6.capitalassetpricingandartgeprngthry

8/8/2019 6.CapitalAssetPricingandArtgeprngthry

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CAPITAL ASSET PRICING AND

ARBITRAGE PRICING THEORY

The Risk Reward Relationship


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OUTLINE

Key Issues

Basic Assumptions

Capital Market Line

Security Market Line

Inputs Required for CAPM

Calculation of Beta Empirical Evidence on CAPM

Arbitrage Pricing Theory


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Key Issues

Essentially, the capital asset pricing model (CAPM) is

concerned with two questions:

What is the relationship between risk and return for an

efficient portfolio?

What is the relationship between risk and return for an

individual security?


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Usefulness of relationship

Provides a benchmark for evaluating securities under

consideration

Helps make an informed guess about unlisted security


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Basic Assumptions

RISK - AVERSION

MAXIMISATION . . EXPECTED UTILITY ..

OVER SINGLE PERIOD HORIZON

HOMOGENEOUS EXPECTATION

PERFECT MARKETS : NO TAXES, PERFECT

COMPETITION, NO TRANSACTION COSTS

INDIVIDUALS CAN BORROW AND LEND AT A

RISK LESS RATE OF INTEREST


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Capital Market Line

EXPECTED

RETURN,E(Rp) Z

L

M

K

Rf

STANDARD DEVIATION, WpE(Rj) = Rf+ j

E(RM) - Rf =

M


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E(RM) -Rf

E(Ri ) =Rf + CiM

WM

Security Market Line

iMi =

WM

E(R

i) =R

f + [E(R

M)-R

f]i

EXPECTED PRETURN SML

14%

8% 0

ALPHA = Actual - FAIR

RETURN RETURN

1.0 i


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Relationship Between SML And CML

SML

E(RM

) -Rf

E(Ri) = Rf + iMM

2

SINCE iM = ViM iM

E(RM) -RfE(Ri) = Rf + ViM i

M

IF iANDMARE PERFECTLY CORRELATED ViM = 1. SOE(RM) -Rf

E(Ri) = Rf + iM

THUS CML IS A SPECIAL CASE OF SML


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Inputs Required For Applying CAPM

RISK-FREE RETURN

RATE ON A SHORT-TERM GOVT SECURITY

RATE ON A LONG TERM GOVT BOND

MARKET RISK PREMIUM

HISTORICAL

DIFFERENCE BETWEEN THE AVERAGE RETURN ON

STOCKS AND THE AVERAGE RISK - FREE RETURN

PERIOD : AS LONG AS POSSIBLE

AVERAGE : A.M VS. G.M.

Beta of a securit


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Determinants of Risk Premium

VARIANCE IN THE UNDERLYING ECONOMY

POLITICAL RISK MARKET STRUCTURE

INANCIAL MARKET E AMPLES PREMIUM OVER THE

CHARACTERISTICS GOVT OND RATE

EMERGING MARKET, WITH SOUTH AMERICAN MARKETS, 7.5 - 9.5

POLITICAL RISK CHINA, RUSSIA

EMERGING MARKETS WITH SINGAPORE, MALAYSIA, 7.5

LIMITED POLITICAL RISK THAILAND, INDIA, SOME EAST

EUROPEAN MARKETS

DEVELOPED MARKETS WITH UNITED STATES, JAPAN, U.K., 5.5

WIDE STOCK LISTINGS FRANCE, ITALY

DEVELOPED MARKETS WITH GERMANY, SWITZERLAND 3.5 - 4.5

LIMITED LISTINGS AND

STABLE ECONOMIES

* Source: Aswath Damodaran Corporate Finance Theoryand Practice, John Wiley.


