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CAPM

CAPMOverview:

CAPM Model:Assumptions

CAPMformulae

SecuritiesMarket line

Limitations

of CAPM

Practical Useof the CAPM

conclusions


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Markowitz, William Sharpe, John Linter and Jan Mossim provided basic structure

for CAPM model.

The Capital Asset Pricing Model(CAPM) helps us to calculate investment risk

and what return on investment we should expect.

This model describes the relationship between risk and expected return

This model starts with the idea that individual investment contains two types of

risk:

Systematic Risk (or Market risk)

Unsystematic Risk (or Specific risk)

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CAPM considers only systematic risk and assumes that unsystematic risk can be

eliminated by diversification. In more technical terms, it represents the

component of a stock's return that is not correlated with general market moves.

No of shares.

Beta

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Beta is used as a measure of systematic risk

In this theory, The required rate of return of an asset is having a linear

relationship with assets beta value

All investor hold only the market portfolio and riskless securities.

Market portfolio consists of the investment in all securities of the market.

Each assets is held in proportion to its market value to the total value of all

risky assts.

For Say if Reliance industry share represents 20% of all risky assets, then the

market portfolio of all individual investors contains 20% of Reliance industry

shares

CAPM is based on the idea that investors demand additional expected return(called the risk premium) if they are asked to accept additional risk.

This model tells us the fair (risk-adjusted) expected return for every individual

asset.

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A market equilibrium model i.e SML equation.

Finally to sum up:

It explains how assets should be priced in the capitalmarket.

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The perfect market assumption

There are no taxes or transaction costs or information costs

Stocks can be bought and sold in any quantity (even fractions)

There is one risk-free asset and all investors can borrow or lend at

that rate


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Capital Asset Pricing Model CAPM formulae

The standard formula remains the CAPM, which describes the relationship between

risk and expected return.

Rs =

CAPM's starting point is the risk-free rate - typically a 10-year government bond yield. To

this is added a premium that equity investors demand to compensate them for the extra

risk they accept. This equity market premium consists of the expected return from themarket as a whole less the risk-free rate of return. The equity risk premium is multiplied

by a coefficient that Sharpe called "beta."

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According to CAPM, beta is the only relevant measure of a stock's risk. It measures a

stock's relative volatality - that is, it shows how much the price of a particular stockjumps up and down compared with how much the stock market as a whole jumps up

and down.

If a share price moves exactly in line with the market, then the stock's beta is 1.

A stock with a beta of 1.5 would rise by 15% if the market rose by 10%, and fall by 15%if the market fell by 10%.

Beta :

Interpreting F

ifF!

asset is risk freeifF!

asset return = market return

ifF"

asset is riskier than market index

Fasset is less risky than market index

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The Security market Line:

The SML line helps to determine the expected return for a given Security beta.

In other words, when beta are given, we can generate expected return for the

given securities.

Positive relationship between systematic risk and return of a portfolio

The line which gives the expected returns-systematic risk combinations of assets

is called the security market line

The overvaluation and undervaluation of stock can be seen.

CAPM is called a single-factor model because the slope of the SML is caused by asingle measure of risk the beta.

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Plot the Risk-Free Rate

Beta Coefficient1.0

Return

%

Rf


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Plot Expected Return on the

Market Portfolio

Beta Coefficient1.0

Return

%

Rf= 4%

km =12%


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Draw the Security Market Line

Beta Coefficient1.0

Return

%

Rf= 4%

km =12%

SML


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Plot Required Return(Determined by the formula = Rf+ Fs[kM - Rf]

Beta Coefficient1.0

Return

%

Rf= 4%

km =12%

SML

1.2

R(k) = 4% + 1.2[8%] = 13.6%

R(k) = 13.6%


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Limitations ofCAPM

It is not realistic in the world.

This assumes that all investors are risk averse and higher the risk, the higher is the

return.

Investors ignore the Transactions cost, information cost. Brokerage, taxes etc and

make decision on single period time horizon.

The investor are given a choice on the basis of risk- return characteristics of an

investment and they can buy at the going rate in the market.

There are many buyers and sellers and the market is competitive and free forces of

supply and demand determine the prices.

CAPM Empirical tests and analyses used ex-post i.e Past data only.

The historical data regarding the market return, risk free rate of return and betas vary

differently for different periods. The various methods used to estimate these inputs

also affect beta value. Since the inputs cannot be estimated precisely, the expected

return found out through the CAPM model is also subjected to criticisms.


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CAPM establishes a measure of risk premium and is measured by F(Rm Rf)

Beta coefficient is the non diversifiable risk of the asset, relative to the risks of

the asset.

Suppose Tisco company has a beta equal to 1.5 and the risk free rate is say 6%

.The required rate of return on the market (Rm) is 15%. Then adopting this

equation, we have

If the market rate is 15% then the return on Tisco should 19.5% because the

larger risk on tisco than on market.

When return on market is zero this model doesnt work accurately .


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Practical Use of the CAPM

It is helpful for finance manager has to keep in mind the expected return to the shareholdersand the returns he provides should be commensurate with the risk. This risk is reflected in his

investment and financing decision.

Used to price initial public offerings (IPOs)

Used to identify over and under value securities

Used to measure the riskiness of securities/companies

Used to measure the companys cost of capital. (The cost of capital is then used to evaluate

capital expansion proposals).

