Capital Asset Pricing Theory and Arbitrage Pricing Therory

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Capital Asset Pricing TheoryCapital Asset Pricing Theory

andand

Arbitrage Pricing TheoryArbitrage Pricing Theory

Chapter 19Chapter 19

11



Learning ObjectivesLearning Objectives

To understand the concept of CAPM theoryTo understand the concept of CAPM theory

To distinguish between CML and SMLTo distinguish between CML and SML

To trace the empirical tests of CAPMTo trace the empirical tests of CAPM

To understand APT theoryTo understand APT theory

22



The CAPM TheoryThe CAPM Theory

Markowitz, William Sharpe, John Lintner andMarkowitz, William Sharpe, John Lintner and

Jan Mossin provided the basic structure for theJan Mossin provided the basic structure for the

CAPM model.CAPM model.

It is a model of linear general equilibrium return.It is a model of linear general equilibrium return.

The required rate return of an asset is having a linear The required rate return of an asset is having a linear

relationship with asset¶s beta valuerelationship with asset¶s beta value i.e.,i.e.,

undiversifiable or systematic risk.undiversifiable or systematic risk.

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AssumptionsAssumptions

An individual seller or buyer cannot affect the priceAn individual seller or buyer cannot affect the priceof a stock.of a stock.

Investors make their decisions only on the basis of Investors make their decisions only on the basis of the expected returns, standard deviations andthe expected returns, standard deviations andcovariances of all pairs of securities.covariances of all pairs of securities.

Investors are assumed to have homogenousInvestors are assumed to have homogenousexpectations during the decisionexpectations during the decision--making period.making period.

The investor can lend or borrow any amount of fundsThe investor can lend or borrow any amount of fundsat the riskless rate of interest.at the riskless rate of interest.

Assets are infinitely divisible.Assets are infinitely divisible.

There is no transaction cost.There is no transaction cost.

There is no personal income tax.There is no personal income tax.

Unlimited quantum of short sales, is allowed.Unlimited quantum of short sales, is allowed. 44



Lending and BorrowingLending and Borrowing

It is assumed that the investor could borrow or lendIt is assumed that the investor could borrow or lend

any amount of money at riskless rate of interest.any amount of money at riskless rate of interest.

R R p p = Portfolio return= Portfolio return

XXf f = The proportion of funds invested in risk free assets= The proportion of funds invested in risk free assets

11 ± ± XXf f = The proportion of funds invested in risky assets= The proportion of funds invested in risky assets

R R f f = Risk free rate of return= Risk free rate of return

R R mm = Return on risky assets= Return on risky assets

The expected return on the combination of risky andThe expected return on the combination of risky and

risk free combination isrisk free combination is

p f f m f R = R X + R (1 ± X )

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The market portfolio comprised of all stocks inThe market portfolio comprised of all stocks in

the market.the market.

Each asset is held in proportion to its marketEach asset is held in proportion to its market

value to the total value of all risky assets.value to the total value of all risky assets.

Market PortfolioMarket Portfolio

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The Capital Market LineThe Capital Market Line

Str onglye

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or mationisr e

lectedon pr ices.Weak lye

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llhistor icalin

or mationisr e

lectedonsecur itySemistr onge

icientmar k et¡

ll pu blicin

or mationisr e

lectedonsecur ity pr icesStr onglye

icientmar k et¡

llin

or mationisr e


icientmar k et¡

llhistor icalin

or mationisr e


icientmar k et¡

ll pu blicin

or mationisr e

lectedonsecur ity pr icesStr onglye

icientmar k et¡

llin

or mationisr e


icientmar k et¡

llhistor icalin

or mationisr e


icientmar k et¡

ll pu blicin

or mationisr e

lectedonsecur ity pr ices

Rp

Rf

S

CML

Wp

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The portfolio along the path R The portfolio along the path R f f S is called lendingS is called lending portfolio, that is some money is invested in the portfolio, that is some money is invested in theriskless asset.riskless asset.

If it crosses the point S, it becomes borrowingIf it crosses the point S, it becomes borrowing portfolio. portfolio.

Money is borrowed and invested in the risky asset.Money is borrowed and invested in the risky asset.

The straight line is called capital market line (CML).The straight line is called capital market line (CML).

The CML represents linear relationship between theThe CML represents linear relationship between therequired rates of return for efficient portfolios andrequired rates of return for efficient portfolios andtheir standard deviations.their standard deviations.

