Capital Asset Pricing Model
(CAPM)


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Valuing stocks, securities, derivatives and/or assets by relating risk and expected return. Explanation of Capital Asset Pricing Model (CAPM) of William Sharpe.



  

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The Capital Asset Pricing Model (CAPM) is an economic model for valuing stocks, securities, derivatives and/or assets by relating risk and expected return. CAPM is based on the idea that investors demand additional expected return (called the risk premium) if they are asked to accept additional risk.

 

Description of CAPM. The Capital Asset Pricing Model is explained.

CAPM was introduced by Treynor ('61), Sharpe ('64) and Lintner ('65). By introducing the notions of systematic and specific risk, it extended the portfolio theory. In 1990, William Sharpe was Nobel price winner for Economics. "For his contributions to the theory of price formation for financial assets, the so-called Capital Asset Pricing Model (CAPM)."

 

The CAPM model says that the expected return that the investors will demand, is equal to: the rate on a risk-free security plus a risk premium. If the expected return is not equal to or higher than the required return, the investors will refuse to invest and the investment should not be undertaken.

CAPM decomposes a portfolio's risk into systematic risk and specific risk. Systematic risk is the risk of holding the market portfolio. When the market moves, each individual asset is more or less affected. To the extent that any asset participates in such general market moves, that asset entails systematic risk. Specific risk is the risk which is unique for an individual asset. It represents the component of an asset's return which is not correlated with general market moves.

According to CAPM, the marketplace compensates investors for taking systematic risk but not for taking specific risk. This is because specific risk can be diversified away. When an investor holds the market portfolio, each individual asset in that portfolio entails specific risk. But through diversification, the investor's net exposure is just the systematic risk of the market portfolio.

 

CAPM formula

The CAPM formula is:

Expected Security Return = Riskless Return + Beta x (Expected Market Risk Premium)

or:
r = Rf + Beta x (RM - Rf)
 

{      Another version of the formula is: r-Rf = Beta x (RM - Rf)      }


where:
- r           is the expected return rate on a security;
- Rf         is the rate of a "risk-free" investment, i.e. cash;
- RM       is the return rate of the appropriate asset class.
 

Beta is the overall risk in investing in a large market, like the New York Stock Exchange. Beta, by definition equals 1,00000 exactly.

Each company also has a Beta. The Beta of a company is that company's risk compared to the Beta (Risk) of the overall market. If the company has a Beta of 3.0, then it is supposed to be 3 times more risky than the overall market. Beta indicates the volatility of the security, relative to the asset class.

 

Investing in individual securities

A consequence of CAPM thinking is that it implies that investing in individual stocks is useless, because one can duplicate the reward and risk characteristics of any security just by using the right mix of cash with the appropriate asset class. This is why die-hard followers of CAPM avoid securities, and instead build portfolios merely out of low-cost index funds.

 

Assumptions of the Capital Asset Pricing Model

Note! The Capital Asset Pricing Model is a ceteris paribus model. It is only valid within a special set of assumptions. These are:

  • Investors are risk averse individuals who maximize the expected utility of their end of period wealth. Implication: The model is a one period model.
  • Investors have homogenous expectations (beliefs) about asset returns. Implication: all investors perceive identical opportunity sets. This means everyone has the same information at the same time.
  • Asset returns are distributed by the normal distribution.
  • There exists a risk free asset and investors may borrow or lend unlimited amounts of this asset at a constant rate: the risk free rate.
  • There is a definite number of assets and their quantities are fixated within the one period world.
  • All assets are perfectly divisible and priced in a perfectly competitive marked. Implication: e.g. human capital is non-existing (it is not divisible and it can't be owned as an asset).
  • Asset markets are frictionless and information is costless and simultaneously available to all investors. Implication: borrowing rate equals the lending rate.
  • There are no market imperfections such as taxes, regulations, or restrictions on short selling.

Normally, all of the assumptions mentioned above are neither valid nor fulfilled. However, CAPM anyway remains one of the most used investments models to determine risk and return.

 

Book: William F. Sharpe - Portfolio Theory and Capital Markets -

Book: Harry M. Markowitz - Mean-Variance Analysis in Portfolio Choice and Capital Markets -

Book: Mary Jackson - Advanced modelling in finance using Excel and VBA -

 

