CONVEXIT Function

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Changes and Enhancements

CONVEXIT Function

calculates and returns a scalar containing the convexity of a noncontingent cash flow

CONVEXIT( times,flows,ytm)

The CONVEXIT function calculates and returns a scalar containing the convexity of a noncontingent cash flow.

times: is an n-dimensional column vector of times. Elements should be non-negative.
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:

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

With cash flows that are not yield-sensitive, and the assumption of parallel shifts to a flat term-structure, convexity 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 statements

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

result in the following output:

   CONVEXIT 
   199.26229

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