Convexity: Difference between revisions

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1. Broadly, convexity measures the curvature of the line representing the relationship between an instrument’s yield and its value.   
Convexity measures the curvature of the profile representing the relationship between an [[instrument]]’s or a [[portfolio]]'s yield and its value.   
Duration and Modified duration can be used as the basis for straight line estimates of the rate of change of price/present value.  Convexity is an estimate of the rate of change of duration.  This is often visualised as the degree of 'curviness' of the line representing value versus yield.
Convexity is calculated as:


'''Sum [PV x t x (t+1)]/Sum(PV)'''


2. More strictly defined, convexity is the rate of change of duration, and modified convexity is the rate of change of modified duration, for small changes in yield from the given starting yield.
Convexity is normally calculated as:
 
Sum(PV  x  t  x  (t + 1) ) / Sum(PV).
 
 
Where:
 
PV = Present Value of individual cash flows.
 
t = timing of cash flows.
 
 
Strictly defined, convexity is the rate of change of [[duration]], and [[modified convexity]] is the rate of change of modified duration, for small changes in yield from the given starting yield.
 
 
More loosely, the terms ''Convexity'' and ''Modified convexity'' are sometimes used interchangeably. 
 
Obviously this can lead to confusion, so it is important to clarify whether convexity or modified convexity is intended.


3. More loosely, the terms ''Convexity'' and ''Modified convexity'' are often used interchangeably.  Obviously this can lead to potential confusion, so it is important to clarify whether convexity or modified convexity is intended in any particular context.


== See also ==
== See also ==
* [[Duration]]
* [[Duration]]
* [[Effective convexity]]
* [[Modified convexity]]
* [[Modified convexity]]
* [[Modified duration]]
* [[Modified duration]]


[[Category:Manage_risks]]
[[Category:Risk_frameworks]]

Latest revision as of 19:18, 15 January 2016

Convexity measures the curvature of the profile representing the relationship between an instrument’s or a portfolio's yield and its value.


Convexity is normally calculated as:

Sum(PV x t x (t + 1) ) / Sum(PV).


Where:

PV = Present Value of individual cash flows.

t = timing of cash flows.


Strictly defined, convexity is the rate of change of duration, and modified convexity is the rate of change of modified duration, for small changes in yield from the given starting yield.


More loosely, the terms Convexity and Modified convexity are sometimes used interchangeably.

Obviously this can lead to confusion, so it is important to clarify whether convexity or modified convexity is intended.


See also

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