The Capital Market Line (Contd.)The Capital Market Line (Contd.)

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ER ER p p = portfolio¶s expected rate of return= portfolio¶s expected rate of return

R R mm = expected return on market portfolio= expected return on market portfolio

WWmm = standard deviation of market portfolio= standard deviation of market portfolio

WW p p

= standard deviation of the portfolio= standard deviation of the portfolio

m f p f p

m

( ± )= ×

The Capital Market Line (Contd.)The Capital Market Line (Contd.)

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R eturnR eturn

The expected return of an efficient portfolio isThe expected return of an efficient portfolio is

Expected return =Expected return =

Price of time + (Price of risk Price of time + (Price of risk Amount of risk)Amount of risk)

Price of time is the risk free rate of returnPrice of time is the risk free rate of return

Price of risk is the premium amount higher andPrice of risk is the premium amount higher and

above the risk free returnabove the risk free return

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Security Market LineSecurity Market Line

Capital market line does not show the risk Capital market line does not show the risk--returnreturn

trade off for other portfolios and individual securities.trade off for other portfolios and individual securities.

Standard deviation includes the systematic andStandard deviation includes the systematic and

unsystematic risk.unsystematic risk.

Unsystematic risk can be diversified and it is notUnsystematic risk can be diversified and it is not

related to the market.related to the market.

Systematic risk could be measured by beta.Systematic risk could be measured by beta. The beta analysis is useful for individual securitiesThe beta analysis is useful for individual securities

and portfolios whether efficient or inefficient.and portfolios whether efficient or inefficient.

1111



The SML helps to determine the expected return for aThe SML helps to determine the expected return for a

given security betagiven security beta

m

m f i f im/

m

± ± OV

Security Market Line (Contd.)Security Market Line (Contd.)

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Security Market LineSecurity Market Line

YRp

Rrn

Rf

01

XBeta

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Evaluation of Securities with Evaluation of Securities with

SMLSML

R

S

T

A

C

U

V

W

Rf

Y

Rp

.9 . . .2

t

SML

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The stocks above the SML yield higher returns for The stocks above the SML yield higher returns for

the same level of risk.the same level of risk.

They are underpriced compared to their beta value.They are underpriced compared to their beta value.

wherewhere PPii ² ²present price present price

PPoo ² ²purchase price purchase price

DivDiv² ²dividend.dividend.

i oi

o

P ± P + DivR =

P

Evaluation of Securities with Evaluation of Securities with

SML (Contd.)SML (Contd.)

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Empirical Tests of the CAPMEmpirical Tests of the CAPM

The studies generally showed a significant positiveThe studies generally showed a significant positiverelationship between the expected return and the systematicrelationship between the expected return and the systematicrisk.risk.

But the slope of the relationship is usually less than that of But the slope of the relationship is usually less than that of predicted by the CAPM. predicted by the CAPM.

The risk and return relationship appears to be linear. EmpiricalThe risk and return relationship appears to be linear. Empiricalstudies give no evidence of significant curvature in thestudies give no evidence of significant curvature in therisk/return relationship.risk/return relationship.

The CAPM theory implies that unsystematic risk is notThe CAPM theory implies that unsystematic risk is notrelevant, but unsystematic and systematic risks are positivelyrelevant, but unsystematic and systematic risks are positively

related to security returns.related to security returns.

The ambiguity of the market portfolio leaves the CAPMThe ambiguity of the market portfolio leaves the CAPMuntestable.untestable.

If the CAPM were completely valid, it should apply to allIf the CAPM were completely valid, it should apply to all

financial assets including bonds.financial assets including bonds. 16

16



Present Validity of CAPMPresent Validity of CAPM

CAPM provides basic concepts which is truly of CAPM provides basic concepts which is truly of

fundamental value.fundamental value.

The CAPM has been useful in the selection of The CAPM has been useful in the selection of securities and portfolios.securities and portfolios.

Given the estimate of the risk free rate, the beta of theGiven the estimate of the risk free rate, the beta of the

firm, stock and the required market rate of return, onefirm, stock and the required market rate of return, one

can find out the expected returns for a firm¶s security.can find out the expected returns for a firm¶s security.

17

17



ArbitrageArbitrage

Arbitrage is a process of earning profit byArbitrage is a process of earning profit by

taking advantage of differential pricing for thetaking advantage of differential pricing for the

same asset.same asset.

The process generates riskless profit.The process generates riskless profit.

