7 th lecture

8/11/2019 7 Th Lecture

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Efficient Markets vs Behavioral Finance

7th lecture

Iuliia Brushko

IES, UK

April 8, 2013
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Capital Asset Pricing ModelArbitrage Pricing Theory

The Efficient Market HypothesisBehavioral Finance

Outline

1 Capital Asset Pricing Model

2 Arbitrage Pricing Theory

3 The Efficient Market Hypothesis

4 Behavioral Finance

Iuliia Brushko Efficient Markets vs Behavioral Finance
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Assumptions

1 There are many investors, who are price takers

2 They plan only for why period ahead what does this imply?

3 Investment possibilities are limited to financial assets

4 No taxes on returns, no transaction costs

5 Investors mean-variance optimizers

6 Investors have same expectations & beliefs what impactwill it have on the portfolio choice?

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Capital Market line

Capital allocation line (CAL) - risk-return combination availabeto the investors.Capital market line (CML) - provides the combination risk andreturn, formed by including 1-month T-bills and a broad index of

common stocks.Investing in the index of common stocks is motivated by:

active strategy is costly

free-rider motivation - knowledgeable investors will move the

price to optimal level

mutual fund theorem: passive strategy of investing in a marketindex portfolio is efficient


C i l A P i i M d l
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Risk Premium on Market Portfolio

= E(rM) rfA2M

E(rM) - return on a market portfolio; market portfolio - wealth ofthe economy; the proportion of each stock in this portfolio equals

the market value of this stock; the proportion invested in aparticular stock is equal the market value of the firm divided by themarket value of all stocks;rf- risk free interest rate; A - risk aversion;

2M- variance of

market portfolio

The model implies: (1) existing ofrf involves borrowing andlending - in equilibrium net borrowing and lending is 0; (2) therepresentative risk aversion is A; (3) = 1 - the average positionin the risky portfolio is 100%

E(rM) rf =A2M risk premium on market portfolio


C it l A t P i i M d l
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Expected Returns on Individual Securities

Consider the market portfolio consistent of 3 assets A, B, & C

Var(ara+ brb+ crc) =aCov(ra; rM) +Var(brb+ crc)+

+Cov(brb+ crc;ara)

where ara+ brb+ crc=rM, i - weights invested in asset i,ii = 1

Asset A contribution to variance=aCov(ra; rM)

Asset A contribution to risk premium =a[E(ra) rf]

Rewardtorisk ratio of asset A =a[E(ra) rf]

aCov(ra; rM) =

E(ra) rfCov(ra; rM)


Capital Asset Pricing Model
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Expected Returns on Individual Securities

Rewardtorisk ratio of asset A =a[E(ra) rf]

aCov(ra; rM) =

E(ra) rfCov(ra; rM)

Reward to risk ratio of market portfolio=

E(rM) rf2M

Basic principal: all investments should provide the samereward-to-risk ratio

E(ra) rfCov(ra; rM)= E(rM) rf2M

E(ra) rf = Cov(ra; rM)

2M[E(rM) rf] =rf + a[E(rM) rf] ()

equation (*) is the expected return-beta relationshipIuliia Brushko Efficient Markets vs Behavioral Finance

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Security Market Line

a =Cov(ra; rM)/2M- beta measures the contribution of asset Ato the variance of the market portfolio as a fraction of totalvariance of the portfolio


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is the appropriate measure of riskp= 1 - you hold the market portfolio of all the assets in the

economy, where p- beta of your portfoliop>1 - aggressive investing (investing in high betas)p


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SML - provides the evaluation of investment performance

E(ra) rf =a[E(rM rf)] compare toE(ra) rf = + a[E(rM) rf]

Stock

s alphaIuliia Brushko Efficient Markets vs Behavioral Finance

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p gArbitrage Pricing Theory


Test of CAPM

Test CAPM with

Ri=i+ iRM+ei

Cov(Ri,RM) =i2M

i= Cov(Ri,RM)

2M

CAPM: all investors hold identical portfolios when newinformation arrives, there is no tradethen why do we observe active trade operations?in reality we have heterogeneous beliefs


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p gArbitrage Pricing Theory


Test of CAPM

Test CAPM with

Ri=i+ iRM+ei

Cov(Ri,RM) =i2M

i= Cov(Ri,RM)

2M

CAPM: all investors hold identical portfolios when newinformation arrives, there is no tradethen why do we observe active trade operations?in reality we have heterogeneous beliefs




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Arbitrage Pricing TheoryThe Efficient Market Hypothesis

Behavioral Finance

Factor Models

sources of uncertainty macroeconomic conditions firm specific risks

Single and multiple factor models:

ri =E(ri) + iF+ei

ri=E(ri) + i1F1+ 12F2+ei

E(ri) - initially expected return on stockFi- deviation of the common factor from its expected value

ij- the sensitivity of firm ito the deviation of the common factorfrom its expectation; factor loadings, factor betas; think ofas ameasure of the exposure of a stock or portfolio to the market-wideof macroeconomic risk factorsei- firm-specific disturbances




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Behavioral Finance

Arbitrage Pricing Theory

Key positions:

security returns can be described by a factor model there are sufficient securities to diversify away idiosyncratic risk well-functioning security markets do not allow for thepersistence of arbitrage opportunityArbitrage opportunity arises when investor can earn risklessprofits without making a net investment: buying the asset where itis cheaper & selling where it is expensive

Law of one price: if two assets are equivalent in all economicallyrelevant respects, they should have the same market priceProperty of risk-free arbitrage portfolio: regardless of riskaversion investors will try to take as high position as possible


Capital Asset Pricing ModelA bi P i i Th
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Behavioral Finance


rp=E(rp) + pF+ep

p= iii; E(rp) =

iiE(ri); ep=

iiei

2p=2p

2F+

2ep, since Cov(F, ei) = 0

2ep=Var(iei) = 2i

2ei

ifi = 1/n (the portfolio is equally weighted)

2ep=

1

n

22ei =

1

n2ei

as n , 2ep 0 - well-diversified portfolio


Capital Asset Pricing ModelA bit P i i Th


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Behavioral Finance


How would you interpret?

APT & CAPM: we get the same beta in both models despiterestrictive assumption of CAPM, expected return-beta relationship

should be at least approximately validIuliia Brushko Efficient Markets vs Behavioral Finance

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Behavioral Finance

Forms of Efficient Market Hypothesis

Kendall (1953): no predictable patterns in the stock prices isthe market erratic & driven by animal spirits?Efficient market hypothesis: the stock prices you observe alreadyreflect all available informationForms of EMH:

weak form - stock prices already reflect all past information

semistrong form- all publicly available information regardingthe prospects of the firm must be reflected in the stock prices

strong form- stock prices reflect all information relevant tothe firm, including information available only to the companyinsiders


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Behavioral Finance

Forms of Efficient Market Hypothesis

Kendall (1953): no predictable patterns in the stock prices isthe market erratic & driven by animal spirits?Efficient market hypothesis: the stock prices you observe alreadyreflect all available informationForms of EMH:

weak form - stock prices already reflect all past information

semistrong form- all publicly available information regardingthe prospects of the firm must be reflected in the stock prices

strong form- stock prices reflect all information relevant tothe firm, including information available only to the companyinsiders

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7 th lecture

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