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Calculation Of Beta

WiMFi =

WM2


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Calculation of Beta CovCov ( R( RAA,R,RMM) =) = (R(RAA RRA(MeanA(Mean ) (R) (RMM

RRM(MeanM(Mean) *1/n) *1/n

= 221/15 = 15.79= 221/15 = 15.79

WWMM22 == (R(RMM RRM(MM(M) ^2 * 1/n) ^2 * 1/n

= 624 /15= 44.57= 624 /15= 44.57

Hence beta for the stock A =15.79/44.57Hence beta for the stock A =15.79/44.57

= 0.354= 0.354


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Estimation Issues

ESTIMATION PERIOD

A LONGER ESTIMATION PERIOD PROVIDES MOREDATA BUT THE RISK PROFILE .. FIRM MAY CHANGE

YEARS

RETURN INTERVAL

DAILY, WEEKLY, MONTHLY

MARKET INDEX

STANDARD PRACTICE

ADJUSTING HISTORICAL BETA

HISTORICAL ALIGNMENT CHANCE FACTOR

A COMPANYS BETA MAY CHANGE OVER TIME

MERILL LYNCH 0. HISTORICAL BETA

O. 4 OTHER FACTORS


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Need for computing beta in

different manner Capital asset may not be tradedCapital asset may not be traded

Assets traded for short periodAssets traded for short period

Assets under manipulative pressureAssets under manipulative pressure


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Betas Based On Fundamental Information

KEY FACTORS EMPLOYED ARE

INDUSTRY AFFILIATION

CORPORATE GROWTH

EARNINGS VARIABILITY

FINANCIAL LEVERAGE

SIZE


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Beta based on fundamental

information Stronger intuitive appealStronger intuitive appeal

Ideal for analysis of nonIdeal for analysis of non trading assetstrading assets

Seems to outperform historical betasSeems to outperform historical betas

Can be based on future descriptorsCan be based on future descriptors likelike

growth orientation in future etc.growth orientation in future etc.


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Betas Based On Accounting Earnings

REGRESS THE CHANGES IN COMPANY EARNINGS

(ON A QUARTERLY OR ANNUAL BASIS) AGAINSTCHANGES IN THE AGGREGATE EARNINGS OF ALL

THE COMPANIES INCLUDED IN A MARKET INDEX.

LIMITATIONS

ACCOUNTING EARNINGS .. GENERALLY SMOOTHED

OUT ..

ACCOUNTING EARNINGS INFLUENCED BY NON -OPERATING FACTORS

LESS FREQUENT MEASUREMENT


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Betas from Cross

Sectional Regressions

1. ESTIMATE A CROSS - SECTIONAL REGRESSION

RELATIONSHIP FOR PUBLICLY TRADED FIRMS:

BETA = 0. 0 + 0. COEFFICIENT OF VARIATION

IN OPERATING INCOME + 0.0 D/E + 0. 4

EARNINGS - .0000 TOTAL ASSETS(MILLION $)

