G.1.2 Macaulay Duration

Question 1

what is the Macaulay Duration of a single cash flow?

Answer 1

The (Macaulay) duration of a single cash flow is the length of time, in years, until the cash flow occurs.

Question 2

what is the Macaulay Duration of multiple cash flows?

Answer 2

Duration is the average time (in years), weighted by the present values of the cash flows.

So, even though there are multiple cash flows, we still have a single value — a particular choice of average — that can function as a “length of time” for the entire group of payments

Question 3

what is the sum eqn for MacD?

Answer 3

MacD = (SUM(t * A_t))/(SUM(A_t)) or Price

Question 4

what is the annuity eqn for MacD?

Answer 4

((Ia) angle m * n)/(m * a angle m*n)

Question 5

what is the MacD of a n year par value bond with m-thly coupons?

Answer 5

MacD of Par Bond = 1/m a due angle n*m j

where j = (i^m)/m