Fi8000Fi8000Capital AssetCapital Asset

Pricing Model & Market Pricing Model & Market EfficiencyEfficiency

Milind ShrikhandeMilind Shrikhande

TodayToday

☺ The Capital Asset Pricing ModelThe Capital Asset Pricing Model

☺ Market EfficiencyMarket Efficiency

The Capital Asset Pricing ModelThe Capital Asset Pricing Model

☺ Sharp (1968), Black (1969) andSharp (1968), Black (1969) and

Lintner (1970)Lintner (1970)

☺ A model that tells us the fair (risk-A model that tells us the fair (risk-adjusted) expected return for every adjusted) expected return for every individual assetindividual asset

☺ A market equilibrium modelA market equilibrium model

The Capital Asset Pricing ModelThe Capital Asset Pricing Model(CAPM): Outline(CAPM): Outline

☺ The assumptions of the modelThe assumptions of the model

☺ The market equilibrium: SML equationThe market equilibrium: SML equation

☺ The two components of risk:The two components of risk:☺ Systematic (non-diversifiable)Systematic (non-diversifiable)☺ Non-systematic (diversifiable)Non-systematic (diversifiable)

☺ Beta as a measure of systematic riskBeta as a measure of systematic risk

☺ The returns and the prices of risky assetsThe returns and the prices of risky assets

The Capital Asset Pricing ModelThe Capital Asset Pricing Model(CAPM): Assumptions(CAPM): Assumptions

☺ There are many investors – each investor is a There are many investors – each investor is a price takerprice taker

☺ All investors plan for one identical holding All investors plan for one identical holding periodperiod

☺ All risky assets are publicly tradedAll risky assets are publicly traded

☺ All investors are risk-averse and Mean-Variance All investors are risk-averse and Mean-Variance optimizersoptimizers

☺ Homogeneous expectations - all investors have Homogeneous expectations - all investors have the same information and interpret it the same the same information and interpret it the same wayway

The CAPM: AssumptionsThe CAPM: Assumptions

☺ The perfect market assumptionThe perfect market assumption☺ There are no taxes or transaction costs or There are no taxes or transaction costs or

information costsinformation costs☺ There are no frictionsThere are no frictions☺ Stocks can be bought and sold in any Stocks can be bought and sold in any

quantity (even fractions)quantity (even fractions)☺ There is one risk-free asset and all investors There is one risk-free asset and all investors

can borrow or lend at that ratecan borrow or lend at that rate

The CAPM: Market EquilibriumThe CAPM: Market Equilibrium

The market portfolio (m) is on the efficient frontier The market portfolio (m) is on the efficient frontier and on the CML. It is the Mean-Variance optimal and on the CML. It is the Mean-Variance optimal

portfolio of risky assets.portfolio of risky assets.

All the investors will invest in the same portfolio of All the investors will invest in the same portfolio of risky assets: m - the market portfolio.risky assets: m - the market portfolio.

The proportion of each asset in the market The proportion of each asset in the market portfolio is simply the asset’s market value divided portfolio is simply the asset’s market value divided

by the total wealth (market value of all assets).by the total wealth (market value of all assets).

The Market PortfolioThe Market Portfolioin the in the μμ--σσ Plane Plane

σ

μThe Capital Market Line: μp= rf+[(μm-rf) / σm]·σp

rf

m

The CAPM: Market EquilibriumThe CAPM: Market Equilibrium

The risk preferences of the investors will The risk preferences of the investors will result in their capital allocation between the result in their capital allocation between the market portfolio and the risk-free asset – i.e. market portfolio and the risk-free asset – i.e. the location of their portfolio on the Capital the location of their portfolio on the Capital

Market Line (CML).Market Line (CML).

