Presentation CAPM

5/23/2018 Presentation CAPM

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Capital Asset Pricing Model (CAPM)

INTRODUCTION

William Sharpe (1964), John Linter (1965)

Widely used to estimate the Cost of Capital and

evaluating portfolio performance Offers predictions about how to measure risk and

relation between expected return & risk

Empirical record of model is poor and most

applications of the model are invalid


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The Logic of CAPM

Builds on model of portfolio choice developed by

Markowitz (1959)

Investor selects a portfolio at time t-1that produce

stochastic (random) return at t

The model assumes investors as risk averse and

choose mean-variance efficient portfolios

Minimize variance of portfolio at a given expectedreturn, and maximize expected return at given

variance (Mean-Variance Model)

Assumptions of Mean-variance risk portfolio Complete Agreement: Given market clearing prices

at t-1, investors agree on joint distribution of assets

returns from t to t-1

Borrowing or lending at Risk Free rate is

independent of how much amount borrowed on lent


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Investment Opportunities

ABC Curve = Minimum variance curve (Tells

combinations of E(R) and Risk for risky assets

portfolio that minimize variance at different levels of

Expected Return. Points above b are mean-


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Investment Opportunities

Adding the Risk Free rate turns efficient portfolio

into a straight line. Consider an investor who invests x portion of

investment in a Risk Free Security and 1-x portion

of investment in risky assets (g).

Combinations of investment in Risk Free Securities

and in g securities is a straight line between Rfand g.

Points to the right of g represents borrowing at g

with the proceeds of borrowing used to increase

investment in portfolio g. Line from Rfto grepresents lending at Rfrate with

risky assets borrowing at point g


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Punch-Line for CAPM

Since investors have complete agreement about

distribution returns, they combine same riskytangency portfolio Twith risk-free lending or

borrowing.

Tmust be the value-weight market portfolio of risky

assets or each risky assets weight in tangency

portfolio (M i.e. Market) M is the total market value of all outstanding units of

assets divided by total market value of all risky

assets.

CAPM assumptions imply that market portfolio Mmust be on minimum variance frontier if assets is to

clear market.

If there are N number of assets then:


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Beta

Sensitivity of a security with respect to market i.e.

how fast a security tends to move/align itself withthe change in market.

It is a systematic risk

Bi,m is the covariance risk of asset iin Mmeasured

relative to the average covariance risk of assets.)


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When a risky assets return is uncorrelated with the

market return, its beta is zero [E(Rzm)].

This type of risky asset is riskless in the market

portfolio as it contributes nothing to the variance ofthe market return.

When there is risk free borrowing or lending, the

expected return of assets that are uncorrelated with

the market [E(Rzm)]must be equal to Rfrate. Hence, the relation between expected return and

beta then becomes:

The Expected return on any asset is the risk free

interest rate Rf, plus a risk premium which is

assets market beta B i,m, times premium per unit

beta risk, E(Rm)-Rf


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Early Empirical Tests

Based on three assumptions

i) Expected returns on all assets are linearly related

to

their betas, and no other variable has marginal

explanatory power.

ii) Beta premium is positive, meaning that theexpected

return on the market portfolio exceeds the

expected

return on assets whose returns are uncorrelatedwith

the market return.

iii) Assets uncorrelated with the market have

expected

returns equal to the risk-free interest rate, and the


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The Black, Jensen, and Scholes test (1972)

If market portfolio is efficient, it follows automatically

that a linear, positively sloped relationship exists

between betas and expected rates of return.

If investors can borrow and lend at a risk-free rate,

it also follows that a zero beta stock or portfolio can

be expected to produce a return equal to the risk-

free rate. The empirical test of BLACK, JENSEN, AND

SCHOLES (BJS) is designed to test these

properties of the security market line.

Hypothesis:Average returns (in a cross section ofstocks) depend linearly (and solely) on asset betas

Individual stock returns are so volatile therefore

Portfolios are being used to test hypothesis


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(Contd..) They calculated beta for all portfolios during the

sub-period (Market index = an equally weighted

portfolio of all stocks on the NYSE). They estimate the beta of each portfolio by relating

the portfolio returns to their market index.

