## Capital Asset Pricing Model (CAPM)

Arbitrage Pricing Theory (APT)

Unit 3 SAPM Notes

**Capital Asset Pricing Model (CAPM)**

Capital
market theory is an extension of the Portfolio theory of Markowitz. The
portfolio theory explains how rational investors should build efficient
portfolio based on their risk-return preferences. Capital Market Asset Pricing
Model (CAPM) incorporates a relationship, explaining how assets should be
prices in the capital market. The capital market theory uses the results of
capital market theory to derive the relationship between the expected returns
and systematic risk of individual securities and portfolios.

Capital asset pricing model is a tool used by investors to
determine the risk associated with a potential investment and also gives an
idea as to what can be the expected return on the investment. It was developed
by William Sharpe along with a formula for working out the risk as who
states that with an investment comes two types of risks:

1) Systematic Risk: These are risks that cannot be
diversified away such as interest rates and recessions. As the market moves and
changes occur which affect the market, each individual asset is affected to
some degree and therefore they are sensitive to change causing a high level of
risk.

2) Unsystematic (Specific): These risk can be diversified
through increasing the size of an investment portfolio as this risk is specific
to individual stocks and effectively represents no correlation between stocks
and market movements.

CAPM states that investors are compensated for taking
systematic risk however not for taking specific risk as an investor can
diversify this risk away. Systematic risk cannot be eliminated of course even
by holding all the shares in a stock market, therefore CAPM has introduced a
method of calculating that risk.

**Mathematical expression of CAPM:**It can be expressed mathematically with the help of following equation:

E(rA) =
rf + Î²A(E(rM) - rf)

where:

E(rA) is the expected return of the
asset

rf is the risk-free rate

E(rM) is the expected return of the
market portfolio

The general idea of CAPM is that
investors should be compensated in two ways: time value of money and risk.

**The time value of money is represented by the risk-free (rf) rate in the formula and compensates the investors for placing money in any investment over a period of time.****The other part of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk. This is done by taking an estimate of risk, (Î²A), and multiplying by the MRP, (E(Rm) - rf).****Graphical Presentation of CAMP**

An asset is expected to earn the
risk-free rate plus a reward for bearing risk as measured by that asset’s beta.
The chart below demonstrates this predicted relationship between beta and
expected return – this line is called the Security Market Line.

For example, a stock with a beta of
1.5 would be expected to have an excess return of 15% in a time period where
the overall market beat the risk-free asset by 10%. The CAPM model is used for
pricing an individual security or a portfolio. For individual securities, the
security market line (SML) and its relation to expected return and systematic
risk (beta) shows how the market must price individual securities in relation
to their security risk class.

As the CAPM predicts expected returns
of assets or portfolios relative to risk and market return, the CAPM can also
be used to evaluate the performance of active fund managers. The difference is
“excess return”, which is often referred to as alpha (Î±). If Î± is greater than
zero, the portfolio lies above the Security Market Line.

###

**Assumptions
of CAPM**

The capital asset pricing model is based on
certain explicit assumptions regarding the behavior of investors. The
assumptions are listed below:

1. Investor
make their investment decisions on the basis of risk-return assessments
measured in terms of expected returns and standard deviation of return.

2. The
purchase or sale of a security can be undertaken in infinitely divisible unit.

3. Purchase
and sale by a single investor cannot affect prices. This means that there is
perfect competition where investors in total determine prices by their action.

4. There are
no transaction costs. Given the fact that transaction costs are small, they are
probably of minor importance in investment decision-making, and hence they are
ignored.

5. There are
no personal income taxes. Alternatively, the tax rate on dividend income and
capital gains are the same, thereby making the investor indifferent to the form
in which the return on the investment is received (dividends or capital gains).

6. The
investor can lend or borrow any amount of fund desired at a rate of interest
equal to the rate of risk less securities.

7. The
investor can sell short any amount of any shares.

8. Investors
share homogeneity of expectations. This implies that investors have identical
expectations with regard to the decision period and decision inputs. Investors
are presumed to have identical expectations regarding expected returns,
variance of expected returns and covariance of all pairs of securities.

