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An estimation of the CAPM and the security market line (purple) for the Dow Jones Industrial Average over 3 years for monthly data.
An estimation of the CAPM and the security market line (purple) for the Dow Jones Industrial Average over 3 years for monthly data.

In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio.

The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset. CAPM assumes a particular form of utility functions (in which only first and second moments matter, that is risk is measured by variance, for example a quadratic utility) or alternatively asset returns whose probability distributions are completely described by the first two moments (for example, the normal distribution) and zero transaction costs (necessary for diversification to get rid of all idiosyncratic risk). Under these conditions, CAPM shows that the cost of equity capital is determined only by beta.[1][2] Despite it failing numerous empirical tests,[3] and the existence of more modern approaches to asset pricing and portfolio selection (such as arbitrage pricing theory and Merton's portfolio problem), the CAPM still remains popular due to its simplicity and utility in a variety of situations.


The CAPM was introduced by Jack Treynor (1961, 1962),[4] William F. Sharpe (1964), John Lintner (1965a,b) and Jan Mossin (1966) independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. Sharpe, Markowitz and Merton Miller jointly received the 1990 Nobel Memorial Prize in Economics for this contribution to the field of financial economics. Fischer Black (1972) developed another version of CAPM, called Black CAPM or zero-beta CAPM, that does not assume the existence of a riskless asset. This version was more robust against empirical testing and was influential in the widespread adoption of the CAPM.


The CAPM is a model for pricing an individual security or portfolio. For individual securities, we make use of the security market line (SML) and its relation to expected return and systematic risk (beta) to show how the market must price individual securities in relation to their security risk class. The SML enables us to calculate the reward-to-risk ratio for any security in relation to that of the overall market. Therefore, when the expected rate of return for any security is deflated by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio, thus:

The market reward-to-risk ratio is effectively the market risk premium and by rearranging the above equation and solving for , we obtain the capital asset pricing model (CAPM).


Restated, in terms of risk premium, we find that:

which states that the individual risk premium equals the market premium times β.

Note 1: the expected market rate of return is usually estimated by measuring the arithmetic average of the historical returns on a market portfolio (e.g. S&P 500).

Note 2: the risk free rate of return used for determining the risk premium is usually the arithmetic average of historical risk free rates of return and not the current risk free rate of return.

For the full derivation see Modern portfolio theory.

Modified betas

There has also been research into a mean-reverting beta often referred to as the adjusted beta, as well as the consumption beta. However, in empirical tests the traditional CAPM has been found to do as well as or outperform the modified beta models.

Security market line

The SML graphs the results from the capital asset pricing model (CAPM) formula. The x-axis represents the risk (beta), and the y-axis represents the expected return. The market risk premium is determined from the slope of the SML.

The relationship between β and required return is plotted on the security market line (SML), which shows expected return as a function of β. The intercept is the nominal risk-free rate available for the market, while the slope is the market premium, E(Rm)− Rf. The security market line can be regarded as representing a single-factor model of the asset price, where β is the exposure to changes in the value of the Market. The equation of the SML is thus:

It is a useful tool for determining if an asset being considered for a portfolio offers a reasonable expected return for its risk. Individual securities are plotted on the SML graph. If the security's expected return versus risk is plotted above the SML, it is undervalued since the investor can expect a greater return for the inherent risk. And a security plotted below the SML is overvalued since the investor would be accepting less return for the amount of risk assumed.

Asset pricing

Once the expected/required rate of return is calculated using CAPM, we can compare this required rate of return to the asset's estimated rate of return over a specific investment horizon to determine whether it would be an appropriate investment. To make this comparison, you need an independent estimate of the return outlook for the security based on either fundamental or technical analysis techniques, including P/E, M/B etc.

Assuming that the CAPM is correct, an asset is correctly priced when its estimated price is the same as the present value of future cash flows of the asset, discounted at the rate suggested by CAPM. If the estimated price is higher than the CAPM valuation, then the asset is overvalued (and undervalued when the estimated price is below the CAPM valuation).[5] When the asset does not lie on the SML, this could also suggest mis-pricing. Since the expected return of the asset at time is , a higher expected return than what CAPM suggests indicates that is too low (the asset is currently undervalued), assuming that at time the asset returns to the CAPM suggested price.[6]

The asset price using CAPM, sometimes called the certainty equivalent pricing formula, is a linear relationship given by

where is the payoff of the asset or portfolio.[5]

Asset-specific required return

The CAPM returns the asset-appropriate required return or discount rate—i.e. the rate at which future cash flows produced by the asset should be discounted given that asset's relative riskiness.

Betas exceeding one signify more than average "riskiness"; betas below one indicate lower than average. Thus, a more risky stock will have a higher beta and will be discounted at a higher rate; less sensitive stocks will have lower betas and be discounted at a lower rate. Given the accepted concave utility function, the CAPM is consistent with intuition—investors (should) require a higher return for holding a more risky asset.

Since beta reflects asset-specific sensitivity to non-diversifiable, i.e. market risk, the market as a whole, by definition, has a beta of one. Stock market indices are frequently used as local proxies for the market—and in that case (by definition) have a beta of one. An investor in a large, diversified portfolio (such as a mutual fund), therefore, expects performance in line with the market.

Risk and diversification

The risk of a portfolio comprises systematic risk, also known as undiversifiable risk, and unsystematic risk which is also known as idiosyncratic risk or diversifiable risk. Systematic risk refers to the risk common to all securities—i.e. market risk. Unsystematic risk is the risk associated with individual assets. Unsystematic risk can be diversified away to smaller levels by including a greater number of assets in the portfolio (specific risks "average out"). The same is not possible for systematic risk within one market. Depending on the market, a portfolio of approximately 30–40 securities in developed markets such as the UK or US will render the portfolio sufficiently diversified such that risk exposure is limited to systematic risk only. In developing markets a larger number is required, due to the higher asset volatilities.

