CONVEXIT Function :: SAS/IML(R) 13.1 User's Guide

CONVEXIT Function

CONVEXIT (times, flows, ytm) ;

The CONVEXIT function computes and returns a scalar that contains the convexity of a noncontingent cash flow. The arguments to the CONVEXIT function are as follows:

times: is an $n$ -dimensional column vector of times. Elements should be nonnegative.
flows: is an $n$ -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.

Convexity is essentially a measure of how duration, the sensitivity of price to yield, changes as interest rates change:

$C = \frac{1}{P} \frac{ d^2 P}{ dy^2 }$

Under certain assumptions, the convexity of cash flows that are not yield-sensitive is given by

$C= \frac{ \sum _{k=1}^{K} t_ k (t_ k+1) \frac{ c(k) }{ (1+y)^{t_ k} } }{ P (1+y)^2 }$

where $P$ is the present value, $y$ is the effective per-period yield-to-maturity, $K$ is the number of cash flows, and the $k$ th cash flow is $c(k)$ $t_ k$ periods from the present.

The following statements compute the convexity of a noncontingent cash flow.

timesn = T(do(1, 100, 1));
flows = repeat(10, 100);
ytm = 0.1;
convexit = convexit(timesn, flows, ytm);
print convexit;

Figure 24.78: Convexity of a Noncontingent Cash Flow

convexit
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