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Capital Asset Pricing Model (CAPM)

By Himani Grewal

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Capital Asset Pricing Model

(CAPM)

The model was introduced by

Jack Treynor(1961, 1962),

William Sharpe (1964), John

Lintner(1965) and Jan Mossin

(1966) independently, buildingon the earlier work ofHarry

Markowitz on diversification and

modern portfolio theory. Sharpe,

Markowitz and Merton Miller

jointly received theNobel

Memorial Prize in Economics for

this contribution to the field of

financial economics

William Sharpe (1964

)

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The model was introduced by Jack Treynor (1961, 1962),

William Sharpe (1964), John Lintner (1965) and Jan

Mossin (1966) independently, building on the earlierwork of Harry Markowitz on diversification and modern

portfolio theory. Sharpe, Markowitz and Merton Miller

jointly received the Nobel Memorial Prize in Economics

for this contribution to the field of financial economics.

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Assumptions of CAPMAll investors :

Are risk-averse.

Are broadly diversified across a range of investments. Are price takers, i.e., they cannot influence prices.

Can lend and borrow unlimited amounts under the risk free rate of

interest.

Assume all information is available at the same time to all investors.

The markets are perfect, thus taxes, inflation, transaction costs, andshort selling restrictions are not taken into account.

All assets are infinitely divisible and perfectly liquid.

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The markets are in equilibrium, and no individual can

affect the price of a security.

The total number of assets on the market and theirquantities are fixed within the defined time frame.

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Risk concept under capm

CAPM decomposes a portfolio's risk into

systematic and specific risk. Systematic risk is

the risk of holding the market portfolio. As themarket moves, each individual asset is more or

less affected. Specific risk is the risk which is

unique to an individual asset. It represents the

component of an asset's return which is

uncorrelated with general market moves.

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The CAPM is a model for pricing an individual security

or a portfolio. For individual securities, we make use of

the security market line (SML) and its relation to expectedreturn and systematic risk (beta) to show how the market

must price individual securities in relation to their security

risk class.

the Capital Asset Pricing Model (CAPM)-

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where:

is the expected return on the capitalasset

is the risk-free rate of interest such as

interest arising from government bonds

(the beta) is the sensitivity of the

expected excess asset returns to the

expected excess market returns, or also

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is the expected return of the market

is sometimes known as the marketpremium orrisk premium (the difference

between the expected market rate of return

and the risk-free rate of return).

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Restated, in terms of risk premium, we find

that:

which states that the individual risk

premium equals the market premium times

.

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Security market line

The SML essentially graphs the results from the

capital asset pricing model (CAPM) formula. The

x-axis represents the risk (beta), and the y-axisrepresents the expected return. The market risk

premium is determined from the slope of the

SML.

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The relationship between and required return is plotted on the

securitiesmarket line (SML) which shows expected return as a function

of . The intercept is the nominal risk-free rate available for the market,

while the slope is the market premium, E(Rm)Rf. The securities market

line can be regarded as representing a single-factor model of the asset

price, where Beta is exposure to changes in value of the Market. The

equation of the SML is thus:

It is a useful tool in determining if an asset being considered for a

portfolio offers a reasonable expected return for risk. Individual

securities are plotted on the SML graph. If the security's expected return

versus risk is plotted above the SML, it is undervalued since the investorcan expect a greater return for the inherent risk. And a security plotted

below the SML is overvalued since the investor would be accepting less

return for the amount of risk assumed.

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What DoesCapital Asset Pricing Model (CAPM)

Mean?

A model that describes the relationship between risk and

expected return; it is used to price securities. The generalidea behind CAPM is that investors need to be

compensated for investing their cash in two ways: (1)

time value of money and (2) risk. (1) The time value of

money is represented by the risk-free (rf) rate in the

formula and compensates investors for placing money in

any investment over period of time. (2) Risk calculates

the amount of compensation the investor needs for

taking on additional risk. This is calculated by taking a

risk measure (beta) that compares the returns of the asset

to the market over a period of time and to the market

premium (Rm-rf).