(The mutual fund theorem)(The mutual fund theorem)

Passive Investment StrategiesPassive Investment Strategiesin the in the μμ--σσ Plane Plane

σ

μThe CML: μp= rf + [(μm-rf) / σm]·σp

rf

mqp

The CAPM: Market EquilibriumThe CAPM: Market Equilibrium

The risk premium of each risky assets will be The risk premium of each risky assets will be proportional to the risk premium of the market proportional to the risk premium of the market portfolio and to the beta coefficient of the risky portfolio and to the beta coefficient of the risky

asset:asset:

i m irf rf

The Capital Asset Pricing Model:The Capital Asset Pricing Model:The Security Market Line (SML)The Security Market Line (SML)

β

μ

m

The SML:μi= rf+ [μm-rf]·βi

rf

q

p

What is Beta?What is Beta?

☺ Beta is a measure of riskBeta is a measure of risk☺ Beta measures how sensitive are the returns Beta measures how sensitive are the returns

of asset of asset ii to the returns of the market to the returns of the market portfolioportfolio

☺ Beta is the slope (coefficient) in the Beta is the slope (coefficient) in the regression of asset regression of asset ii’s return (risk premium) ’s return (risk premium) on the market’s return (market risk premium)on the market’s return (market risk premium)

☺ Beta is a relative measure of riskBeta is a relative measure of risk· Beta < 1 : defensive assetBeta < 1 : defensive asset· Beta = 1: neutral assetBeta = 1: neutral asset· Beta > 1: aggressive assetBeta > 1: aggressive asset

BetaBeta

Rm-rf

Ri-rf

βi

Calculating BetaCalculating Beta

2im i im

im m

The CAPM Market Equilibrium:The CAPM Market Equilibrium:Outline of the ProofOutline of the Proof

☺ The risk-free asset is on the SMLThe risk-free asset is on the SML☺ Calculate the beta of the risk-free assetCalculate the beta of the risk-free asset

☺ The market portfolio is on the SMLThe market portfolio is on the SML☺ Calculate the beta of the market portfolioCalculate the beta of the market portfolio

☺ Any M-V efficient portfolio Any M-V efficient portfolio pp is on the SML is on the SML☺ Calculate the beta of an efficient portfolioCalculate the beta of an efficient portfolio

☺ Any risky asset Any risky asset ii is on the SML is on the SML

The Benefits of DiversificationThe Benefits of Diversification

np

σp

Diversifiable Risk

Systematic Risk

The RiskThe Risk

☺ The risk of any risky asset has two componentsThe risk of any risky asset has two components☺ σσDD - The diversifiable (non-systematic, idiosyncratic, - The diversifiable (non-systematic, idiosyncratic,

firm-specific) risk can be eliminated by adding assets firm-specific) risk can be eliminated by adding assets to the portfolioto the portfolio

☺ σσNDND - The systematic (non-diversifiable, market) risk - The systematic (non-diversifiable, market) risk

can not be eliminated through diversificationcan not be eliminated through diversification

☺ According to the CAPM, investors are According to the CAPM, investors are compensated only for the systematic compensated only for the systematic component of the total asset risk (component of the total asset risk (σσNDND).).

The Components of RiskThe Components of Riskin the in the μμ--σσ Plane Plane

σ

μ

i

The CML

rf

mp

σDσND

σ

The CAPM Market EquilibriumThe CAPM Market Equilibrium

Find beta in the following planesFind beta in the following planes

RRii-R-Rm m or (R or (Rii-rf) – (R-rf) – (Rmm-rf)-rf)

μμ--σσ (the CML) (the CML)

μμ--ββ (the SML) (the SML)

The CAPM: Market EquilibriumThe CAPM: Market Equilibrium

β

μ

m

rfOverpriced – return is too low

Underpriced – return is too high

SML

The Return and the Current Price:The Return and the Current Price:Inversely RelatedInversely Related

A and B are two risky stocks. An analyst found that they A and B are two risky stocks. An analyst found that they have the following parameters:have the following parameters:

μμAA=15% and =15% and ββAA=0.5;=0.5; μμBB=22% and =22% and ββBB=2.=2.

The risk-free rate is rf=10% and the expected return of the The risk-free rate is rf=10% and the expected return of the market portfolio is market portfolio is μμmm=18%.=18%.

