Consumption-based capital asset pricing model: Difference between revisions

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The '''consumption-based capital asset pricing model''' ('''CCAPM''') is a model of the determination of [[Discounted cash flow#Discount rate|expected (i.e. required) return]] on an investment.<ref>[https://macroeconomicanalysis.com/macroeconomics-wikipedia/consumption-based-capital-asset-pricing-model/ Consumption-based Capital Asset Pricing Model] {{Webarchive|url=https://web.archive.org/web/20190410080919/https://macroeconomicanalysis.com/macroeconomics-wikipedia/consumption-based-capital-asset-pricing-model/ |date=2019-04-10 }}, macroeconomicanalysis.com</ref> The foundations of this concept were laid by the research of [[Robert Lucas Jr.|Robert Lucas]] (1978) and [[Douglas Breeden]] (1979).<ref>{{Cite journal|last=Lucas|first=Robert E.|date=November 1978|title=Asset Prices in an Exchange Economy|journal=Econometrica|volume=46|issue=6|pages=1429–1445|doi=10.2307/1913837|issn=0012-9682|jstor=1913837}}</ref>

{{Orphan|date=February 2009}}

The '''consumption-based capital asset pricing model''' (CCAPM) is used in finance and economics as an expansion of the [[capital asset pricing model]] (CAPM). The CCAPM factors in consumption as a means of understanding and calculating an [[expected return]] on investment.

The model is a generalization of the [[capital asset pricing model]] (CAPM). While the CAPM is derived in a static, one-period setting, the CCAPM uses a more realistic, multiple-period setup. The central implication of the CCAPM is that the expected return on an asset is related to "consumption risk", that is, how much uncertainty in consumption would come from holding the asset. Assets that lead to a large amount of uncertainty offer large expected returns, as investors want to be compensated for bearing consumption risk.

The CCAPM implies that the expected [[risk premium]] on a risky asset, defined as the expected return on a risky asset less the risk free return, is proportional to the covariance of its return and consumption in the period of the return.The consumption beta is included and the expected return is calculated as follows:<ref name="Romer">Romer, David. Advanced Macroeconomics, ch. 7.</ref>

The CAPM can be derived from the following special cases of the CCAPM: (1) a two-period model with quadratic utility, (2) two-periods, exponential utility, and normally-distributed returns, (3) infinite-periods, quadratic utility, and stochastic independence across time, (4) infinite periods and log utility, and (5) a first-order approximation of a general model with normal distributions.<ref>{{Cite book|title=Asset Pricing : (Revised Edition).|last=Cochrane, John H.|date=2009|publisher=Princeton University Press|isbn=9781400829132|oclc=1038790818}}</ref>

r= rf + B(rm - rf)

TheFormally, the CCAPM impliesstates that the expected [[risk premium]] on a risky asset, defined as the expected return on a risky asset less the risk free return, is proportional to the [[covariance]] of its return and consumption in the period of the return. The consumption [[beta (finance)|beta]] is included, and the expected return is calculated as follows:<ref name="Romer">Romer, David. Advanced Macroeconomics, ch. 7.</ref>

r = expected return on security or portfolio

rf = risk free rate

<math>E[r_i]-r^f=\beta(r^m-r^f)</math>

B = consumption beta (of individual company or weighted average of portfolio), and

:where

rm = return from the market

r ::<math>E[r_i]</math> = expected return on security or portfolio

rf::<math>r^f</math> = risk free rate

B::<math>\beta</math> = consumption beta (of individual company or weighted average of portfolio), and

rm::<math>r^m</math> = return from the market

==References==

{{reflistReflist}}

{{Authority control}}

==External links==

*{{cite web |url=http://www.investopedia.com/terms/c/ccapm.asp

|title=Investopedia "Consumption Capital Asset Pricing Model - CCAPM"

|accessdate=2006-11-04}}

*{{cite web|url=http://www.investopedia.com/articles/06/CCAPM.asp

|title=Investopedia "Catch On To The CCAPM"

|accessdate=2006-11-04}}

*[http://www.tcd.ie/Economics/staff/waltis/EC4050/ec4050_ccapm.pdf Sebastien Walti - Derivation of the consumption-CAPM]

[[Category:Mathematical finance]]

[[Category:Financial economics]]

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