ContentsIntroduction.........................................................2

Literature Review....................................................3The Basics of CAPM..................................................3

The issue of principals and agents..................................4New Approaches to CAPM and its alternatives.........................6

Arbitrage Pricing Theory..........................................6Fama French Model (Three Factor Model)............................7

Carhart Model.....................................................9Pastor and Stambough Model........................................9

Illustration and Comparison among the models.......................10Conclusion..........................................................14

References..........................................................15

The Existence of CAPM: Is it really dead?

IntroductionThe pricing of assets is one of the most important issues

relating to financial analysis of an organization. When an

investor in common stock or equity investment, he has to assume

equity risks. Equity risk premium is the incremental or

additional return that an investor seeks to hold the assets. It

is the variation between the required return on equity and the

current expected return on risk free assets. One of the most

common ways to determine required return on equity is using CAPM.

The Capital Asset Pricing model (CAPM) was first introduced by

Sharpe (1964), Lintner (1965) and Mossin (1966). Since then it

has been a central point of discussion for financial analysts.

According to Graham and Harvey (2001), CAPM is the most effective

model that estimates the cost of equity. However, according to

researchers like (Fama and French, 1992; Strong and Xu, 1997;

Jagannathan and Wang, 1996 and Let-tau and Ludvigson, 2001), CAPM

performs poorly for cross-section of return from different

regions. Due to the seemingly poor performance, many researchers

have either declared CAPM as a dead theory, while others have yet

again proved that it was not dead. The Economist, in the time

period of 1999-2000 had published a series of articles that

portrayed that CAPM was in a threat from the flow of funds theory

and real options theory. Still no one could nullify the existence

of CAPM absolutely.

This piece of work explains CAPM theory and shows why the theory

is so charming. This article then shows simple logics on the

validity of the previous tests of CAPM. A common belief is that

CAPM is very simple but its appeal is restricted to only a small

class of investors of the market. But the change of behavior of

individuals and pension system can create a huge impact in its

applicability. This piece of work finally shows some new ways

that can create a new possibility for asset pricing.

Literature Review

The Basics of CAPM

According to CAPM, the relation between an asset’s return and risk is as follows,

Where,

= Risk free rate of return

= Expected return on the asset

= the volatility of the asset’s return with the return ofthe market/ Beta

= Risk premium of equity

The Capital Asset pricing model is the market equilibrium model

that estimates the required return of assets as a linear function

of its systematic risk measured by asset’s beta. The key

assumption of CAPM is that the investors will measure the risk of

an asset in comparison to the contribution in makes to the

systematic or market risk of the portfolio. The CAPM assumes that

the investors in the market are perfectly rational and want more

wealth. It is also assumed that rational investors are risk

averse. When an investor thinks of holding a security, he

considers the amount of extra risk that will added to his

portfolio. Also, the investor requires additional risk premium to

hold the additional market risk. The expected premium for

additional risk (expected return less risk free rate) is the

product of the beta and the market risk premium. Here in the

theory, the portfolio of market is the value weighted average

portfolio of all the risky securities of the market. In most of

the cases the market portfolio is not calculated or takes a lot

of time. In these cases, market proxies such as Wilshire 5000 and

S & P 500 indexes are considered.

Beta is also a requirement for the CAPM formula to be enacted. A

beta is a measurement of covariance of a security with the

overall market. A beta less than one shows that the portfolio

will have a return less than the market and a higher than one

shows that the return will be higher than market. A zero beta

implies a riskless security such as government bonds. The riskier

assets have greater betas. All the investors in the market tend

to balance their investment risk by investing in some risky

assets and some risk less ones. This idea is called the “Two Fund

Separation Theorem”. In this way a risk lover investor will take

more risky securities and a risk-averse investor will be

investing in more risk free assets.

There are other complex versions of CAPMs available as well.

Researchers have extended the basic CAPM theory to be compared

over different regional returns and over different periods of

time as well. CAPM is the simplest process available for asset

pricing. Its assumptions are quite simple on the basis of the

rationality of the investors in market and thus there is an

opportunity for improvement in the theory.

An investor must also look at the time period of investment. At

one’s investment decision, time dimension plays an important role

as the value of return tends to fall over longer periods of time.