In the security market, it is of selling securityIn the security market, it is of selling security

at a high price and the simultaneous purchaseat a high price and the simultaneous purchaseof the same security.of the same security.

18

18



The AssumptionsThe Assumptions

The investors have homogenous expectations.The investors have homogenous expectations.

The investors are risk averse and utilityThe investors are risk averse and utility

maximisers.maximisers.

Perfect competition prevails in the market andPerfect competition prevails in the market and

there is no transaction cost.there is no transaction cost.

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Arbitrage PortfolioArbitrage Portfolio

According to the APT theory, an investor tries to findAccording to the APT theory, an investor tries to find

out the possibility to increase returns from hisout the possibility to increase returns from his

portfolio without increasing the funds in the portfolio. portfolio without increasing the funds in the portfolio.

He also likes to keep the risk at the same level.He also likes to keep the risk at the same level.

If X indicates the change in proportion,If X indicates the change in proportion,

((XXAA

++ ((XXBB

++ ((XXCC

= 0= 0

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Factor SensitivityFactor Sensitivity

The factor sensitivity indicates the responsiveness of The factor sensitivity indicates the responsiveness of

a security¶s return to a particular factor. Thea security¶s return to a particular factor. The

sensitiveness of the securities to any factor is thesensitiveness of the securities to any factor is the

weighted average of the sensitivities of the securities.weighted average of the sensitivities of the securities. Weights are the changes made in the proportion. For Weights are the changes made in the proportion. For

example bexample bAA, b, bBB and band bCC are the sensitivities, in anare the sensitivities, in an

arbitrage portfolio the sensitivities become zero.arbitrage portfolio the sensitivities become zero.

b bAA ((XXAA + b+ bBB ((XXBB + b+ bCC ((XXCC = 0= 0

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The APT ModelThe APT Model

According to Stephen Ross, returns of the securities areAccording to Stephen Ross, returns of the securities areinfluenced by a number of macro economic factors.influenced by a number of macro economic factors.

The macro economic factors are: growth rate of The macro economic factors are: growth rate of

industrial production, rate of inflation, spread betweenindustrial production, rate of inflation, spread betweenlong term and short term interest rates and spreadlong term and short term interest rates and spread between low grade and high grade bonds. The arbitrage between low grade and high grade bonds. The arbitragetheory is represented by the equation:theory is represented by the equation:

R R ii == PP00 ++ PP11 bi bi11 ++ PP22 bi bi22 « +« + PP j j bi bi j j

wherewhere R R ii = average expected return= average expected return

PP11 = sensitivity of return to bi= sensitivity of return to bi11

bi bi11 = the beta co= the beta co--efficient relevant to the particular factor efficient relevant to the particular factor 2222



Arbitrage Pricing EquationArbitrage Pricing Equation

In a single factor model, the linear relationship betweenIn a single factor model, the linear relationship between

the return R the return R ii and sensitivity band sensitivity bii can be given in thecan be given in the

following formfollowing form

R R ii == PPoo ++ PPii b bii

R R ii = return from stock A= return from stock A

PPoo = riskless rate of return= riskless rate of return

b bii = the sensitivity related to the factor = the sensitivity related to the factor

PPii = slope of the arbitrage pricing line= slope of the arbitrage pricing line

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APT and CAPMAPT and CAPM

The simplest form of APT model is consistent withThe simplest form of APT model is consistent withthe simple form of the CAPM model.the simple form of the CAPM model.

APT is more general and less restrictive than CAPM.APT is more general and less restrictive than CAPM.

The APT model takes into account of the impact of The APT model takes into account of the impact of numerous factors on the security.numerous factors on the security.

The market portfolio is well defined conceptually. InThe market portfolio is well defined conceptually. InAPT model, factors are not well specified.APT model, factors are not well specified.

There is a lack of consistency in the measurements of There is a lack of consistency in the measurements of the APT model.the APT model.

The influences of the factors are not independent of The influences of the factors are not independent of each other.each other.

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Chapter SummaryChapter Summary

By now, you should have:By now, you should have:

Understood the concept of CAPM theoryUnderstood the concept of CAPM theory

Learnt to distinguish between CML and SMLLearnt to distinguish between CML and SML

Traced the empirical tests of CAPMTraced the empirical tests of CAPM

Understood the concept of APTUnderstood the concept of APT

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Capital Asset Pricing Theory and Arbitrage Pricing Therory

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