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PORTFOLIO

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POR

TFOLIO.. A portfolio is a collection of investments held by

an institution or an individual.

Holding a portfolio is a part of an investment and

risk-limiting strategy called diversification. Byowning several assets, certain types of risk can bereduced. The assets in the portfolio could includebank accounts, stocks, bonds, options, warrants,gold certificates, real estate, futures contracts,production facilities, or any other item that isexpected to retain its value.

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PORTFOLIO.

In building up an investment portfolio a

financial institution will typically conduct

its own investment analysis, while a private

individual may make use of the services of

a financial advisor or a financial institution

which offers portfolio managementservices.

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Models

Some of the financial models used in the process of

valuation, stock selection, and management of portfolios include:

Maximizing return, given an acceptable level of risk

Modern portfolio theorya model proposed by Harry

Markowitz among others The single-index model of portfolio variance

Capital asset pricing model

Arbitrage pricing theory

The Jensen Index The Treynor Index

The Sharpe Diagonal (or Index) model

Value at risk model

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Modern portfolio theory......

MPT was developed in the 1950s through

the early 1970s and was considered an

important advance in the mathematical

modelling of finance. Since then, many

theoretical and practical criticisms have

been levelled against it.

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Modern portfolio theory

Modern portfolio theory (MPT) is a

theory of investment which attempts to

maximize portfolio expected return for a

given amount of portfolio risk, or

equivalently minimize risk for a given level

of expected return, by carefully choosingthe proportions of various assets.

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Modern portfolio theory.... MPT is a mathematical formulation of the concept

of diversification in investing, with the aim of selecting a collection of investment assets that hascollectively lower risk than any individual asset.For example, as prices in the stock market tend tomove independently from prices in the bondmarket, a collection of both types of assets cantherefore have lower overall risk than either individually. But diversification lowers risk even ifassets' returns are not negatively correlatedindeed, even if they are positively correlated.

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DiversificationDiversification has two faces:

1. Diversification results in an overall reduction

in portfolio risk (return volatility over time)

with little sacrifice in returns, and

2. Diversification helps to immunize the

portfolio from potentially disastrous eventssuch as the outright failure of one of the

constituent investments.

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Principles of Diversification Why do people invest?

Investment positions are undertaken with the goal of earningsome expected return. Investors seek to minimize inefficientdeviations from the expected rate of return

Diversification is essential to the creation of anefficient investment, because it can reduce thevariability of returns around the expected return.

A single asset or portfolio of assets is considered to

be efficient if no other asset or portfolio of assetsoffers higher expected return with the same (orlower) risk, or lower risk with the same (or higher)expected return.

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Diversification Will diversification eliminate all our risk?

It reduces risk to an undiversifiable level.

Simple diversificationrandomly selectedstocks, equally weighted investments

Diversification across industriesinvesting instock across different industries such

transportation, utilities, energy, consumerelectronics, airlines, computer hardware,computer software, etc.

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MARKOWITZ MODEL ORMODERN PORTFOLIO

THEORY

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Markowitz Diversification

Combining assets that are less than perfectlypositively correlated in order to reduce portfoliorisk without sacrificing portfolio returns.

It is more analytical than simple diversification andconsiders assets correlations. The lower thecorrelation among assets, the more will be riskreduction through Markowitz diversification

Markowitz emphasized that quality of a portfoliowill be different from the quality of individualassets with in it.

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Markowitz Diversification

Although there are no securities with

perfectly negative correlation, almost all

assets are less than perfectly correlated.

Therefore, you can reduce total risk (Wp)

through diversification. If we consider

many assets at various weights, we cangenerate the efficient frontier.

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ASSUMPTIONS OF

MARKOWITZ MODEL

Efficient market.

Investors have free access to fair andcorrect information on the returns and risk.

Investors are risk averse. And try to

minimize the risk and maximize return.