###
**Advantages of CAPM**

CAPM has been a popular model for calculating risk for over
40 years now and is therefore a proven method, some advantages are:

a)
Ease-of-use: CAPM
is a simplistic calculation that can be easily stress-tested to derive a range
of possible outcomes to provide confidence around the required rates of return.

b)
Systematic Risk: It considers only systematic risk, reflecting
a reality in which most investors have diversified portfolios from which
unsystematic risk has been essentially eliminated.

c)
Business and
Financial Risk Variability: When businesses investigate opportunities, if the
business mix and financing differ from the current business, then other
required return calculations, like weighted average
cost of capital (WACC)
cannot be used. However, CAPM can.

d)
Determination of firm’s
required return: To develop this overall cost of capital, the manager must have
an estimate of the cost of equity capital. To calculate a cost of equity, some
managers estimate the firm’s beta (often from historical data) and use the CAPM
to determine the firm’s required return on equity.

e)
Public utility: The CAPM can also be used by
the regulations of public utilities. Utilities rates can be set so that all
costs, including costs of debt and equity capital, are covered by rates charged
to consumers. In determining the cost of equity for the public utility, the
CAPM can be used to estimate directly the cost of equity for the utility in
question. The procedure is like that followed for any other firm. The beta and
risk-free and market rates of return are estimated, and the CAPM is used to
determine a cost of equity.

f)
Useful tool for investment managers:
Investment practitioners have been more enthusiastic and creative in adapting
the CAPM for their uses. The CAPM has been used to select securities, construct
portfolios, and are forecastle considered under-valued, that is, attractive
candidates for purchase.

g)
Most reliable and effective
tool: Furthermore, in the opinion of most experts it is a more reliable and
effective method of calculating risk than other models such as the Dividend
Growth Model as CAPM takes into account a company's level of systematic risk
against the stock market as a whole; this is a benefit as it allows for a
company to compare itself to the market.

**Drawbacks
of CAPM**

Despite the consistent use of the model over the years there
has been some criticism for a few reasons:

1)
Unrealistic assumptions:
Capital asset pricing model is based on a number of assumptions that are far
from the reality. For example it is very difficult to find a risk free
security. A short term highly liquid government security is considered as a
risk free security. It is unlikely that the government will default, but
inflation causes uncertain about the real rate of return.

2)
Based on future expectations:
The CAPM is based on expectations about the future but empirical tests and data
for practical use are exclusively based on historical returns.

3)
Risk-free Rate (Rf): The
commonly accepted rate used as the Rf is the yield on short-term
government securities. The issue with using this
input is that the yield changes daily, creating volatility.

4)
Return on the Market (Rm):
The return on the market can be described as the sum of the capital
gains and dividends for the market. A problem arises when at any given time, the
market return can be negative. As a result, a long-term market return is
utilized to smooth the return. Another issue is that these returns are
backward-looking and may not be representative of future market returns.

5)
Ability to Borrow at a
Risk-free Rate: CAPM is built on four major assumptions, including one that
reflects an unrealistic real-world picture. This assumption, that investors can
borrow and lend at a risk-free rate, is unattainable in reality. Individual
investors are unable to borrow (or lend) at the rate the US government can
borrow at. Therefore, the minimum required return line might actually be less
steep (provide a lower return) than the model calculates.

6)
Determination of Project
Proxy Beta: Businesses that use CAPM to assess an investment need to find a
beta reflective to the project or investment. Often a proxy beta is necessary.
However, accurately determining one to properly assess the project is difficult
and can affect the reliability of the outcome.

7)
Single-period investment
appraisal: One disadvantage in using the CAPM in investment appraisal is that
the assumption of a single-period time horizon is at odds with the multi-period
nature of investment appraisal. While CAPM variables can be assumed constant in
successive future periods, experience indicates that this is not true in
reality.

**Arbitrage Pricing Theory (APT)**

Arbitrage
Pricing Theory (APT) is an alternate version of

**Capital Asset Pricing Model (CAPM)**. This theory, like CAPM provides investors with estimated required rate of return on risky securities. It is a multifactor mathematical model used to describe the relation between the risk and expected return of securities in financial markets. It computes the expected return on a security based on the security’s sensitivity to movements in macroeconomic factors. The resultant expected return can then be used to price the security.
The
Arbitrage pricing theory based model aims to do away with the limitations of
one factor model (CAPM) that different stocks will have different sensitivities
to different market factors which may be totally different from any other stock
under observation. In layman terms, one can say that not all stocks can be
assumed to react to single and same parameter always and hence the need to take
multifactor and their sensitivities. The formula includes a variable for each
factor, and then a factor beta for each factor, representing the security’s
sensitivity to movements in that factor. A two-factor version of the arbitrage
pricing theory would look like as:

**r = E(r) + B**

_{1}F_{1}+ B_{2}F_{2}+ e
r
= return on the security

E(r)
= expected return on the security

F

_{1}= the first factor
B

_{1}= the security’s sensitivity to movements in the first factor
F

_{2}= the second factor
B

_{2}= the security’s sensitivity to movements in the second factor
e
= the idiosyncratic component of the security’s return

As
the formula shows, the expected return on the asset/stock is a form of liner
regression taking into consideration many factors that can affect the price of
the asset and the degree to which it can affect it i.e. the asset’s sensitivity
to those factors.

