Why is there a negative sign?

Quantitative Finance Level 1

The formula for the modified duration is

M o d D ( y ) = − 1 P ∂ P ∂ y Mod \, D(y) = - \frac{1}{P} \frac{ \partial P } { \partial y }

What is the reason for the negative sign?

To account for the fact that bond prices are negative This was defined historically, and we do not want to change the convention Negative duration implies that an increase in yield causes a decrease in price When you differentiate 1 x \frac{1}{ x} , you get − 1 x 2 - \frac{1}{x^2 }

View wiki
Calvin Lin by Calvin Lin

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Chew-Seong Cheong
Feb 19, 2015

In general, the yield y y of a bond is inversely proportional to its price P P . This means that as the yield increases, the price decreases and vice versa ( see more here ). Therefore, ∂ P ∂ y \dfrac {\partial P} {\partial y} has a negative sign.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...