DURP Function

Returns the modified duration for a periodic cash flow stream, such as a bond.

Category:

Financial

Syntax

DURP(A,c,n,K,k₀,y)

Required Arguments

A

specifies the par value.

Range

A > 0

c

specifies the nominal per-period coupon rate, expressed as a fraction.

Range

0 ≤ c< 1

n

specifies the number of coupons per period.

Range

n > 0 and is an integer

K

specifies the number of remaining coupons.

Range

K > 0 and is an integer

k₀

specifies the time from the present date to the first coupon date, expressed in terms of the number of periods.

Range

0 < k₀ ≤ 1/n

y

specifies the nominal per-period yield-to-maturity, expressed as a fraction.

Range

y > 0

Details

The DURP function returns the value

\begin{matrix} D = \frac{1}{n} \frac{Σ_{k = 1}^{K} t_{k} \frac{c (k)}{{(1 + \frac{y}{n})}^{t_{k}}}}{P (1 + \frac{y}{n})} \end{matrix}

The following relationships apply to the preceding equation:

$t_{k} = n k_{0} + k - 1$
$c (k) = \frac{c}{n} A f o r k = 1, \dots, K - 1$
$c (K) = (1 + \frac{c}{n}) A$

The following relationship applies to the preceding equation:

\begin{matrix} P = Σ_{k = 1}^{K} \frac{c (k)}{{(1 + \frac{y}{n})}^{t_{k}}} \end{matrix}

Example

data _null_;
d=durp(1000,1/100,4,14,.33/2,.10);
put d;
run;

The value returned is 3.26496.

DURP Function

Syntax

Required Arguments

A

c

n

K

k0

y

Details

Example

k₀