If
one is able to identify a single factor which singly affects the price, the
CAPM model shall be sufficient. If there are more than one factor affecting the
price of the asset/stock, one will have to work with a two factor model or a
multi factor model depending on the number of factors that affect the stock
price movement for the company.

**Basic assumptions of Arbitrage Pricing Theory**

a)
It is based on the principle of capital market
efficiency and hence assumes all market participants trade with the intention
of profit maximisation.

b)
The Investors have homogenous
beliefs/expectations.

c)
Risk-return analysis is not the basis.

d)
It assumes no arbitrage exists and if it
occurs participants will engage to benefit out of it and bring back the market
to equilibrium levels.

e)
Capital markets are perfectly competitive.

f)
The security returns are generated according
to a factor model. Several factors affect the return on a security.

g)
There are no transaction costs, no taxes,
short selling is possible and infinite number of securities is available.

h)
The relationship between security returns and
factors is linear.

**Advantages of Arbitrage Pricing Theory**

a)
APT model is a multi-factor model. So, the
expected return is calculated taking into account various factors and their
sensitivities that might affect the stock price movement. Thus it allows
selection of factors that affect the stock price largely and specifically.

b)
APT model is based on arbitrage free pricing
or market equilibrium assumptions which to a certain extent result in fair
expectation of the rate of return on the risky asset.

c)
APT based multi factor model places emphasis
on covariance between asset returns and exogenous factors unlike CAPM. CAPM
places emphasis on covariance between asset returns and endogenous factors.

d)
APT model works better in multi period cases
as against CAPM which is suitable for single period cases only.

e)
APT can be applied to cost of capital and
capital budgeting decisions.

f)
The APT model does not require any assumption
about the empirical distribution of the asset returns unlike CAPM which assumes
that stock returns follow a normal distribution and thus APT a less restrictive
model.

**Limitations of Arbitrage Pricing Theory:**

a)
Problems in listing of various factors: The
model requires listing of factors that have impact on the stock under
consideration. Finding and listing all factors can be a difficult task and
there is a risk that some or the other factor being ignored. Also risk of
accidental correlations may exist which may cause a factor to become
substantial impact provider or vice versa.

b)
Expected return of various factors: The
expected returns for each of these factors will have to be arrived at, which
depending on the nature of the factor, may or may not be easily available
always.

c)
Difficult to measure Sensitivities of factors:
The model requires calculating sensitivities of each factor which again can be
a tedious task and may not be practically possible.

d)
Change in factors from time to time: The
factors that affect the stock price for a particular stock may change over a period
of time. Moreover, the sensitivities associated may also undergo shifts which
need to be continuously monitored making it very difficult to calculate and
maintain.

e)
Existence of arbitrage is essential: The APT
model will prevail only if there is a opportunity of arbitrage. If arbitrage
opportunity is not available, then this model does not prevail.

f)
Uncertain size or sign of factors: APT makes
no statement about the size of sign of the factors.

g)
Unrealistic assumption: It is based on some
assumptions which are not practical.

**Difference between APT and CAPM**

a)
APT computes the expected return on a security
based on the security’s sensitivity to movements in macroeconomic factors.
Whereas, CAPM is a tool used by investors to
determine the risk associated with a potential investment and also gives an
idea as to what can be the expected return on the investment.

b)
The APT can be set up to consider several risk
factors, such as the business cycle, interest rates, inflation rates, and
energy prices. The model distinguishes between systematic risk and
firm-specific risk and incorporates both types of risk into the model for each
given factor. Where as CAPM considers only
systematic risk, reflecting a reality in which most investors have diversified
portfolios from which unsystematic risk has been essentially eliminated.

c)
APT is based on factor model of return and
arbitrage Whereas CAPM is based on investors’ portfolio demand and equilibrium.

d)
APT is a multifactor model where as CAPM is a
single factor model.

e)
APT places emphasis on covariance between
asset returns and exogenous factors whereas CAPM places emphasis on covariance
between asset returns and endogenous factors.

f)
APT model works better in multi period cases
as against CAPM which is suitable for single period cases only.