Overview
Sensitivity based measures are measures that indicate hom much the value of an instrument changes with respect to the change of some underlying variable.
The most commonly used variable in sensitivity analysis, is the bonds yield. (see duration and convexity below) However, any function which calculates the value of the security based on a set of inputs, can be used to calculate a sensitivity to any of its inputs.
{% value = f(x_1,x_2, ... , x_n) %}
The sensitivity to a particular input {% x_i %} is computed to be
{% sensitivity = \frac{1}{P} \frac{\partial f}{\partial x_1} %}
(see model based sensitivity
for more information)
Duration and Convexity
The most commonly used sensitivity based measures are the duration and convexity, which measure the sensitivity of price with respect to the securities yield.
The two measures can be used to approximate the change in price of a fixed income instrument with the following formulate for the approximate change in the price of the instrument.
{% \Delta P / P \approx -D \times \Delta y + \frac{1}{2} \times C \Delta y^2 %}
The mathematical basis of this type of analysis can be viewed at
taylor series foundation.
Hedging
Hedging a portfolio means to trade the portfolio so as to reduce or eliminate some of the risk in the portfolio. The market risk in a portfolio of fixed income assets comes from fluctuations in the yield curve. All bonds can lose value from interest rate fluctuations, except floating rate instruments.
The typical method of hedging a fixed income portfolio utilizing the Duration and Convexity is to trade the portfolio so as to get the duration (and possibly the convexity also) to zero. In such a case, we then have
{% \Delta P / P \approx 0 %}