Capital Asset Priceing Model

8/12/2019 Capital Asset Priceing Model

1/5


2/5

CAPITAL ASSET PRICEING MODEL

In financial markets, people invest in assets (a security / equity / tradable stocks / portfolio

etc) with the expectation of return in future from such assets. But, with the expectation there

is always uncertainty that is with such investments risk is associated and for which such

assets categorized as risky assets. The relationship between expected return from a risky asset

and risk associated with it and to quantify the relationship, has been an interested research

area in financial economics. To minimize the risk of an asset Markowitz (1952) suggested

diversification of investments in different assets known as portfolio theory, a seminal work in

the relationship between risk and return. Sharpe (1964) extended the work of Markowitzs

portfolio theory with some assumption and developed a model known as Capital Asset

Pricing Model (CAPM). Thus CAPM is based on two parameter portfolio analysis modeldeveloped by Markowitz (1952). In CAPM model risk decomposed in two parts. One is the

risk of being in the market, which Sharpe called systematic risk. This risk, later dubbed

"beta," cannot be diversified away. The otherunsystematic riskis specific to a company's

fortunes and this risk can be mitigated through appropriate diversification. Thus according to

CAPM model a portfolio's expected return hinges solely on its betaits relationship to the

overall market based on this Sharpe (1964) developed a linear model, CAPM. The CAPM

helps measure portfolio risk and the return an investor can expect for taking that risk.

CAPM model is based on the following assumptions,

All investors are rational and risk-averse and have homogeneous expectations. They hold diversified portfolio. It implies that they deal only with systemic risk. Investors are price takers, i.e., they cannot influence prices. They can lend and borrow unlimited amounts under the risk free rate of interest.

All assets are perfectly divisible and liquid All information such as covariances, variances, mean rates of return of stocks and so

on is freely available at the same time to all investors

There is no transaction or taxation costs. There is large numbers of buyers and sellers in the market.

Based on above assumption, the linear relationship between the expected return required on

an investment in a risky assets and its systematic risk is represented by the CAPM formula as

follows


3/5

( ) [ ( ) ]

( )

i f i m f

m fimf

m m

E R R E r R

E R RR

(1)

Where,

( )iE R is expected return on asset i,

fR is the risk free rate of return,

( )mE R is expected return on market proxy generally measured on market portfolio

i is a measure of risk specific to asset i

im mand are covariance between asset i and market portfolio and variance of market

portfolio respectively.

The relationship between expected return on asset i and expected return on market portfolio is

also called security market line. If CAPM holds true, all securities will lie in a straight line

called the security market line (SML) in the ( ),i iE R frontier. The security market line

implies that return is a linearly increasing function of risk.

Figure 1: Security Market Line

Thus SML essentially 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

and required return is plotted on thesecurities market line(SML), which shows expected


4/5

return as a function of . The intercept is the nominal risk-free rate available for the market,

while the slope is the market premium, E(Rm)Rf. The securities market line can be regarded

as representing a single-factor model of the asset price, where Beta is exposure to changes in

value of the Market. So the equation of the SML is same as equation 1

The parameteri

measure of risk for the asset i. We are often interested ini

being equal to

1, less than 1, or greater than 1. If beta is greater than 1, the asset's returns are more volatile

than the market's rate of return; if it's less than 1, its returns are less volatile than the market's;

and if it's equal to 1, its returns are just as volatile as the market's rate of return.

The equation can be reformulated in terms of risk premium as follows

( ) [ ( ) ]i f i m f E R R E r R (2)

The variable on the left side of equation (2) is the risk premium for the asset i and, on the

right side of equation (2), this asset's beta is multiplied by the risk premium on the market

portfolio.

The CAPM is called an asset-pricing model, even though it is most often expressed in terms

of a required expected rate of return rather than in terms of an appropriate price. Fortunately,

the two are equivalentone can always work with the CAPM return first, and discount the

expected cash flow into an appropriateprice second. A given expected rate of return implies a

given price. It is called certainty equivalence.

Advantages of CAPM model

The CAPM has several advantages over other methods of calculating required return,

explaining why it has remained popular for more than 40 years:

It considers only systematic risk, reflecting a reality in which most investors havediversified portfolios from which unsystematic risk has been essentially eliminated

It generates a theoretically-derived relationship between required return andsystematic risk which has been subject to frequent empirical research and testing.

Criticism of CAPM

CAPM mostly has been criticised for its simplistic assumptions


5/5

The model assumes that the variance of returns is an adequate measurement of risk.Which is not a sufficient measure of risk, as risk in financial investments is not

variance in itself, rather it is the probability of losing: it is asymmetric in nature in

real world.

The model assumes that all active and potential shareholders have access to the sameinformation and agree about the risk and expected return of all assets which does not

hold true in real market.

The model assumes that there are no taxes or transaction costs, which also does nothold true in real practice. Although this assumption may be relaxed with more

complicated versions of the model.

It also assumes that all assets are infinitely divisible as to the amount which may beheld or transacted. This is also not valid in real market activities.

CAPM assumes that all active and potential shareholders will consider all of theirassets and optimize one portfolio. This is in sharp contradiction with portfolios that

are held by individual shareholders: humans tend to have fragmented portfolios or,

rather, multiple portfolios: for each goal one portfolio

Empirical tests show market anomalies like the size and value effect that cannot beexplained by the CAPM.

CONCLUSION

Research has shown the CAPM to stand up well to criticism, although attacks against it have

been increasing in recent years. Until something better presents itself, however, the CAPM

remains a very useful item in the financial management toolkit.

References:

Sharpe, William F. (1964). Capital asset prices: A theory of market equilibrium under

conditions of risk,Journal of Finance, 19 (3), 425-442.

Markowitz, H. (1952) Portfolio Selection. The Journal of Finance,7 (1): 77-91.

Documents

Capital Asset Priceing Model