chapter 8 capital asset pricing & artge prng thry

7/29/2019 Chapter 8 Capital Asset Pricing & Artge Prng Thry

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Chapter 8

CAPITAL ASSET PRICING ANDARBITRAGE 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 concernedwith two questions:

What is the relationship between risk and return for anefficient portfolio?

What is the relationship between risk and return for an

individual security?


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Basic Assumptions

Riskaversion

Maximisation . . expected utility

Homogeneous expectation

Perfect markets


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Capital Market LineExpected

Return, E(Rp) Z

L

M

K

Rf

Standard Deviation, pE(Rj) = Rf+ j

E(RM) - Rf

=M


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E(RM) -Rf

E(Ri ) =Rf + CiM

M

Security Market Line

iMi =

ME (R i ) = R f + [ E (R M)- R f]i

PReturn SML

14%

8% 0

Alpha = Expected - Fair

Return Return

1.0 i

R l i hi B SML A d CML


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Relationship Between SML And CML

SML

E(RM ) - Rf

E(Ri) = Rf + iMM

2

Since iM = iM iM

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

M

IF i and M are perfectly correlated iM =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.


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Determinants of Risk Premium

Variance in the underlying economy

Political risk

Market structure

FINANCIAL MARKET EXAMPLES PREMIUM OVER

THE

CHARACTERISTICS GOVT BOND 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 EASTEUROPEAN 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 Theory and Practice, John Wiley.


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Triumph Of Optimists

Elroy Dimson, Paul March, and Michael Stanton triumph of theOptimists, (2001)

Equity returns 16 rich countries data 1900

Global historical risk premium 20TH century .. 4.6%

Best estimate of equity premium worldwide in future is 4 to 5

percent


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Calculation Of Beta

Rit = i + i RMt + eit

iMi =M 2


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Calculation Of Beta

Period

Return on

stockA, RA

Return on

marketportfolio, RM

Deviation of

return on stockA

from its mean

(RA - RA)

Deviation of

return on marketportfolio from its

mean (RM - RM)

Product of the

deviation,(RA - RA)

(RM - RM)

Square of the

deviation of

return on marketportfolio from its

mean

(RM - RM)2

1 10 12 0 3 0 9

2 15 14 5 5 25 25

3 18 13 8 4 32 16

4 14 10 4 1 4 15 16 9 6 0 0 0

6 16 13 6 4 24 16

7 18 14 8 5 40 25

8 4 7 -6 -2 12 4

9 - 9 1 -19 -8 152 64

10 14 12 4 3 12 9

11 15 -11 5 -20 -100 40012 14 16 4 7 28 49

13 6 8 -4 -1 4 1

14 7 7 -3 -2 6 4

15 - 8 10 -18 1 -18 1

RA = 150 RM = 135 (RA - RA) (RM - RM) 2RA =10 RM = 9 (RM - RM) = 221 = 624


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Estimation Issues

Estimation Period

A longer estimation period provides more data butthe risk profile .. firm may change

5 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 0.66 Historical beta

O.34 Market beta


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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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Betas Based On Accounting Earnings

Regress the changes in company earnings (on a quarterly or annual

basis) against changes in the aggregate earnings of all the companies

included in a market index.

Limitations

Accounting earnings .. generally smoothed out ..relative .. value of the company

Accounting earnings influenced by non - operating

factors

Less frequent measurement


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Betas from CrossSectional Regressions

1. Estimate a cross - sectional regressionRelationship for publicly traded firms:

Beta = 0.6507 + 0.27 coefficient of variation

In operating income + 0.09 D/E + 0.54

Earnings - .00009 total assets(million $)

2. Plug the characteristics of the project, division, or

unlisted company in the regrn reln to arrive at an

estimate of beta

Beta = 0.6507 + 0.27 (1.85) + 0.09 (0.90) + 0.54 (0.12) -

0.00009 (150) = 1.2095


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Empirical Evidence On CAPM

1. Set up the sample data

Rit , RMt , Rft

2. Estimate the security characteristic linesRit - Rft = ai +bi (RMt -Rft) + eit

3. Estimate the security market line

Ri =0 +1 bi + ei , i= 1, 75


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General Findings

The relation appears .. linear

0 > Rf 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 thevariance 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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ArbitragePricing Theory

Return generating process

Ri = ai +bi 1 I1+ bi2 I2 +bij Ij+ ei

Equilibrium riskreturn relationshipE(Ri) = 0 + bi1 1 + bi2 2 + bijjj = Risk premium for the type ofRisk associated with factor j


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Comparison of CAPM and APT

CAPM APT

Nature of relation Linear Linear

Number of risk factors 1 k

Factor risk premium [E(RM)Rf] ljFactor risk sensitivity bi bij

Zero-beta return Rf l0


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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 identify of risk factors and specifies the

multifactor model of the following kind.Rit = ai +[bit F1t + bi2 F2t+.. + bik Fkt] + eit

where Rit is the return on security i in period t, and Fjt is the returnassociated with thej th 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 of such 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 model proposed by

Chen, Roll, and Ross in their classic paper, "Economic Forces and

the Stock Market," published in the April 1986 issue ofJ ournal ofBusiness.

Rit = ai + bi1 Rmt + bi2 MPt + bi3DEI t + bi4UI t + b5UPRt + bi6 UTSt + 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 USconsumer price index, UI is the difference between actual and

expected levels of inflation, UPR is the unanticipated change in the

bond credit spread (Baa yieldRFR), and UTS is the unanticipated

term structure shift (long term RFRshort term RFR).

Mi i B d Ri k F M d l


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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 this approach 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 1993 issue of the J ournal of FinancialEconomics:

(RitRFRt) = i + bi1 (RmtRFRt) + bi2SMBt + bi3HMLt + eitIn this model, in addition to (R

mtRFR

t), the excess return on a

stock market portfolio, there are two other microeconomic riskfactors: SMB

t and HML

t. SMB

t(i.e.,

contd


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St k M k t C l


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Stock Market as a Complex

Adaptive System

To understand what a complex adaptive system is let us begin with asimple situation where two people are put in a room and asked totrade 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 remains static and lifeless comparedto what we see in the capital markets. As more and more people are

added to the system, something remarkable happens: it acquires

lifelike characteristics.As Mauboussin put it: In a tangible way, the

system becomes more complex than the pieces that it comprises.

Importantly, the transitionoften called self-organised criticalityoccurs without design or help from outside agent. Rather, it is a

direct function of the dynamic interactions among the agents in the

system.

P ti f C l Ad ti S t


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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 rules ensures 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 the output ofone 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 (fattails) in return distribution suggeststhat 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 theheterogeneous expectations of investors would yield prices

that are similar to intrinsic values. However, if certain

decision rules become pervasive, the resulting homogeneity ofviews may lead to self-reinforcing trends, leading to booms

and crashes.

4. The poor performance of active portfolio managers is

consistent with the classical market theory as well as thecomplex adaptive model. Still, it is possible that some

investors would do well. As Mauboussin put it: That point

made, it remains possible under theory that certain investors

Warren Buffett and Bill Miller, e.g. may be hard-wired tobe successful investors. In this sense, hard-wired suggest

innate mental processes, fortified with practice, that allow for

systematically superior security selection.

I li ti f th N M d l


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Implications of the New ModelThe 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

what the 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.

5. 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 gotoo far astray. However, complex adaptive systems may

provide a useful perspective in areas like risk management

and investor communication.

S mming Up


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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+ i 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 i The beta of a security is the slope of the following

regression relationship:

Rit = i + iRMt + 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 appealing

and 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.

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