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Recent User Comments
 - Kenya Calculating Company Beta "How do we find beta for a company?"    0
Saud - Saudi Arabia CAPM usage by Fund Managers "What is the relevance of the capital asset pricing model (CAPM) to a fund manager in the equity markets? How is it being used?"    1
Haseeb - Pakistan Application of Capital Asset Pricing Model in Pakistan "I would like to know how companies in Paskistan use the CAPM model... What are the benefits and demerits???"    4
Anna - UK Are US Treasury Bills still Zero Beta? "The books say that beta can be zero for absolutely risk-free stocks. US Treasury Bills are generally perceived to be such assets as well as other governments' bonds. Considering the present economic turmoil, I have doubts that this theory will hold. I don't know about negative beta :)"    0
 - Pakistan CAPM "In this model another assumption is that the number of assets are fixed in a portfolio. But this is a confusing thing as well, because it neglects the concept of marginality i.e. the overall change due to the increase of one asset in a portfolio."    0
Best User Comments
Melvin - USA Can the Beta of a stock be zero? "Question on CAPM: I know that in the CAPM Model the Beta for a stock can be less than one. If the company has a Beta of 0.33, then it is supposed to be 3 times less risky than the overall market. But can Beta also be zero? And can it be negative?"    7
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  ● Pete (USA) US Treasury Bills "Indeed Anna, US treasury bills or government bonds were always considered to be risk-free. The reason behind this was originally that our US economy was so strong and the country so big and solid. In the last decade or so this changed and the reason became that we all agreed that we would consider the risk to be zero (even if we had some doubts already). In the last couple of years we still kept to this agreement even if we knew things had changed, because nobody was willing to accept the consequence (a system crisis). Now that we have the crisis it is obvious that the old paradigm no longer holds: US Treasury bills can no longer be considered risk-free."


  ● Pereira (Portugal) Can Beta be zero ? "Assuming a Beta=0 is the same as to say that the r=Rf. Then, the security under valuation has the same expected earnings as a risk free asset. Finally, the only asset with a risk free rate is assumed to be government bonds.
So, saying that some asset has Beta=0 is equivalent to say that asset is risk free or is a government bond"
  ● CSB Nair (India) Stock Beta =<0 "The beta can well be 0 or negative if the expected earnngs are below the risk free rate."
  ● Thomas (USA) Stocks with a negative ß "A company with a ß of 1.000 has the same expected return rate as the risk free rate.
I therefore believe that CSB Nair is incorrect: if the expected earnings are just lower than the risk free rate, then the company has a ß between 0 and 1, but not negative.
Yet it is possible to imagine a company with a negative beta! This is (only) the case when its returns are counter-cyclical and move opposite to the market.
Of course, the beta of most companies' stock is positive. But there are financial assets which are designed to have negative betas. For example, funds that engage exclusively in short-selling make money when the market is falling and lose when the market is rising. Including these assets in your portfolio decreases your volatility."
  ● Harold (Canada) Beta of a stock "A beta of one means the stock moves with the market: in other words when the market moves up 5% the stock moves up 5%.
A stock with a beta between 0 and 1 moves with the market but to a lessor degree. Such a stock can be called a conservative investment.
A stock with a beta greater than 1 is a stock which moves in the same direction as the market but it moves more than the market moves. Such a stock can be referred to as aggressive. In other words when the market moves up 5%, a stock with a Beta of 2 moves up 10%.
A stock which has a negative beta moves in the opposite direction as the market. A stock with a beta of -2 declines 8% if the market goes up by 4% and conversely climbs 8% if the market falls by 4%."
  ● Walter (UK) Gold "Gold-related stocks are typically beta-negative."
  ● Bikash (India) What about cash?? "Assets with beta 0 are same as risk-free assets and have same expected return and not assets with beta 1 as Thomas believes. Can assets have negative beta? Well, I don't think so. Beta is a measure of risk and accordingly determines expected return and not the other way round. So, an asset class (say short selling) gives opposite return to market does not mean it is less risky than a risk-free return and so we would expect it to yield lesser return than risk-free rate. In fact, we would not expect any asset class to give return less than risk-free rate? would we?? No-one, not even the most risk-averse investor, need an asset class with negative beta. Yes, the ways to determine beta might give a negative value (Say for a security that have performed counter to the market in past say 2 yrs), but that is a limitation of determining beta and not that beta is negative. But yeah, I am not sure on the beta of cash....."
  ● Rusell Aguilar (Peru) BETA of Peru "How much is beta of Peru and Latinamerica, Who has the quantity. Please I need your answer for my homework, thank you."
  ●  (Pakistan) CAPM "It is the theory that relates the expected return with the risk, so when we say that the beta is zero then it means that the security is risk free and then the expected return should be none too. It is impossible in fact insane to consider a security bearing no risk, other than those who come under the definition of risk free securities. An investor in the market is not for doing a picnic, rather he is there to get some return on his investment. Even a risk-averse investor cannot compromise on return. So, I think that those who are of the opinion that there can be zero risk are not actually looking the situation with the right spectacles on."
  ● Anna (UK) CAPM "Risk-free security does not necessarily mean zero return-the return will be equal to the interest rate-i.e. Government bonds with 5% return-they are considered as risk-free, but still generate 5 % return although it could be argued how much of that 5 % is real money and how much is eaten by inflation etc."