. PLUG THE CHARACTERISTICS OF THE PROJECT,

DIVISION, OR UNLISTED COMPANY IN THEREGRN RELN TO ARRIVE AT AN ESTIMATE OF

BETA

BETA = 0. 0 + 0. (1.8 ) + 0.0 (0. 0) + 0. 4 (0.1 ) -

0.0000 (1 0) = 1. 0


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Empirical Evidence

On CAPM

1. SET UP THE SAMPLE DATA

Rit ,RMt,Rft

. ESTIMATE THE SECURITY CHARACTER-

-ISTIC LINES

Rit - Rft = ai + bi(RMt - Rft) + eit

. ESTIMATE THE SECURITY MARKET LINE

Ri = K0 + K1 bi+ ei , i= 1,


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Evidence

IF CAPM HOLDS

THE RELATION LINEAR .. TERMS LIKE bi2 .. NO

EXPLANATORY POWER

K 0 Rf

K 1 RM - Rf

NO OTHER FACTORS, SUCH AS COMPANY SIZE

OR TOTAL VARIANCE, SHOULD AFFECTRi

THE MODEL SHOULD EXPLAIN A SIGNIFICANT

PORTION OF VARIATION IN RETURNS AMONG

SECURITIES


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General Findings

THE RELATION APPEARS .. LINEAR

K 0 > Rf

K 1 < RM - Rf

IN ADDITION TO BETA, SOME OTHER FACTORS,

SUCH AS STANDARD DEVIATION OF RETURNS

AND COMPANY SIZE, TOO HAVE A BEARING ON

RETURN

BETA DOES NOT EXPLAIN A VERY HIGH

PERCENTAGE OF THE VARIANCE IN RETURN


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Conclusions

PROBLEMS STUDIES USE HISTORICAL RETURNS AS

PROXIES FOR EXPECTATIONS

STUDIES USE A MARKET INDEX AS A PROXY

POPULARITY

SOME OBJECTIVE ESTIMATE OF RISK PREMIUM

.. BETTER THAN A COMPLETELY SUBJECTIVE

ESTIMATE

BASIC MESSAGE .. ACCEPTED BY ALL

NO CONSENSUS ON ALTERNATIVE


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Arbitrage Pricing Theory

RETURN GENERATING PROCESS

Ri = ai + bi1 I1 + bi I + bijI1 + ei

EQUILIBRIUM RISK RETURN

RELATIONSHIP

E(Ri) = P0 + bi1 P1 + bi2P2 + bijPj

Pj = RISK PREMIUM FOR THE TYPE OF

RISK ASSOCIATED WITH FACTORj


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Comparison of CAPM and APT

CAPMCAPM APTAPT

Nature of relationNature of relation LinearLinear LinearLinear

Number of riskNumber of risk

factorsfactors

11 kk

Factor risk premiumFactor risk premium [[E(RE(RMM))RRff]] PPjj

Factor risk sensitivityFactor risk sensitivity FFii bbijij

ZeroZero--beta returnbeta return RRff PP00


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Multifactor Models

Given the practical difficulties in using the above

approach, researchers have followed a different approach

that captures the essence of the APT. In this approach, the

researcher chooses a priorithe exact number and identifyof risk factors and specifies the multifactor model of the

following kind.

Rit= ai+ [bitF1t+ bi2 F2t+.. + bikFkt] + eit

where Rit is the return on security i in period t, and F1t is

the return associated with thejth risk factor in period t.


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The advantage of a factor model like this is that the

researcher can specify the risk factors; the disadvantage ofsuch a model is that there is very little theory to guide it.

Hence, developing a useful factor model is as much an art

as science.

The variety of multifactor models employed in practice

may be divided into two broad categories: macro-economic

based risk factor models and micro-economic based risk

factor models.


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Macroeconomic Based Risk Factor Models

These models consider risk factors that are macroeconomic in

nature. Typical of this approach is the following modelproposed by Chen, Roll, and Ross in their classic paper,

"Economic Forces and the Stock Market," published in the

April 1 8 issue of Journal of Business.

Rit= ai + bi1Rmt+ bi2MPt+ bi3DEIt+ bi4UIt+ b5UPRt+ bi6UTSt+ eit

where Rm is the return on a value weighted index of NYSE

listed stocks, MP is the monthly growth rate in the US

industrial production, DEI is the change in inflation, measured

by the US consumer price index, UI is the difference between

actual and expected levels of inflation, UPR is the

unanticipated change in the bond credit spread (Baa yield

RFR), and UTS is the unanticipated term structure shift (long

term RFR short term RFR).


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Microeconomic Based Risk Factor Models

Instead of specifying risk in macroeconomic terms, you

can delineate risk in microeconomic terms. Typical of thisapproach is the following model proposed by Fama and

French in their celebrated paper "Common Risk Factors

in the Returns on Stocks and Bonds," published in the

January 1 issue of the Journal of FinancialEconomics:

(Rit RFRt) =Ei+ bi1 (Rmt RFRt) + bi2SMBt+ bi3HMLt+ eit

In this model, in addition to (Rmt RFRt), the excessreturn on a stock market portfolio, there are two other

microeconomic risk factors:SMBt

andHMLt.SMB

t(i.e.,

contd


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contd..

small minus big) is the return to a portfolio of smallcapitalisation stocks less the return to a portfolio of large

capitalisation stocks andHMLt(i.e., high minus low) is the

return to a portfolio of stocks with high ratios of book-to-

market values less the return to a portfolio of low book-to-

market value stocks.

In this model, SMB is intended to capture the risk

associated with firm size while HML is meant to reflect

risk differentials associated with "growth" (i.e., low book-

to-market ratio) and "value" (i.e., high book-to-market

ratio).