CAPM implies that a modern investor will be happy to invest if

the investment portfolio gives a relatively higher return over

time over the market portfolio. Although the inter-temporal CAPM

considers time period in the analysis, it is usually not enough

to satisfy the investors. The contemporary investors are also

concerned about the time period like the modern investors.

The issue of principals and agents

At this point, it is necessary to distinguish the two related

parties of investment. One is the principal who owns money but do

not actively manage the portfolio and the other is the agent who

makes decisions regarding investment on behalf of the principal.

Since the ease of investment, the investment in portfolios has

increased all over the world. In USA, the active management has

increased from $400 billion in 1981 to $6.7 trillion in 1998.

Also, the passive portfolio management has risen from $241

billion to $5.5 trillion. So the application of agents has

increased over the time as well.

But this is to be noted that whether active management or passive

management, neither the principal nor the agent should be

ignorant about the industry benchmark or the peer portfolios.

Ignoring the benchmark can be hazardous to the returns and it

often takes a lot of courage to construct portfolios

independently. In case of principals, since they know the basis

of their investment decision can ignore benchmarks and can apply

their own money in any way they prefer. But the agent, dealing

with the principals’ money, has to have justification for any

actions they take. That is why, for the agents, other factors

like proper valuation of securities in the portfolio influence

buy and sell decisions, thus affecting the overall price of the

securities. So in order to create a perfect measuring mechanism,

all these factors must be incorporated in the model. But sadly,

the previous CAPM models only considered investors are

principals. That is why important factors such as market

structure and behavioral patterns of different investors and

agents are overlooked. That is why although the previous tests

had correctly rejected the CAPM, did so on wrong and incomplete

assumptions.

As spoken earlier, there is an increasing trend in investment in

pension funds and mutual funds. So, according to the principal-

agent theory or agency theory by Fama and Jensen (1983), there is

high probability that the agents will continue to misprice the

securities. Unless the use of agents is completely abolished or

the investment in pensions is completely eradicated, the regular

CAPM system will not be able to predict the pricing of securities

correctly. Since it seems none is going to happen, the agency

risk will continue to mislead the current CAPM model.

New Approaches to CAPM and its alternatives

As stated earlier, the existing model of CAPM is not the best

possible model for asset pricing. It has the simplest assumptions

and often does not provide accurate result. So there are

opportunities for better and more complex models. That is why,

multifactor models were brought into action. There are a number

of multifactor models such as Arbitrage pricing theory, the Fama

French Model (three factor model), Carhart Model, Pastor and

Stambough model and other build up models. Let us discuss them

accordingly.

Arbitrage Pricing Theory

According to CAPM, the required return on asset has a linear

relationship with only the systematic or market risk. But studies

show that considering market risk as the only risk is not an

appropriate system. Recent studies show that an additional risk

variable is needed to calculate the expected return on assets.

A set of results suggest that it is possible to use the knowledge

of the market and securities to produce profitable strategies.

According to Banz (1981), stocks with small capitalization can

perform better than large capitalization stocks. According to

Basu (1977), low P/E stocks can perform better than high P/E

stocks. Even the “value” stocks, which have large book value to

market value ratio can, perform better than “growth” stocks,

which have low book value to market value ratio (Fama and French,

1995).

Since there were so many limitations to CAPM, the Arbitrage

Pricing Theory (APT) was introduced (Ross, 1976). This model had

only a few assumptions and better variables for risk measurement

were allowed. According to APT, there is not only a single risk

factor, but a number of risk factors in a perfectly competitive

capital market. Investors in such market prefer more wealth to

less. The formula to APT is represented as,

E(rj) = rf + bj1RP1 + bj2RP2 + bj3RP3 + bj4RP4 + ... + bjnRPn

Where,

E(rj) = Expected return on the asset

rf = Risk free rate of return

bj = the volatility of the asset’s return with the return of the market/ Beta

RP = Risk premium of the associated factors.

According to APT, there are many factors that create impact on

the expected return of the assets. These factors can be different

for individual region and economy. These factors usually consist

of expected inflation in economy, uptrend and downtrend in the

Gross Domestic Product (GDP), political turmoil, change of

interest rates and others. In this case, all these factors do not

have the same level of impacts on the return. The sensibility of

all these individual factors is measured by bj or the beta.

Considering such factors will give more accurate result than just

a single market factor. Thus the Arbitrage Pricing Theory is a

better predictor of expected return than CAPM.

