capm_apt

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Chandra Shekar BMFaculty & Research ScholarDept of Commerce,

Bangalore University

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The model was developed by three researchers in the mid of 1960s

William Sharpe

John Lintner and

Jan Mossin

It is an extension of Portfolio theory of Markowitz

Portfolio theory is a description of how rational investors should build efficient

portfolios and select the optimal portfolio

Capital Asset Pricing model derives the relationship between the expected return

and risk of individual securities and portfolios in the capital markets if everyone

behaved in the way the portfolio theory suggested.

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William Sharpe

John Lintner and

Jan Mossin







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William Sharpe

John Lintner and

Jan Mossin







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Risk and Return are two imp characteristics of every investment

Risk is measured by variability in returns

Investors attempt to reduce the variability of returns through diversification

With a given no of securities you can create any no of portfolios altering

proportionsAmong these some dominate others and some are more efficient

Even well diversified portfolios are not risk free

Risk = Systematic risk + Unsystematic Risk

Systematic risk cannot be eliminated through diversification & affects all securities

Systematic risk is measured by Beta

All securities do not have same level of systematic risk. Therefore, the required rate

of return goes with the level of systematic risk.

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Assumes investors are rational

Rational investors expect the return on a security to commensurate with its risk

Since the relevant risk is market risk / systematic risk, it is implied that the return

is expected to be correlated with this risk only.

CAPM gives the nature of the relationship between the

expected return and systematic risk of a security

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In simple words

The relationship between the risk and return established by the security

market line . It is basically a simple linear relationship.

The model shows that the expected return of a security consists of the

risk-free rate of interest and the risk premium. The CAPM, when plotted on

a graph paper is known as the Security Market Line (SML).

mon security (Ri)

Expected return on security = Risk free return + Beta (risk premium)

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A major implication of CAPM is that not only every security but valid for

all portfolios whether efficient or inefficient. CAPM can be used to estimate

the expected return of any portfolio with the following formula.

=

E(Rp) = Expected return of the portfolio

Rf = Risk free rate of return

Bp = Portfolio beta i.e. market sensivity index

E (Rm) = Expected return on market portfolio.E (Rm) Rf = Market risk premium.

CAPM provides a conceptual frame work for evaluating any investment

decision where capital is committed with a goal of producing future returns.

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(i) The Investors objective is to maximise the utility of terminal wealth;

(ii) Investors make choices on the basis of risk and return;

(iii) Investors have homogenous expectations of risk and return;

(iv) Investors have identical time horizon;

(v) Information is freely and simultaneously available to investors;

(vi) There is a risk-free asset, and investors can borrow and lend unlimited

amounts at the risk-free rate;

(vii) There are no taxes, transaction costs, restrictions on short rates, or other

market

imperfections;

(viii) Total asset quantity is fixed, and all assets are marketable and divisible.

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CML provides a risk return relationship and a measure of risk for efficient portfolios

A line formed by the action of all investors mixing the market portfolio with the

risk free asset is known as Capital Market Line. All efficient portfolios of all

investors will lie along this capital market line

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The relationship between the return and risk of any efficient

portfolio on the CML can be expressed in the form offollowing equation

-

Expected Return = Price of time + ( Risk Premium * Amount of Risk)

e e m

m

WhereRe = Return on Efficient portfolio


Rm = Return on Market Portfolioe = SD of efficient portfoliom = SD of Market portfolio

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SML provides the relationship between the expected return and beta of a security or

portfolio.

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The relationship between the return and risk of any security on

the SML can be expressed in the form of following equation

Expected Return = Price of time + ( Risk Premium * Beta)

Risk premium of a security is directly proportional to the risk measured

by Beta.

m

WhereRi = Return on Security


Rm = Return on Market Portfolioi = Beta of the Security

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CML SMLIn CML the risk is defined as total risk

In SML the risk is defined as

and is measured by Standard Deviation Beta

Capital Market line is valid only forefficient portfolios

Security Market Line is valid for all

portfolios and all individual securities

as well

CML is the basis of the Capital MarketTheory

SML is the basis of the CAPM

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1. Based on highly restrictive assumptions

a) we made the assumption that investors had identical

preferences, had the same information, and hold the same

portfolio (the market).b) Also, there is the problem that identifying and measuring

the market return is difficult, if not impossible

2. The market factor is not the sole factor influencing the stock

returns

3. There are serious doubts about its testability

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The APT model was developed as an alternative to the CAPM.

Like the CAPM, this model provides implications for the

relationship between expected returns and risk on securities.

However, the model differs from CAPM in its assumptions,its implications, and in the way that equilibrium prices are

reached.

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The APT is an approach to determining asset values based on

law of one price and no arbitrage.

It is a multi-factor model of asset pricing.

T e APT mo e was eve ope as an a ternat ve to t e CAPM.Like the CAPM, this model provides implications for the

relationship between expected returns and risk on securities.

However, the model differs from CAPM in its assumptions, its

implications, and in the way that equilibrium prices are reached.

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In APT, the assumption of investors utilizing a mean-

variance framework is replaced by an assumption of the

process of generating security returns.

APT requires that the returns on any stock be linearly related

to a set of indices.

In APT, multiple factors have an impact on the returns of an

asset in contrast with CAPM model that suggests that return

is related to only one factor, i.e., systematic risk

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1. Capital markets are perfectly competitive

2. Investors always prefer more wealth to less wealth withcertainty

3. The stochastic rocess eneratin asset returns can be

presented as a k- factor model

4. Others

a) All securities havefi

nite expected values and variances.b) Some agents can form well diversified portfolios

c) There are no taxes

d) There are no transaction costs

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Multiple factors expected to have an impact on all assets:

Inflation

Growth in GNP

Changes in interest rates And many more.

Contrast with CAPM assumption that only beta is relevant

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Ri = Rf + 1f1 + 2f2 + 3f3 + ...+ kfk + ei

Ri = Return on asset i during a specified time period

Rf = Risk free rate of return (Alpha)

1 = eac on n asse s re urns o movemen s n acommon factor 1

f1 = A common factor with a zero mean that influences the

returns on all asset

ei = unsystematic risk

K = Number of factors

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Measurse how each asset (i) reacts to a common factor (k)

Each asset may be affected by a factor, but the effects will

differ

In application of the theory, the factors are not identified

Similar to the CAPM, the unique effects are independentand will be diversified away in a large portfolio

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Studies by Roll and Ross and by Chen support APT by

explaining different rates of return with some betterresults than CAPM

Reinganums study indicated that the APT does notexplain small-firm results

Dhrymes and Shanken question the usefulness of APTbecause it was not possible to identify the factors and

therefore may not be testable

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