phantom text current bond price cdots 1030 div 1 03 6 phantom text current bond price 1 000 phantom text current bond price text denominator end aligned current bond price pv cash flows 1 6 current bond price 30 1 03 1 30 1 03 2current bond price 1030 1 03 6current bond price 1 000current bond price denominator note that since the coupon rate and the interest rate are the same the bond will trade at par macaulay duration 5 579 71 1 000 5 58 begin aligned text macaulay duration 5 579 71 div 1 000 5 58 end aligned macaulay duration 5 579 71 1 000 5 58 a coupon paying bond will always have its duration less than its time to maturity in the example above the duration of 5 58 half years is less than the time to maturity of six half years in other words 5 58 2 2 79 years which is less than three years 