Fama French Model (Three Factor Model)

According to the basic CAPM theorem, the only factor that

influences the required return of equity is the systematic or

market risk. But after 1980’s, the empirical studies showed that

only market factor cannot explain the return. Empirical studies

of stock markets show that “Value stocks” often provide greater

return than the “Growth Stocks”. Whereas CAPM, due to its

unconcern of the size factor of stocks cannot predict such

trends.

According to Fama and French (1993), CAPM model considers only

one risk factor (market factor), which makes it vulnerable to

misinterpretation. This is why these researchers introduced the

Three Factor Model.

The 3 factors are:

Market Factor: This is similar to the single factor CAPM model.

This factor considers only the market value index which is excess

of risk free rate.

Size Factor: This factor considers the size of stocks in relation

with the market capitalization. It is calculated as return to a

portfolio consisting of small capitalization stocks return less

the large capitalization stocks return.

Value Factor: This factor is considered in the Fama-French three

factor model. It is calculated as the return of the portfolio of

high book-to-market value stocks less the return of the portfolio

of low book-to-market value stocks.

The formula of the model is depicted as,

Ri = Rf + b1 market factor RMRF + b2

size factor SMB + b3 value factor HML

Here,

Ri = the expected return on portfolio

b1,2,3 = Sensitivity to the factors/ Beta

RMRF = market factor

SMB = Small minus Big/ Size factor

HML = High minus Low/ Value factor

So, clearly, as there are more considerations in the Three Factor

Model about the variability available in the market, it will

definitely provide better predictions about the expected return

of the portfolio. This comparison will be discussed in the later

part of the article.

Carhart Model

In the field of asset pricing and risk return estimate, there

have been other researches and findings. First of it was the

Carhart (1997) model, where Carhart has extended the three factor

model of Fama and French. Carhart model assumes that there is a

fourth risk factor that must be evaluated. This factor is named

as the “Momentum factor”. This factor is calculated on the fact

that the stocks with positive past returns will be likely to

produce positive future returns. The factor is calculated by

considering the average returns of a number of stocks which have

provided the best possible returns over last few years less the

average returns of a number of stocks which have provided the

worst returns over last few years. This factor is recognized as

PR1YR.

The formula of the model is depicted as,

Ri = Rf + b1 market factor RMRF + b2

size factor SMB + b3 value factor HML + b4

momentum

factor PR1YR

Carhart has showed that adding the momentum factor in calculation

increases the accuracy of prediction as much as 15 percent and

argues that the factor variable is usually positive in nature.

Pastor and Stambough Model

Another important finding was found by Pastor and Stambough

(2003). The Pastor and Stambough Model or PSM dictates that the

interested investors need an incentive to hold the illiquid

share. Thus the liquidity factor is the fourth factor to the

Fama-French Model. The liquidity factor can be calculated by

considering the average return on illiquid shares and the liquid

shares. The return on liquid shares is subtracted from the return

on illiquid shares. This factor is called the liquidity factor

and tries to equate the difference between liquid and illiquid

shares. The model can depicted in the following form,

Ri = Rf + b1 market factor RMRF + b2

size factor SMB + b3 value factor HML + b4

liquidity

factor LIQ

Illustration and Comparison among the models

Capital Asset Pricing Model (CAPM):

The CAPM considers only a single factor to calculate the expected

return on stocks, the market factor. For this calculation

purpose, let us assume that the risk free rate (Rf) at a given

point of time is 6%. The sensibility (b1) of the shares of a

hypothetical company X to the market factor is 1.1. Let us

further assume that the market factor is 8%.

So, according to CAPM, the estimated return stands,

Rx = Rf + b1 market factor RMRF

= 6% + 1.1 * 8%

= 6%+ 8.8%

= 14.8%

So, the expected return on Company X’s stocks is almost 14.8%.

