DURATION Function

Chapter Contents

Language Reference

DURATION Function

calculates modified duration of a non-contingent cashflow

DURATION( times, flows, ytm)

The inputs to the DURATION statement are as follows:

times: is an n-dimensional column vector of times.
flows: is an n-dimensional column vector of cash flows.
rates: is the per-period yield-to-maturity of the cash flow stream.

The DURATION function returns a scalar which is the duration of a non contingent cash flow. Duration of a security is generally defined as

D = -[( [dP/P] )/ dy ]

In other words, it is the relative change in price for a unit change in yield. Since prices move in the opposite direction to yields, the sign change preserves positivity for convenience. With cash flows that are not yield-sensitive and the assumption of parallel shifts to a flat term-structure, duration is given by

$D_{\rm mod} = \frac{1}{P(1+y)} \sum_{k=1}^K t_k \frac{c(k)}{(1+y)^{t_k}}$

where P is the present value, y is the per period effective yield-to-maturity, and K is the number of cash flows, the k^th cash flow being c(k), t_k periods from the present. This measure is referred to as modified duration to differentiate it from the first duration measure ever proposed, Macaulay duration:

$D_{\rm Mac} = \frac{1}P \sum_{k=1}^K t_k \frac{c(k)}{(1+y)^{t_k}}$

This expression also reveals the reason for the name duration, since it is a present-value-weighted average of the duration, that is, timing of all the cash flows and is hence an "average time-to-maturity" of the bond.

Chapter Contents
Previous
Next
Top