calculates and returns a scalar containing the modified duration of
a noncontingent cash flow.
- DURATION( times,flows,ytm)
The DURATION function returns the modified duration of a noncontingent
cash flow as a scalar.
- is an -dimensional column vector of times.
Elements should be nonnegative.
- is an -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
is the present value,
is the per-period effective yield-to-maturity,
is the number of cash flows, and the
cash flow is
periods from the present.
This measure is referred to as modified duration
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 (that is,
timing) of all the cash flows and is hence an ``average
time-to-maturity'' of the bond.
For example, consider the following statements:
These statements produce the following output:
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