CONVXP Function

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

Category:

Financial

Syntax

CONVXP(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 < k_{0} \leq \frac{1}{n}

y

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

Range

y > 0

Details

The CONVXP function returns the value

\begin{matrix} C = \frac{1}{n^{2}} (\frac{Σ_{k = 1}^{K} t_{k} (t_{k} + 1) \frac{c (k)}{{(1 + \frac{y}{n})}^{t_{k}}}}{P {(1 + \frac{y}{n})}^{2}}) \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

In the following example, the CONVXP function returns the convexity of a bond that has a face value of 1000, an annual coupon rate of 0.01, 4 coupons per year, and 14 remaining coupons. The time from settlement date to next coupon date is 0.165, and the annual yield-to-maturity is 0.08.

data _null_;
   y=convxp(1000,.01,4,14,.33/2,.08);
   put y;
run;

The value that is returned is 11.729001987.

CONVXP Function

Syntax

Required Arguments

A

c

n

K

k0

y

Details

Example

k₀