Price Sensitivity
The sensitivity of a bond's market price to interest rate (i.e. yield) movements is measured by its duration, and, additionally, by its convexity.
Duration is a linear measure of how the price of a bond changes in response to interest rate changes. It is approximately equal to the percentage change in price for a given change in yield, and may be thought of as the elasticity of the bond's price with respect to discount rates. For example, for small interest rate changes, the duration is the approximate percentage by which the value of the bond will fall for a 1% per annum increase in market interest rate. So the market price of a 17-year bond with a duration of 7 would fall about 7% if the market interest rate (or more precisely the corresponding force of interest) increased by 1% per annum.
Convexity is a measure of the "curvature" of price changes. It is needed because the price is not a linear function of the discount rate, but rather a convex function of the discount rate. Specifically, duration can be formulated as the first derivative of the price with respect to the interest rate, and convexity as the second derivative (see: Bond duration closed-form formula; Bond convexity closed-form formula). Continuing the above example, for a more accurate estimate of sensitivity, the convexity score would be multiplied by the square of the change in interest rate, and the result added to the value derived by the above linear formula.
Read more about this topic: Bond Valuation
Famous quotes containing the words price and/or sensitivity:
“The price of hating other human beings is loving oneself less.”
—Eldridge Cleaver (b. 1935)
“Freedom of choice for women, at the expense of the caring, warmth, and sensitivity to others so often associated with them, may be empty. In the thrust to redefine male and female roles, women must not become men; nor can men be permitted the continual dehumanization of their roles.”
—Kathleen Weibel (b. 1945)