calculates and returns a scalar containing the modified duration of
a non-contingent cash-flow.
The Duration function returns the modified duration of a non-contingent
cash-flow as a scalar.
- is an n-dimensional column vector of times.
Elements should be non-negative.
- is an n-dimensional column vector of cash-flows.
- is the per-period yield-to-maturity of the
This is a scalar and should be positive.
Duration of a security is generally defined as:
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 = -[( [dP/P] )/ dy ]
where P is the present value,
y is the per period effective yield-to-maturity,
K is the number of cash-flows, the k-th
cash flow being c(k), tk periods from the present.
This measure is referred to as modified duration to
differentiate it from the first duration measure ever proposed,
This expression also reveals the reason for the name duration, since
it is a present-value-weighted average of the duration (i.e. timing) of
all the cash-flows and is hence an "average time-to-maturity" of the
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.