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Stock Market as a Complex

Adaptive System

To understand what a complex adaptive system is let us begin

with a simple situation where two people are put in a room and

asked to trade a commodity. What happens? Hardly anything.If a few more people are added, the activity picks up, but the

interactions remain somewhat subdued. The system remainsstatic and lifeless compared to what we see in the capital markets.As more and more people are added to the system, something

remarkable happens: it acquires lifelike characteristics. AsMauboussin put it: In a tangible way, the system becomes morecomplex than the pieces that it comprises. Importantly, thetransition often called self-organised criticality occurs

without design or help from outside agent. Rather, it is a directfunction of the dynamic interactions among the agents in the

system.


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Properties of a Complex Adaptive System

Aggregation The collective interactions of many less-

complex agents produces complex, large-scale behaviour.

Adaptive Decision Rules Agents in the system take

information from the environment and develop decision

rules. The competition between various decision rulesensures that eventually the most effective decision rules

survive.

Non-Linearity Unlike a linear system, wherein the value of

the whole is equal to the sum of its parts, a non-linear

system is one wherein the aggregate behaviour is very

complex because of interaction effects.

contd...


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contd

Feedback Loops In a system that has feedback loops theoutput of one interaction becomes the input of the next. A

positive feedback can magnify an effect, whereas a

negative feedback can dampen an effect.


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How Does the New Model Compare with

Classical Market Theory

The complex adaptive expectations model seems to

conform to reality better than the classical capital market

theory. The following evidence bears this out:

1. The high kurtosis (fat tails) in return distribution

suggests that periods of stability are interspersed by

rapid change.

2. The price behaviour in a complex adaptive system would

not be very different from a classic random walk.

However, the new model explains better the observed

persistence in returns, to the extent that the same

exists.


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3. Under most circumstances, the aggregation of the

heterogeneous expectations of investors would yield prices

that are similar to intrinsic values. However, if certain

decision rules become pervasive, the resulting

homogeneity of views may lead to self-reinforcing trends,

leading to booms and crashes.

4. The poor performance of active portfolio managers isconsistent with the classical market theory as well as the

complex adaptive model. Still, it is possible that someinvestors would do well. As Mauboussin put it: Thatpoint made, it remains possible under theory that certain

investors Warren Buffett and Bill Miller, e.g. may

be hard-wired to be successful investors. In this sense,hard-wired suggest innate mental processes, fortified

with practice, that allow for systematically superior

securit selection.


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Implications of the New Model

The important implications of the new model for investors

and corporate practitioners are as follows:

1. While the CAPM is still probably the best available estimate

of risk for most corporate investment decision, managers must

recognise that their stock price may fluctuate more than whatthe standard theory suggests.

2. The market is usually smarter than the individual. Hence

managers should weight the evidence of the market over the

evidence of experts.

3. Markets function well when participants pursue diverse

decision rules and their errors are independent. Markets,

however, can become very fragile when participants display

herd-like behaviour, imitating one another.


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4. It may be futile to identify the cause of a crash or boom

because in a non- linear system small things can cause large-

scale changes.

. The discounted cash flow model provides an excellent

framework for valuation. Indeed, it is the best model for

figuring out the expectations embedded in stock prices.

Mauboussin summed up the implications of the new model as

follows: From a practical standpoint, managers who

subscribe to standard capital market theory and operate on

the premise of stock market efficiency will probably not go too

far astray. However, complex adaptive systems may provide a

useful perspective in areas like risk management and investor

communication.


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SUMMING UP

The relationship between risk and expected return for

efficient portfolios, as given by the capital market line, is:

E (Ri) =Rf+ P Wi

The relationship between risk and expected return for an

inefficient portfolio or a single security as given by the

security market line is:

E (Ri) =Rf+ E(RM) Rf x

The beta of a security is the slope of the following

regression relationship:

Rit= Ei + FiRMt+ eit


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The commonly followed procedure for testing CAPM involves

two steps. In the first step, the security betas are estimated. In

the second step, the relationship between security beta and

return is examined.

Empirical evidence is favour of CAPM is mixed.

Notwithstanding this, the CAPM is the most widely used risk-

return model because it is simple and intuitively appealingand its basic message that diversifiable risk does not matter is

generally accepted.


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The APT is much more general in that asset prices can be

influenced by factors beyond means and variances. The APT

assumes that the return on any security is linearly related

to a set of systematic factors.

6.capitalassetpricingandartgeprngthry

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