Macaulay Duration

CFA Level II
#1

This is probably real simple, but I can’t figure out why the Macaulay Duration is calculated. For example a 4 year 6% annual pay coupon bond with a yield of 5.5% would be calculated as follows:

6.00/1.055+6.00/1.055^2+6.00/1.055^3+106.00/1.055^4

=5.6872+5.3907+5.1097+85.5650=101.7526

respective weights are:0.0559;0.0530;0.0502;0.8409

Macaulay Duration=0.0559*1+0.530*2+0.0502*3+3.3636*4=3.6761

What I don’t understand is why the cash flows weight of the present value of all cash flows is multiplied by the time period to get the duration. I understand that we are wanting to measure the amount of time it will take for us to recoup our investment and I understand taking the weights of the value to be repaid but I don’t understand why those cash flows are mulitplied by the time period. Can anyone shed some light on this?

#2

Try to think of it in terms of having a portfolio, whose total value is 101.7526 say. If you hold different instruments with varying maturities, say 1 year to 4 years, but with different amounts of initial investment as a percentage (which for your case is 5.59%.5.3%,5.02% and 84.09%), then the Macaulay Duration is the weighted maturity date of your Portfolio.

#3

One way to think is - McD is the weighted average time of the diff cash flows. Now the times are 1yr, 2yr, 3yr, 4yr. And the weights you calculated separately - say w1, w2, w3, w4. Now to calculate the weighted average time all you need is w1*1+ w2*2 + w3*3 + w4*4

#4

I get it know, thanks guys!

#5

Weighted avg. maturity…