The relationship they find between beta and

average rate of return is depicted in the followingfigure:


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(Contd..)

BJS concluded that their results are

consistent with the form of the CAPM thatallows for riskless lending but doesntallow

riskless borrowing.

The Fama-Macbeth (FM)study (1974)

Like BJS, the finding of FM is again

consistent with the form of the CAPM where

lending at the risk-free rate is permitted but

borrowing is precluded.On average, positive trade off between risk

and return


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Different studies with their findings

Studies Findings

Black, Jensen, and

Scholes (1972)

Fama and MacBeth

(1973)Reinganum (1981)

Lakonishok and

Shapiro (1986)

Fama and French

(1992)

Positive relation between average return and market

beta (1926-1968).

The relation between and average return disappears

during the more recent period (1963-1990)


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Studies Findings

Banz (1981)

Bhandari (1988)

Basu (1983)

A strong negative relation between average return and

firm size. When stocks are sorted on market

capitalization, average returns on small stocks are

higher than predicted by the CAPM.

Average return is positively related to leverage. Returns

on highly geared firms are too high relative to their

market betas.

A positive relation between average return and E/P.

When common stocks are sorted on earnings-price

ratios, future returns on high E/P stocks are higher than

predicted by the CAPM.


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Studies Findings

Stattman (1980)

Rosenberg, Reid,

and Lanstein (1985)

Chan, Hamao, and

Lakonishok (1992)

A positive relationship between average return and

book-to-market equity for US stocks.

Stocks with high book-to-market equity ratios have highaverage returns that are not captured by their betas.

BE/ME is a powerful variable for explaining average

returns on Japanese stocks.


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ICAPM extension of the Capital Asset Pricing Model

(Metron, 1973)

In the CAPM, investors care only about the wealth

theirportfolio produces at the end of the current period.

In the ICAPM, investors are concerned not only with

their end-of-period payoff, but also with the

opportunities they will have to consume or invest the

payoff.

Thus, when choosing a portfolio at time t -1, ICAPM

investors consider how their wealth at tmight vary

with future state variables, including labor income,

the prices of consumption goods and the nature ofportfolio opportunities at t, and expectations about

the labor income, consumption and investment

opportunities to be available after t.

As a result, optimal portfolios are multifactorefficient, which means the have the lar est ossible


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Fama and French (1992)

Their bottom line results are

(a) Beta does not seem to help explain the

cross-section of average stock returns

(b) The combination of size and book-to-market equity seems to absorb the roles of

leverage and E/P in average stock returns,

at least during their 1963-1990 sample

period


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Fama and French

"Beta," the measure of market exposure of agiven stock or portfolio, which was previouslythought to be the measurement of stockrisk/return, is of only limited use. It did notexplain the returns of all equity portfolios,although it is still useful in explaining the returnof stock/bond and stock/cash mixes.

Fama and French (1992) confirm the evidencethat the relation between average return andbeta for common stocks is even flatter after thesample periods used in the early empiricalworks on the CAPM.

If betas do not suffice to explain expectedreturns, the market portfolio is not efficient, andthe CAPM is dead in its tracks.


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The Fama-French Three-Factor Model

Return is explained by three factors:

Market factor (market index)

Size factor (market capitalization)

Book- to-market ratio (Book Equity/MarketEquity)


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The additional factors are empiricallymotivated by the observations that

historical-average returns on stocks of

small firms and on stocks with highratios of book equity to market equity

(B/) are higher than predicted by the

security market line of the CAPM.


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To create portfolios that track the firm sizeand book-to-market factors, Davis, Fama,

and French (2000) sorted firms annually by

size (market capitalization) and by book-to-

market (B/M) ratio.

The small-firm group (S) :all firms with 33%

lowest market capitalization.

Medium firm group (M) :all firm with next34%.

Big-firm group (B):all firm with 33% highest

market capitalization


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Similarly, firms are annually sorted intogroups based on (B/M) ratio.

A low-ratio group (L) with 33% lowest B/M

ratioA medium-ratio group (M) with next 34%

A high ratio group (H) with 33% highest B/M

ratio.

A high ratio firm is called value firm and the

low ratio firm is called growth firm.


