Skip to content
All library documents

Modified Duration and Absolute Versus Percentage Bond Price Changes

Article Quant Q&A · Author: M00000001
Read the original

Summary

The document asks how modified duration translates a yield change into a bond price change when the quoted price is expressed as a percentage of face value. Its example uses a bond quoted at 103 with modified duration of 4.62 years and a one percentage point rise in yield. Under the usual approximation, the price falls by about 4.62% of its current value, so the estimated new quote is 103 multiplied by 1 minus 0.0462, rather than 103 plus or minus 4.62 price points.

The corresponding mathematical definition is the negative relative price sensitivity, −(1/P)(∂P/∂y); without the negative sign, the derivative itself is typically negative for a conventional bond. The estimate is local and approximate: duration summarizes first-order sensitivity, while convexity and other effects can make actual price changes differ, especially for larger yield moves.

Key ideas

  • Modified duration measures percentage price sensitivity to a change in yield.
  • For a one percentage point yield rise, the example implies an approximate 4.62% decline from the bond’s current quoted price.
  • A relative price change is applied multiplicatively to the current quote, rather than added as a number of price points.
  • The signed derivative ∂P/∂y is negative for a conventional bond, while modified duration is usually defined with a leading minus sign.
  • Duration gives a first-order approximation and omits convexity effects.

Tags

Fixed incomeDerivatives pricingRisk management
Full text
# Bond Change in Absolute or Relatively Percentage


# Bond Change in Absolute or Relatively Percentage












Since most of the bonds prices are quoted in price, for example, bond price of 103 means 103% of the principal or face value (ex. $1000). Suppose a bond has modified duration of 4.62 years. If yield to maturity increase by 1%, bond price will decrease by 4.62% (0.01*-4.62*100%), so should the bond price be : 1. 103*(1+4.62%) OR 2. 103+4.62

If we express modified duration using mathematical formula, should it be $\frac{\partial P}{\partial y}*\frac{1}{\ P}$ or $\frac{\partial P}{\partial y}$

Note: $P$ is bond price in percentage; $y$ is yield to maturity

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.