Báo cáo đề tài Mô hình định giá tài sản vốn The Capital Asset Pricing Model: Theory and Evidence

Báo cáo đề tài Mô hình định giá tài sản vốn The Capital Asset Pricing Model:Theory and Evidence The attraction of the CAPM is that it offers powerful and intuitively pleasing predictions about how to measure risk and the relation between expected return and risk. Unfortunately, the empirical record of the model is poor—poor enough to invalidate the way it is used in applications.

The Capital Asset Pricing Model:

Theory and Evidence

Eugene F Fama and Kenneth R French

ABSTRACT

The attraction of the CAPM is that it offers powerful and intuitively pleasing predictions about how to measure risk and the relation between expected return and risk Unfortunately, the empirical record of the model is poor—poor enough to invalidate the way it is used in applications.

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The Logic of the CAPM

Early Empirical Tests

Alternative models

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The Logic of the CAPM

Investors choose variance-efficient” portfolios.

“mean-minimize the variance of

portfolio return, given expected

return

maximize expected return, given variance

Markowitz’s model

The model assumes investors are risk averse and, when choosing among portfolios, they care only about the mean and

variance of their one-period investment return

• Investors agree on the joint distribution

of asset returns from t – 1 to t.

• And this distribution is the true one

complete agreement

there is borrowing and lending at a risk-free rate, which is the same for all investors and does not depend on the amount borrowed or lent

risk-free rate

The Logic of the CAPM

Sharpe (1964) and Lintner (1965) add two key assumptions

The Logic of the CAPM

E(Ri) = RF + [E(RM) – RF] βiM

Market portfolio M must be on the minimum variance frontier

The Logic of the CAPM

Fischer Black (1972)

Unrestricted risk-free borrowing

and lending is an unrealistic

assumption

The market portfolio is efficient, which means that the minimum variance condition for M given above holds

E(R ZM ) must be less than the expected market return, premium

for beta is positive

allowing unrestricted short

sales of risky assets

The assumption that short selling is unrestricted is

unrealistic

Jensen (1968)

Blume (1970), Friend & Blume (1970)

and Black, Jensen & Scholes (1972)

Merton 1973

)

Basu (1977)

Banz (1981)

Early Empirical Tests

Gibbons, Ross & Shanken (1989) Fama and MacBeth (1973) Statman (1980), Rosenberg, Reid & Lanstein (1985)

Friend & Blume (1970), Black, Jensen

& Scholes (1972), Stambaugh (1982) Fama and French (1992, 1993)…

Beta premium is

positive

Assets uncorrelated with the market have expected returns equal to the risk-free interest rate, and the beta premium is the expected market return minus the risk-free rate

Expected returns on all assets are linearly related to their betas, and no other variable has marginal explanatory power

Tests of the CAPM are based on three implications

Early Empirical Tests

Tests on Risk Premiums

French and Blume (1970) and Black, Jensen and Scholes (1972) work with portfolios, rather than individual securities to reduces the critical errors

in variables problem

The regression

residuals

Estimates of beta for

individual assets are

imprecise

Fama and MacBeth (1973) propose a method for addressing the

inference problem caused by correlation of the residuals in cross- section regressions

Fama-Macbeth 1973

Tests on Risk Premiums

Douglas (1968), Black, Jensen and Scholes (1972),

Miller and Scholes (1972), Blume and Friend (1973),

Fama and MacBeth (1973)

The intercept is greater than the average risk-free rate and the coefficient on beta is less than the average excess market return

The evidence show that the relation between beta and average return is too flat

Friend and Blume (1970), Black, Jensen and

Scholes (1972) and Stambaugh (1982)

The intercepts in time-series regressions of excess asset returns

on the excess market return are positive for assets with low betas and negative for assets with high betas

Blume (1970), Friend &Blume (1970)

and Black, Jensen &Scholes (1972)

Fischer Black (1972)

Fama-Macbeth 1973

Blume (1970), Friend &Blume (1970) and Black, Jensen &Scholes (1972)

Bhandari (1988)

Banz

(1981)

Basu

(1977) when common stocks are sorted on earnings-price

ratios, future returns on high E/P stocks are higher than predicted by the CAPM.

high debt-equity ratios are associated with returns that are too high relative to their market betas

a size effect: when stocks are sorted on market capitalization, average returns on small stocks are higher than predicted by the CAPM

Statman (1980) and Rosenberg, Reid and Lanstein (1985)

stocks with high book-to-market equity ratios have high average returns that are not captured by their betas

Basu

(1977)

Fama and French (1992)

size, E/P, D/E and B/M ratios add to the explanation of expected stock returns provided by market beta

Merton 1973 - ICAPM

the market portfolio is multifactor efficient but it requires additional betas, along with a market beta, to explain expected returns ICAPM investors consider how

their wealth at t might vary with

future state variables, including

labor income, the prices of

consumption goods and the

nature of portfolio opportunities

at t, and expectations about

ICAPM investors prefer high expected return and low

return variance But ICAPM investors are also concerned with the covariances of

portfolio returns with state variables

Chen-Roll-Ross 1986

Three-factor model

Fama and French (1993, 1996)

SMBt is the difference between the returns on diversified portfolios of small and big stocks

HMLt is the difference between the returns on diversified portfolios of high and low B/M stocks

Carhart 1997

Early Empirical Tests

Their view is based on evidence that stocks with high ratios of book value

to market price are typically firms that have fallen on bad times, while low B/M is associated with growthfirms (Lakonishok, Shleifer and Vishny, 1994; Fama and French, 1995) The behavioralists argue that sortingfirms on book-to-market ratios exposes investor overreaction to good and bad times Investors overextrapolate past performance, resulting in stock prices that are too high for growth (low B/M) firms and too low for distressed (high B/M, so-called value)firms

Explanations: Irrational Pricing or Risk

The need for a more complicated asset pricing model The CAPM is based

on many unrealistic assumptions

If international capital markets are open and asset prices conform to an international version of the CAPM, the market portfolio should include international assets

betas for a global stock market

portfolio cannot explain the high average returns observed

around the world on stocks with high

BE/ME or high E/P ratios.

When proxies are used in tests

of the model show up as bad estimates of expected returns

in applications: estimates of the cost of equity capital that are too low for small stocks and for stocks with high BE/ME ratios

The Market Proxy Problem

The CAPM, like Markowitz’s (1952, 1959) portfolio model

on which it is built, is nevertheless a theoretical tour de force We continue to teach the CAPM as an introduction to the fundamental concepts of portfolio theory and asset pricing, to be built on by more complicated models like Merton’s (1973) ICAPM But we also warn students that despite its seductive simplicity, the CAPM’s empirical problems probably invalidate its use in applications.

PHẦN MỞ RỘNG

Với trường hợp có thuế

Với sự hiện diện chi phí giao dịch: các chứng khoán sẽ nằm rất gần với đường SML nhưng không phải nằm đúng trên đó Độ rộng của dải phân bố này là một hàm của các chi phí giao dịch.

Nhà đầu tư có thể đi vay với lãi suất Rb nào đó, lúc đó điểm tiếp xúc của đường thẳng xuất phát từ đường hiệu quả xảy ra tại điểm K nào đó khác T

Nhà đầu tư có thể cho vay với rf và đầu tư số tiền này vào M trên đường hiệu quả Nhưng không thể mở rộng đường này về phía phải nếu không thể đi vay với rf để đầu tư thêm vào M

Các giả định của CAPM

Arbitrage pricing theory

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Bốn giả định

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Thị trường tài chính số lượng chứng khoán

TSSL

cơ hội kinh doanh chênh lêch

Arbitrage pricing theory

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