Question

Compute the Macaulay duration for a 9-year zero-coupon bond having a yield to maturity of 13%.

	a.	7.96
	b.	9.26
	c.	7.70
	d.	9.00
	e.	8.92 please explain in steps

Answer 1

Macaulay duration is the weighted average time to maturity of a bond.

The formula for macaulay's duration is

Where, PV is the present value of the bond at a given yield to maturity.

C_1, C_2, C_{3, ...} C_T the cash flows from the bond at time period 1, 2, 3, .... , T respectively.

Now, since the given bond is a Zero coupon bond, therefore is only one cash flow, i.e at the end of the period.

Thus, C_1, C_2, C_3, are all 0

Thus, duration = 0 + 0 + 0 + ...............+ 9 * PV (C_T) / PV

Since the present value of the future cash flow is same as the present value of the bond, therefore

Duration = 9 years.

Explained differently, duration of a zero coupon bond is always the years to maturity since the whole amount is to be received at the end of the maturity.