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## DURATION Function

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.

times
is an -dimensional column vector of times. Elements should be nonnegative.
flows
is an -dimensional column vector of cash flows.
ytm
is the per-period yield-to-maturity of the cash-flow stream. 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
where is the present value, is the per-period effective yield-to-maturity, is the number of cash flows, and the th cash flow is , periods from the present. This measure is referred to as modified duration to differentiate it from the first duration measure ever proposed, Macaulay duration:
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:


times={1};
ytm={0.1};
flow={10};
duration=duration(times,flow,ytm);
print duration;


These statements produce the following output:


DURATION
0.9090909


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