Interpretation of Macaulay Duration

Question

I am having a difficulty conceptualizing the meaning of "Macaulay duration" - I want to note I completely understand the math, this isn't the issue. Modified duration & Efficitive Duration make total sense to me as they are refer to a first order approximation of a change in yield on the price of a bond (eg, a 100 bp change in yield causes price to increase/decrease 110 bp). But Macaulay duration is usually quoted in years/time. How does one interpret this? What does it mean for a bond to have a duration of 6 yrs? Can someone help enlighten me? Thank you!

Answer 1

The simple but accurate answer should be that Macaulay Duration is the weighted average maturity of cash flows (in years). That is how it is defined in almost every text book and looked at by most market practitioners. That is why its quoted in years and it gives an indication of when, on a weighted basis, cash flows are paid out (mature). For example, in the image of phi, the pv of cash flow at t1 (9.61) is paid out/matures at t1. In his example MD is 1.78 meaning the bulk of the maturity of cash flows occurs close to t2, simply because the last coupon is paid at t2 plus the par value is returned to the investor. I would not make it more complicated than it really is.

Edit: The following link may make it clearer in case there is still confusion out there: http://www.econ.ohio-state.edu/jhm/ts/duration.htm

Just keep in mind the MD of a zero-coupon bond equals the maturity of the bond.

Answer 2

Maccauly Duration means nothing else than that after the given amount of years, you will have your capital investment back as nominal amount.

If you have \$100 invested, and you have a duration of two years, after two years you will have gotten \$100 repaid, not directly dependent of interest rate or payment scheduling (indirectly they are of course!).

I found this image helpful:

In this example, the bond will be valued at 130.45, which is the sum of PV's of all CF's. After the MD - 1.78 years - you will have received exactly your capital investment, which was the nominal amount of the bond. You are investing the nominal amount and this series of cashflows is valued higher (which is economically reasonable, due to risk exposure!). So while the value of the bond is 130.45, after 1.78 years you will have exactly 100 in your hands, and receive the remainder - 30.45 - in the remaining lifetime of the bond (here thats 0.22 years).

You can see how the small payments sum up to the invested amount, and why the Macaulay Duration is always shorter than the period of payments of the bond.

Of course this number is not exact! You will not have 100 on your account after 1.78 years, but less. You will have to wait for the coupon payment after the MD to actually surpass the 100\$ (in the example thats the final payment.)