Investors base decisions on expected

returns and variance or standard deviation

of these returns from the mean.

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ASSUMPTIONS Investors prefer higher returns to lower

returns for a given level of risk.

A portfolio of assets under the aboveassumptions is considered efficient if no otherassets or portfolio of assets offers a higherexpected return with the same or lower risk or

lower risk with the same or higher expectedreturn. Diversification is the method by whichabove objectives can be secured.

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Portfolio Expected Return A weighted average of the expected returns of individual

securities in the portfolio.

The weights are the proportions of total investment ineach security

n

E(Rp) = wi x E(Ri)

i=1 Where n is the number of securities in the portfolio

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Expected Return of a PortfolioExamplePortfolio value = $2,000 + $5,000 = $7,000

rA = 14%, rB = 6%,

wA = weight ofsecurity A = $2,000 / $7,000 = 28.6%

wB = weight ofsecurity B = $5,000 / $7,000 = (1-28.6%)=71.4%

%288.8%284.4%004.4

)%6(.714)%14(.286)(n

1i

!!

vv!v!!

iip EE

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Portfolio Risk

When two or more securities or assets are

combined in a portfolio, their covariance or

interactive risk is to be considered. Thus if

the returns on two assets move together,

their covariance is positive and the risk is

more on such portfolio. If on the other hand, returns move independently or in opposite

directions, the covariance is negative and

the risk in total will be lower.

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Significance of Covariance

An absolute measure of the degree of

association between the returns for a pair of

securities.

The extent to which and the direction in

which two variables co-vary over time

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Why Correlation? What is correlation?

Perfect positive correlation The returns have a perfect direct linear relationship

Knowing what the return on one security will do allows an

investor to forecast perfectly what the other will do

Perfect negative correlation Perfect inverse linear relationship

Zero correlation No relationship between the returns on two securities

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PORTFOLIO MANAGEMENT

STAGE 1

INVESTMENT OBJECTIVES

CHOICE OF ASSETS MIX

STAGE 2

FORMULATION OF PORTFOLIO STRATEGY

PORTFOLIO EXECUTION

STAGE 3

PORTFOLIO REVISION

PORTFOLIO EVALUATION

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SPECIFICATION OF INVESTMENT

OJECTIVES AND CONSTRAINTS

THE INVESTMENT POLICY MAY BE

EXPRESSED as follows.

Objectives

Return requirements

Risk tolerance

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SPECIFICATION . The commonly stated investment goals are.

Income Growth

Stability

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SPECIFICATION .

Constraints and preferences

Liquidity

Investment horizon

Taxes

Unique circumstances

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SELECTION OF ASSETS MIX

Based on your objectives and constraints,you have to specify your asset allocation,

that is, you have to decide how much of

your portfolio has to be invested in each of

the following asset categories.

Cash

Bond

Real estates

Precious metals

Others

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FORMULATION OF PORTFOLIO

STRATEGY There are 2 kinds of portfolio strategy..

1. Active Strategy

2. Passive Strategy

3. Choice of Strategy

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Arbitrage Pricing Theory

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Arbitrage Pricing Theory (APT) Based on the law of one price. Two items

that are the same cannot sell at different

prices

If they sell at a different price, arbitrage

will take place in which arbitrageurs buy

the good which is cheap and sell the onewhich is higher priced till all prices for the

goods are equal

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APT In APT, the assumption of investors utilizing a

mean-variance framework is replaced by an

assumption of the process of generating securityreturns.

APT requires that the returns on any stock belinearly related to a set of indices.

In APT, multiple factors have an impact on thereturns of an asset in contrast with CAPM modelthat suggests that return is related to only onefactor, i.e., systematic risk

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Factors that have an impact the returns ofall assets may include inflation, growth in

GNP, major political upheavals, or changesin interest rates

ri = ai + bi1F1 + bi2F2 + +bikFk+ ei

Given these common factors, the biktermsdetermine how each asset reacts to thiscommon factor.

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THANK YOU

END OF THESYLLABUS