Duration & Convexity Calculation Example: Working with Convexity and Sensitivity

A working example of convexity and sensitivity calculation. Earlier we had reviewed the calculation process for Effective Duration. In this post we will see how convexity is calculated. We will also see how the Effective Duration and Convexity are brought together to estimate the % change in price brought about by a % change in yields, in other words, the sensitivity of the sample instrument to interest rate changes.

Effective Convexity

Effective Convexity is calculated using the following formula:

Effective Convexity = (97.2691+99.0768-2*98.1666)/(2*98.1666*1%^2) = 0.6461

Sensitivity

Using Effective Duration and Convexity, it is possible to estimate by how much the price of the instrument will change in response to a change in yield rates. The estimate of the % change in price is given by the following formula:

Total estimated percentage price change= -Duration×?i×100+Convexity×(?i)²×100

So for a 1% decrease in the yield rates the total estimated percentage price change is:

-.9208 * (-1%) * 100 + 0.6461 *(- 1%)^2*100 = 0.9272%

This means that a 1% decline in yield rates will result in a 0.9272% increase in price.

Applying this to the initial price (P₀) we see that a 1% decline in yield rates will cause prices to rise from 98.1666 to 99.0768 [= 98.1666*(1+.9272%)]. This as we can see from the calculation of P- above is equal to the actual price when the yield decreased from 12% to 11%.

In this post we have seen how Effective Convexity has been calculated. We have also seen how the Effective Duration and Convexity metrics are used to estimate the % change in price of an interest rate sensitive instrument when yield rates changed.

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