Tuesday, May 19, 2009

Bond Duration, Quantifying Yield Sensitivity

One concept which I find surprisingly and needlessly confusing is the idea of bond duration. I say surprisingly because most people would associate the word duration with time, however, in this context, it relates to the approximate sensitivity of a bond's price change in dollars given a change in yield.

Aside from that, the math involved is actually quite simple. The formula for Duration is:

Duration = - % Change in Bond Price / Yield Change in %

Dollar Duration is the special case where the change in yield is 1oo basis points (100 bps = 1%).

The duration is the relationship between price and yield as shown below:
Note that like elasticity which is done in percentages, the average bond price is used to calculate the duration so that a more accurate value can be produced for a yield change on either side of the average (rate shock increase or decrease).

However, also note that due to the convexity of the yield curve, duration's approximation of sensitivity under compensates for the sensitivity. In calculus terms, duration is merely an approximation (based on first principles) of the slope of the curve (derivative).

1 comment:

Anonymous said...

Hi , Can you please explain how the duration number is got and how or why it explains the relationship between price and interest rates (not as a mathematical formula but the logic please).