Relative to the CAPM equilibrium prices, which stock is Relative to the CAPM equilibrium prices, which stock is underpriced and which is overpriced?underpriced and which is overpriced?

1 1

0

P1

P

E DivE R k

Project Valuation – Example 1Project Valuation – Example 1

Firm XYZ usually invests in projects with a risk level of Firm XYZ usually invests in projects with a risk level of ββ=0.8. It is considering an investment in a new project =0.8. It is considering an investment in a new project which is expected to produce a CF of $12.6M a year which is expected to produce a CF of $12.6M a year from now, and this CF is expected to grow at a from now, and this CF is expected to grow at a constant rate of 2% per year forever. This CF is only constant rate of 2% per year forever. This CF is only an expectation and the firm’s economist estimates it’s an expectation and the firm’s economist estimates it’s Std to be $3M.Std to be $3M.

What is the present value of the CFs of this project, if What is the present value of the CFs of this project, if the expected annual return of the market portfolio is the expected annual return of the market portfolio is 12%, the annual return of money market instruments is 12%, the annual return of money market instruments is 4% and the market is in equilibrium (CAPM)?4% and the market is in equilibrium (CAPM)?

(k = 10.4%; PV = $150M)(k = 10.4%; PV = $150M)

Project Valuation – Example 2Project Valuation – Example 2

Joseph is looking for a treasure ship in the Mediterranean Joseph is looking for a treasure ship in the Mediterranean sea. He plans to keep looking for a year, and at the end of sea. He plans to keep looking for a year, and at the end of that year the value of his firm will be determined by the that year the value of his firm will be determined by the outcome of his quest. The probability of finding the $25M outcome of his quest. The probability of finding the $25M treasure is only 10% but he is more likely to end up with a treasure is only 10% but he is more likely to end up with a smaller catch of only $5M.smaller catch of only $5M.

Obviously, the outcome of Joseph’s quest is independent of Obviously, the outcome of Joseph’s quest is independent of any macroeconomic risks, but we know that the expected any macroeconomic risks, but we know that the expected annual return of the market portfolio is 14%, it’s Std is 22% annual return of the market portfolio is 14%, it’s Std is 22% and the annual return of money market instruments is 6%. and the annual return of money market instruments is 6%. What is the value of Joseph’s firm if the market is in What is the value of Joseph’s firm if the market is in equilibrium (CPAM)?equilibrium (CPAM)?

(PV = $6.604M)(PV = $6.604M)

CAPM ReviewCAPM Review

Under strict assumptions, the CAPM results Under strict assumptions, the CAPM results in in a prescription for a fair return (price)a prescription for a fair return (price): : The fair expected return on an asset The fair expected return on an asset depends on the depends on the market risk premiummarket risk premium and and on on betabeta..

Stocks with high betas have higher return, Stocks with high betas have higher return, but there is no compensation for any risk but there is no compensation for any risk factor other than the systematic market risk.factor other than the systematic market risk.

CAPM CritiqueCAPM Critique

☺Roll (1977) points out that the CAPM is not Roll (1977) points out that the CAPM is not directly testabledirectly testable

☺It is a one period modelIt is a one period model☺The market portfolio cannot be identifiedThe market portfolio cannot be identified☺To test the model, we need the market portfolio to be To test the model, we need the market portfolio to be

on the “efficient frontier” (proxies won’t work)on the “efficient frontier” (proxies won’t work)

☺Indirect tests fail to support the CAPMIndirect tests fail to support the CAPM☺Other risk factors are compensated (size, book-to-Other risk factors are compensated (size, book-to-

market ratio), but there is no theoretical explanation for market ratio), but there is no theoretical explanation for these risk factors.these risk factors.

