Capital asset pricing model and Convexity: Difference between pages

From ACT Wiki
(Difference between pages)
Jump to navigationJump to search
imported>Doug Williamson
(Layout.)
 
imported>Doug Williamson
(Standardise appearance of page)
 
Line 1: Line 1:
(CAPM).  
Convexity measures the curvature of the profile representing the relationship between an [[instrument]]’s or a [[portfolio]]'s yield and its value.




The capital asset pricing model links the expected rates of return on traded assets with their relative levels of market risk (beta).
Convexity is normally calculated as:


The model’s uses include estimating a firm’s market cost of equity from its beta and the prevailing theoretical market risk-free rate of return.
Sum ( PV x t x ( t + 1 ) ) / Sum (PV).
 
The CAPM assumes a straight-line relationship between the beta of a traded asset and the expected rate of return on the asset.
 
 
__TOC__
 
 
==CAPM calculation==
 
Expressed as a formula:
 
Re = Rf + beta x ( Rm - Rf )




Where:
Where:


Re = return on security.
PV = Present Value of individual cash flows.
 
Rf = theoretical [[risk free rate of return]].
 
Beta = relative market risk.
 
Rm = average expected rate of return on the market.
 
 
<span style="color:#4B0082">'''Example'''</span>
 
Rf = theoretical risk free rate of return = 4%.
 
Beta = relative market risk = 1.2.
 
Rm = average expected rate of return on the market = 9%.
 
 
Return on security (Re):
 
= 4 + 1.2 x ( 9 - 4 )
 
= 10%.
 
This investment requires an expected <u>rate of return</u> of 10%, higher than average rate of return on the market as a whole of only 9%, because its market <u>risk</u> (measured by beta = 1.2) is greater than the average market risk of only 1.0.
 
 
Under the capital asset pricing model only the (undiversifiable) market risk of securities is rewarded with additional returns, because the model assumes that rational market participants have all fully diversified away all specific risk within their investment portfolios.


t = timing of cash flows.




== Use of the CAPM to quantify cost of equity ==
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.


When the CAPM is used to calculate an estimate of the cost of equity, it is conventionally expressed as:


Ke = Rf + beta x ( Rm - Rf )
More loosely, the terms ''Convexity'' and ''Modified convexity'' are sometimes used interchangeably. 
 
Where:


Ke = cost of equity.
Obviously this can lead to confusion, so it is important to clarify whether convexity or modified convexity is intended.




== See also ==
== See also ==
* [[Beta]]
* [[Duration]]
* [[Business risk]]
* [[Effective convexity]]
* [[Capital gain]]
* [[Modified convexity]]
* [[CertFMM]]
* [[Modified duration]]
* [[Cost of equity]]
* [[Equity beta]]
* [[Equity risk]]
* [[Equity risk premium]]
* [[Financial risk]]
* [[Market risk]]
* [[Market risk premium]]
* [[Modern Portfolio Theory]]
* [[Risk]]
* [[Security Market Line]]
* [[Specific risk]]
* [[Systematic risk]]


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

Revision as of 12:11, 21 March 2015

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

Retrieved from ‘https://wiki.treasurers.org/w/index.php?title=Capital_asset_pricing_model&oldid=11565’