Arbitrage Pricing Theory (APT):

Let us assume that there are two risk variables in action. The

first one is the change in inflation rate (RP1) and the second

one is the change in Real GDP (RP2). So,

RP1 = Unusual changes in the level of inflation. The risk premium

for such factor is 2 percent for every 1 percent change in the

rate. (k1=0.02)

RP2 = Unusual changes in the increase in real GDP. The risk

premium for such factor is 3 percent for every 1 percent change

in the rate. (k2=0.03)

rf = The return on a zero-beta or zero systematic risk asset

(risk free asset) is 6 percent (k0=0.06). Let us assume that

there are two assets (namely asset x and y).

bx1 = the sensitivity of asset x to the change in inflation is

0.50 (bx1 = 0.50)

bx2 = the sensitivity of asset x to the change in real GDP is 1.50

(bx2 = 1.50)

by1 = the sensitivity of asset y to the change in inflation is

2.00 (by1 = 2.00)

by2 = the sensitivity of asset y to the change in real GDP is

1.75 (by2 = 1.75)

All these factors can be explained as the same process as beta in

CAPM equation. Since asset y is a higher risk asset than asset x,

its expected return should be greater. So, the overall expected

return equation will be:

E(rj) = rf + bj1RP1 + bj2RP2 = 0.06 + (0.02)bi1 + (0.03)bi2

So, for asset x and y,

E(rx)= 0.06 + (0.02)(0.50) + (0.03)(1.50)

= 0.1150

= 11.50%

E(ry)= 0.06 + (0.02)(2.00) + (0.03)(1.75)

= 0.1525

= 15.25%

This gives a better result than CAPM, because of it considers two

separate factors and their sensitivity. Also, in this process,

expected returns of each of the assets included in the portfolio

can be separately calculated. So in this sense, APT gives a

better prediction and result than the traditional CAPM.

Fama-French Model (Three Factor Model):

The Fama-French Model or Three Factor Model considers three risk

factors to estimate the expected rate of return. These factors

are market factor, value factor and size factor. For the company

X, let us assume that the risk free rate (Rf) at a given point of

time is 6%. The sensibility of the shares of a hypothetical

company X to the market factor (b1) is 1.1, sensibility to size

factor (b2) is 1.5 and sensibility to value factor (b3) is -0.5.

So, according to FFM, the estimated return stands,

Ri = Rf + b1 market factor RMRF + b2

size factor SMB + b3 value factor HML

= 6% + 8% * 1.1 + 4.33% * 1.5+ 3.17% * -(0.5)

= 6%+ 8.8% + 6.495% – 1.585%

= 19.71%

At the same level of risk free rate and market risk factor, the

expected return in CAPM is lower than the FFM return. This is due

to the reason the reason that CAPM believes that the investors

are not interested in the size factor premium and value factor

premium. As CAPM believes that market factor premium covers all

this issues. Or it believes that the size factor premium and

value factor premium are a result of inefficiency in the market.

But studies have shown that neither market factor premium is

enough to cover all the associated risks, nor is the market

always inefficient. The studies show that companies with small

market capitalization and high book-to-market value company

shares can easily perform better than the big market

capitalization and low book-to-market value company shares over a

long time horizon in an efficient market such as US or UK.

Conclusion

CAPM has its own drawbacks. There have been many researches for

and against the CAPM method and thus it is very hard to come to a

clear and unambiguous solution. But it is also to be mentioned

that there are strong evidences that the assumptions of CAPM

hinders it from providing an actual result. The main school of

researchers, who oppose the CAPM, are not really clear as well.

This school is led by Fama, who has been a strong supporter of

CAPM until the 1990s.

Another fact that makes it difficult to come to a conclusion is

that the tests used to analyze the existence of CAPM have been

little measurable and also lack in real world applicability. To

utilize the world of real world economics actual data analysis is

very important but this also creates problems when actual human

behaviors are considered. The fact that economic theories are

mostly related with human behavior is a truth and it is also true

that often human behaviors are not quantitatively measurable.

When economists try to replace quantitative data with human

behaviors, problem occurs due to the uncertain and complex past,

present and future economic environment.

But despite all the limitations, it can be said that although

CAPM has been providing an insight to the researchers about the

asset pricing. The CAPM has been quite incomplete due to its

incomplete assumptions. Extended model of CAPM like FFM, Carhart

Model and Pastor-Stambough has been more accurate than the

original theory due to their extended assumptions. However even

if all the evidences are against CAPM model, investment analysts

and researchers will probably have to continue to use some kind

of an index or CAPM based model to estimate the asset pricing

until a better, unbiased and complete model can be introduced for

calculation of asset returns and pricing.

At last, it can be concluded that although “CAPM is dead” but it

cannot yet be buried entirely. Until a completely new and

unbiased model can be introduced, the asset pricing system will

have to use this dead theory.

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