A rational investor should not take on any diversifiable risk, as only non-diversifiable risks are rewarded within the scope of this model. Therefore, the required return on an asset, that is, the return that compensates for risk taken, must be linked to its riskiness in a portfolio context—i.e. its contribution to overall portfolio riskiness—as opposed to its "stand alone risk". In the CAPM context, portfolio risk is represented by higher variance i.e. less predictability. In other words, the beta of the portfolio is the defining factor in rewarding the systematic exposure taken by an investor.

Efficient frontier

Main article: Efficient frontier

The (Markowitz) efficient frontier. CAL stands for the capital allocation line.
The (Markowitz) efficient frontier. CAL stands for the capital allocation line.

The CAPM assumes that the risk-return profile of a portfolio can be optimized—an optimal portfolio displays the lowest possible level of risk for its level of return. Additionally, since each additional asset introduced into a portfolio further diversifies the portfolio, the optimal portfolio must comprise every asset, (assuming no trading costs) with each asset value-weighted to achieve the above (assuming that any asset is infinitely divisible). All such optimal portfolios, i.e., one for each level of return, comprise the efficient frontier.

Because the unsystematic risk is diversifiable, the total risk of a portfolio can be viewed as beta.


All investors:[7]

  1. Aim to maximize economic utilities (Asset quantities are given and fixed).
  2. Are rational and risk-averse.
  3. Are broadly diversified across a range of investments.
  4. Are price takers, i.e., they cannot influence prices.
  5. Can lend and borrow unlimited amounts under the risk free rate of interest.
  6. Trade without transaction or taxation costs.
  7. Deal with securities that are all highly divisible into small parcels (All assets are perfectly divisible and liquid).
  8. Have homogeneous expectations.
  9. Assume all information is available at the same time to all investors.


In their 2004 review, economists Eugene Fama and Kenneth French argue that "the failure of the CAPM in empirical tests implies that most applications of the model are invalid".[3]

See also


  1. ^
  2. ^ James Chong; Yanbo Jin; Michael Phillips (April 29, 2013). "The Entrepreneur's Cost of Capital: Incorporating Downside Risk in the Buildup Method" (PDF). Retrieved 25 June 2013.
  3. ^ a b Fama, Eugene F; French, Kenneth R (Summer 2004). "The Capital Asset Pricing Model: Theory and Evidence". Journal of Economic Perspectives. 18 (3): 25–46. doi:10.1257/0895330042162430.
  4. ^ French, Craig W. (2003). "The Treynor Capital Asset Pricing Model". Journal of Investment Management. 1 (2): 60–72. SSRN 447580.
  5. ^ a b Luenberger, David (1997). Investment Science. Oxford University Press. ISBN 978-0-19-510809-5.
  6. ^ Bodie, Z.; Kane, A.; Marcus, A. J. (2008). Investments (7th International ed.). Boston: McGraw-Hill. p. 303. ISBN 978-0-07-125916-3.
  7. ^ Arnold, Glen (2005). Corporate financial management (3. ed.). Harlow [u.a.]: Financial Times/Prentice Hall. p. 354.
  8. ^ French, Jordan (2016). "Back to the Future Betas: Empirical Asset Pricing of US and Southeast Asian Markets". International Journal of Financial Studies. 4 (3): 15. doi:10.3390/ijfs4030015.
  9. ^ French, Jordan (2016). Estimating Time-Varying Beta Coefficients: An Empirical Study of US & ASEAN Portfolios. Research in Finance. 32. pp. 19–34. doi:10.1108/S0196-382120160000032002. ISBN 978-1-78635-156-2.
  10. ^ "News and insight | Wealth Management | Barclays" (PDF).
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  12. ^ de Silva, Harindra (2012-01-20). "Exploiting the Volatility Anomaly in Financial Markets". CFA Institute Conference Proceedings Quarterly. 29 (1): 47–56. doi:10.2469/cp.v29.n1.2. ISSN 1930-2703.
  13. ^ Baker, Malcolm; Bradley, Brendan; Wurgler, Jeffrey (2010-12-22). "Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly". Financial Analysts Journal. 67 (1): 40–54. doi:10.2469/faj.v67.n1.4. ISSN 0015-198X. S2CID 12706642.
  14. ^ Blitz, David; Van Vliet, Pim; Baltussen, Guido (2019). "The volatility effect revisited". Journal of Portfolio Management. 46 (1): jpm.2019.1.114. doi:10.3905/jpm.2019.1.114. S2CID 212976159.
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  16. ^ Roll, R. (1977). "A Critique of the Asset Pricing Theory's Tests". Journal of Financial Economics. 4 (2): 129–176. doi:10.1016/0304-405X(77)90009-5.
  17. ^ Stambaugh, Robert (1982). "On the exclusion of assets from tests of the two-parameter model: A sensitivity analysis". Journal of Financial Economics. 10 (3): 237–268. doi:10.1016/0304-405X(82)90002-2.
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  19. ^ Doeswijk, Ronald; Lam, Trevin; Swinkels, Laurens (2014). "The global multi-asset market portfolio, 1960-2012". Financial Analysts Journal. 70 (2): 26–41. doi:10.2469/faj.v70.n2.1. S2CID 704936.
  20. ^ Doeswijk, Ronald; Lam, Trevin; Swinkels, Laurens (2019). "Historical returns of the market portfolio". Review of Asset Pricing Studies. X (X): XX.
  21. ^ "Archived copy" (PDF). Archived from the original (PDF) on 2014-07-25. Retrieved 2012-05-08.CS1 maint: archived copy as title (link)
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