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For each year, the size premium (SMB) isconstructed as the difference in returns

between small and large firms.

Similarly, the book-to-market effect is

calculated from the difference in returnsbetween high B/M ratio and low B/M ratio firms.

The monthly returns on the market portfolio

were calculated from the value-weighted

portfolio of all firms listed on the NYSE, AMEX,

and NASDAQ.

The risk-free rate was the return on 1-month

T/bills.


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Interpretation of the results

The findings:

Small firms have higher average returns

than large firm.

Firms with high ratios of book value tomarket value of common equity have higher

average returns than firms with low book-to-

market ratios.

Since the CAPM does not explain thispattern in average returns, it is typically

called anomaly.


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Interpretation

How should we interpret these results?

One argument is that size and relative

value (as measured by the B/M ratio) proxy

for risk is not captured by the CAPM betaalone.

Another explanation attributes these

premium to irrational investors preferences

for large size or low B/M firms (growthfirms). This evidence may be more relevant

for the B/M or value factor in light of the

evidence that size premium has largely

vanished in recent years.


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Interpretation

The irrational investor preference for valuepremium explanation says it is due to

investor overreaction to firm performance.

High BE/ME stocks tend to be firms that are

weak on fundamentals like earnings and

sales, while low BE/ME stocks tend to have

strong fundamentals. Investors overreact to

performance and assign irrationally lowvalues to weak firms and irrationally high

values to strong firms. When the

overreaction is corrected, weak firms have

high stock returns and strong firms have


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Three-Factor Model: Evaluating Fund Managers

This model can also used to measure historical fund

manager performance to determine the amount of

value added by management.

Where , I is the Y-intercept of the equation, is the

Active Returnand defined as:

= Active Return = (Portfolio Actual Return -Benchmark Actual Return)

Historical data is utilized in a multiple regression

analysis to determine the value ofAlpha indicates how well the fund manager is

capturing the expected returns, given the portfolio'sexposure to the

If the fund manager captures the factor exposures

perfectly, the expected alpha would be zero, minus

the expense ratio (ER) of the fund.


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Three-Factor Model: Evaluating Fund Managers

Alpha greater than this suggests that the fund

manager is adding value beyond the underlying

factor exposures.

From a theoretical perspective, the main shortcoming

of the three-factor model is its empirical motivation.

The small-minus-big (SMB) and high-minus-low(HML) explanatory returns are not motivated by

predictions about state variables of concern to

investors. Instead they are brute force constructs

meant to capture the patterns uncovered by previous

work on how average stock returns vary with size andthe book-to-market equity ratio.


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Three-Factor Model


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Market Proxy Problem

Richard Roll (1977) thinks that the CAPM and themarket portfolio are untestable without accurate

specification of the true market portfolio. Roll

(1978) strengthens his argument by showing that

different indexes used as proxies for the marketportfolio can cause different portfolio-performance

rankings.

It is not theoretically clear which assets (for

example, human capital) can legitimately be

excluded from the market portfolio, and data

availability substantially limits the assets that are

included. As a result, tests of the CAPM are forced

to use proxies for the market portfolio.


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Market Proxy Problem

Since the relation between expected returnand market beta of the CAPM is just the

minimum variance condition that holds in

any efficient portfolio, applied to the market

portfolio. Thus, if we can find a market

proxy that is on the minimum variance

frontier, it can be used to describe

differences in expected returns. It is always possible that researchers will

redeem the CAPM by finding a reasonable

proxy for the market portfolio that is on the

minimum variance frontier.


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Summary: Three-Factor Model

"Beta," the measure of market exposure of a given

stock or portfolio, which was previously thought to be

the measurement of stock risk/return, is of onlylimited use. It did not explain the returns of all equity

portfolios, although it is still useful in explaining the

return of stock/bond and stock/cash mixes.

The return of any stock portfolio can be explainedalmost entirely (around 95%) by including two

additional factors: Market cap ("Size") and

book/market ratio ("Value").

Therefore, a portfolio with a small median market cap

and a high book/market ratio will have a higher

Expected return than a portfolio with a large median

market cap and a low book/market ratio

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