The Efficient Market HypothesisThe Efficient Market Hypothesis

☺The Efficient Markets Hypothesis (EMH) The Efficient Markets Hypothesis (EMH) specifies three forms of efficiency:specifies three forms of efficiency:

☺Weak form market efficiencyWeak form market efficiency☺Semi-Strong form market efficiencySemi-Strong form market efficiency☺Strong form market efficiencyStrong form market efficiency

☺Note that EMH is an HypothesisNote that EMH is an Hypothesis☺We should look for evidence that reject the hypothesisWe should look for evidence that reject the hypothesis☺We should look for evidence to decide which form of We should look for evidence to decide which form of

EMH is more likelyEMH is more likely

Weak Form EfficiencyWeak Form Efficiency

☺Definition: Definition: A market is weak form efficient if the current A market is weak form efficient if the current asset prices reflect all historical price asset prices reflect all historical price informationinformation

☺Implication:Implication:Trading strategies based on the analysis of Trading strategies based on the analysis of historical prices should not yield abnormal historical prices should not yield abnormal returns (on average!)returns (on average!)

Normal and Abnormal ReturnsNormal and Abnormal Returns

☺Normal returns: Normal returns: Fair or equilibrium returns given by a Fair or equilibrium returns given by a theoretical model like the CAPMtheoretical model like the CAPM

☺Abnormal returns:Abnormal returns:Returns that are systematically higher than the Returns that are systematically higher than the normal returnsnormal returns

Normal and Abnormal ReturnsNormal and Abnormal Returns

☺ For each asset For each asset ii the CAPM predicts a normal, risk- the CAPM predicts a normal, risk-adjusted rate of return (expected return):adjusted rate of return (expected return):

E(RE(Rii) = rf + ) = rf + ββii [ E(R [ E(Rmm) – rf ]) – rf ]

☺ We observe asset We observe asset ii over time, and compare the realized over time, and compare the realized return Rreturn Rii to the expected CAPM return: to the expected CAPM return:

ααitit = R = Ritit – E(R – E(Rii) = R) = Ritit – { rf + – { rf + ββii [ E(R [ E(Rmtmt) – rf ] }) – rf ] }

☺ If asset If asset ii is systematically beating the CAPM expected is systematically beating the CAPM expected return, we say that the return of asset return, we say that the return of asset ii is abnormal. is abnormal.

Abnormal return: Average[ Abnormal return: Average[ ααit it ] = 1/T [] = 1/T [ααi1i1 + + ααi2i2 +…+ +…+ ααiTiT] >] > 0 0

Semi-Strong Form EfficiencySemi-Strong Form Efficiency

☺Definition: Definition: A market is semi-strong form efficient if the A market is semi-strong form efficient if the current asset price reflects all publicly available current asset price reflects all publicly available informationinformation

☺Implication:Implication:Trading strategies based on the analysis of Trading strategies based on the analysis of publicly available information (fundamental publicly available information (fundamental analysis such as analyst reports) should not analysis such as analyst reports) should not yield abnormal returns (on average!)yield abnormal returns (on average!)

Strong Form EfficiencyStrong Form Efficiency

☺Definition: Definition: A market is strong form efficient if the current A market is strong form efficient if the current asset price reflects all information (including asset price reflects all information (including private / insider information)private / insider information)

☺Implication:Implication:There is no (legal) trading strategy that yields There is no (legal) trading strategy that yields abnormal returns (on average!). One cannot abnormal returns (on average!). One cannot make money even by following the trades of make money even by following the trades of insider information.insider information.

NestingNesting

☺Information: Information: Information about past prices is included in the Information about past prices is included in the set of publicly available information, which is set of publicly available information, which is included in the complete set of information.included in the complete set of information.

☺Market efficiency:Market efficiency:The strong form of market efficiency implies the The strong form of market efficiency implies the semi-strong, which implies the weak form. Note semi-strong, which implies the weak form. Note that the strongest form of the MEH is the that the strongest form of the MEH is the strongest and the most restricting assumption.strongest and the most restricting assumption.

Evidence of Weak Form MEHEvidence of Weak Form MEH

☺Consistent evidence: Consistent evidence: Technical trading rules, based on past price Technical trading rules, based on past price patterns, do not appear to be profitable.patterns, do not appear to be profitable.

☺Contradicting evidence:Contradicting evidence:The “January” effect – almost every January, The “January” effect – almost every January, stock returns (usually for small stocks) are stock returns (usually for small stocks) are positive.positive.

Evidence ofEvidence ofSemi-Strong Form MEHSemi-Strong Form MEH

☺Consistent evidence: Consistent evidence: New publicly available information (such as earnings New publicly available information (such as earnings release) affects prices quickly.release) affects prices quickly.

☺Contradicting evidence:Contradicting evidence:Small stocks and stocks with high ratio of book-value to Small stocks and stocks with high ratio of book-value to market-value have, on average, higher returns.market-value have, on average, higher returns.

Some portfolio managers consistently outperform the Some portfolio managers consistently outperform the market (Peter Lynch, Warren Buffet, John Templeton market (Peter Lynch, Warren Buffet, John Templeton and John Neff are in Paul Samuelson’s hall of fame, and John Neff are in Paul Samuelson’s hall of fame, 1989).1989).

Evidence of Strong Form MEHEvidence of Strong Form MEH

☺Consistent evidence: Consistent evidence: Insiders of corporations appear able to earn abnormal Insiders of corporations appear able to earn abnormal returns from their trades. On average, price increases returns from their trades. On average, price increases just after insiders purchase the stock and decreases just after insiders purchase the stock and decreases just after a they sell the stock.just after a they sell the stock.

☺Contradicting evidence:Contradicting evidence:Prices react to public information that had been private. Prices react to public information that had been private. For example, prices react to earning announcements For example, prices react to earning announcements even though someone must have know their contents even though someone must have know their contents before the official announcement day.before the official announcement day.

Market Efficiency and EquilibriumMarket Efficiency and Equilibrium

☺An efficient market is a market in An efficient market is a market in equilibriumequilibrium

☺Inefficient markets occur when asset Inefficient markets occur when asset prices are different from their equilibrium prices are different from their equilibrium pricesprices

☺In theory, traders who exploit market In theory, traders who exploit market inefficiencies should move the market back inefficiencies should move the market back to equilibriumto equilibrium

The Joint Hypothesis ProblemThe Joint Hypothesis Problem

☺A test of market efficiency can only be A test of market efficiency can only be conducted by using a theoretical model to conducted by using a theoretical model to define normal (fair) returns (prices)define normal (fair) returns (prices)

☺Finding an abnormal average return can Finding an abnormal average return can be interpreted in more than one way:be interpreted in more than one way:☺Reject the Market Efficiency Hypothesis (MEH)Reject the Market Efficiency Hypothesis (MEH)☺Reject the theoretical model of normal returnsReject the theoretical model of normal returns☺Reject bothReject both

MEH – Are Markets Efficient?MEH – Are Markets Efficient?

☺ Grossman and Stigliz (1980): the logical question must Grossman and Stigliz (1980): the logical question must always be to what extent markets are efficientalways be to what extent markets are efficient

☺ Empirical evidenceEmpirical evidence

☺ Implications for trading strategies?Implications for trading strategies?☺Technical analysisTechnical analysis☺Fundamental analysisFundamental analysis☺Trading on insider information (SEC regulations)Trading on insider information (SEC regulations)

☺ Is there a portfolio manager who systematically Is there a portfolio manager who systematically outperforms the market?outperforms the market?

☺Is a small abnormal return detectable?Is a small abnormal return detectable?☺Will they tell us about their winning strategy (selection bias)?Will they tell us about their winning strategy (selection bias)?☺How can we distinguish between luck and talent?How can we distinguish between luck and talent?

Practice ProblemsPractice Problems

BKM Ch. 9: 1-2, 4-17, 21-28BKM Ch. 9: 1-2, 4-17, 21-28

BKM Ch. 12: 1-9, 14, 16-18, 25, 27-28BKM Ch. 12: 1-9, 14, 16-18, 25, 27-28