The model helps us understand the variables that can affect stock pricesand this guides

managerial decisions.

SML provides a benchmark reflecting the equilibrium position in the relationship between

the risk and return.


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Focuses on the Market Risk. Thus makes investors to think about riskiness of the

assets in general.

It has been useful in the selection of securities and portfolios. Securities withhigher returns are considered to be undervalued and attractive for buy. The below

normal expected return yielding securities are considered to be overvalued and

suitable for sale.

In the CAPM it has been assumed that investor consider only the market risk ,

Given the estimate of the risk free rate, the beta of the firm, stock and requiredmarket rate of return, one can find out the expected returns for the firms security.

This expected return can be used as an the cost of retained earnings.


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Conclusions: CAPM

It is called a pricing model because it can be used to help us determine appropriateprices for securities in the market.

The CAPM suggests that investors demand compensation for risks that they are

exposed toand these returns are built into the decision-making process to invest

or not.

The CAPM is a fundamental analysts tool to estimate the intrinsic value of a

stock.

The analyst needs to measure the beta risk of the firm by using either historical or

forecast risk and returns.

The analyst will then need a forecast for the risk-free rate as well as the expected

return on the market.

These three estimates will allow the analyst to calculate the required return that

rational investors should expect on such an investment given the other

benchmark returns available in the economy.


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Introduction Assumptions ArbitragePortfolio

The APT

model

Factorsaffecting the

return

Arbitage One

Factor Model

APT and CAPM


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Introduction

This model developed in asset pricing by Stephen Ross

Arbitrage pricing theory is one of the tools used by the investors and portfolio

managers.

The capital asset pricing theory explains the returns of the securities on the basis oftheir respective betas.

The investor chooses the investment on the basis of expected return and variance.

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Arbitrage: Meaning

Arbitrage is a process of earning profit by taking advantage of differential pricing

for the same asset. The process generates riskless profit.

In the security market , it is of selling security at a high price and the

simultaneous purchase of the same security at a relatively lower price.

The profit earned through arbitrage is riskless.

The buying and selling of the arbitrageur reduces and eliminates the profit

margin. Thus bringing the market price to the equilibrium level.


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For same risks

Asset U has higher return than Asset O

Asset U is underpriced and assets O is overpriced.

Sell asset O or go short on O

Buy asset U or go long on U

@Investor makes Riskless profit

Impact

Demand on asset U goes up and supply of O also goes up

@Price of U increases and price of O decreases

Thus, Arbitrage goes on till prices are traded at same level.

Arbitrage Mechanism

Arbitrage Pricing Theory


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Assumptions

The investors have homogeneous expectation.

The investors are risk averse and utility maximizes.

Perfect competition prevails in the market and there is no transaction cost.


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Arbitrage doesnt assume

Single period investment horizon.

No taxes

Investors can borrow and lend at risk free rate of interest.

The selection of the portfolio is based on the mean and variance analysis.


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Arbitrage Portfolio

According to the APT theory an investor tries to find out the possibility toincrease return from his portfolio without increasing the funds in theportfolio. He also likes to keep the risk at the same level.

For eg:-, the investor holds A, B and C securities and he wants to changethe proportion of the securities without any additional financial

commitment. Now the change in proportion of securities can be denotedby by XA , XB , and XC. The increase in the investment in security A could becarried out only if he reduces the proportion of investment either in B or Cbecause it has already stated that the investor tries to earn more incomewithout increasing his financial commitment.

Thus, the changes in different securities will add up to zero. This is thebasic requirement of an arbitrage portfolio.


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If X indicates the change in proportion,

XA+ XB+ XC=0

The factor sensitivity indicates the responsiveness of a securitys return to a

particular factor. The sensitiveness of the securities to any factor is the weighted

average of the sensitivities of the securities, weights being the changes made in

the proportion

For eg:-bA, bB, Bc are the sensitivities, in an arbitrage portfolio the sensitivities

become zero.

bA XA + bB XB + bC XC =0


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The APT model:

According to Stephen Ross, returns of the securities are influenced by a number of

macro economic factor.

The macro economic factors are:

Growth rate of industrial production,

Rate of inflation,

Spread between long term and short term interest rates and

Spread between low grade and high grade bonds.

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APT

Ri = P0 + P1 Fi1 + P2 Fi2 + P3 Fi3 + . + Pk Fik

Where,

Ri = Expected Return on asset i.e. on well diversified portfolio

P0 = Expected Return on asset with zero systematic risk

P1 = The risk premium related to each of the common factor e.g. the risk premium

related to interest rate risk.

Fij = the pricing relationship between the risk premium and asset i i.e. how

responsive asset i is to this common factor j i.e. sensitivity or beta coefficient

for security i that is associated with index j

Arbitrage Pricing Theory

The arbitrage theory is represented by the equation:


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If the portfolio is well diversified one, unsystematic risk tends

to be zero and systematic risk is represented by F 1 and F 2 F

n in the equation.


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Factors Affecting The Return

The specification of the factors is carried out by many financial analysts. Chen, Roll

and Ross have taken four macro economic variables and tested them. According tothem the factors are

Inflation,

Inflation affects the discount rate or the required rate of return and the size of the

future cash flows.

The term structure of interest rates,

Risk premia and

Industrial production.


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Burmeister and McElroy have estimated the sensitivities with some other factors. They

are

Default risk

Time premium

Deflation

Change in expected sales

The market return not due to the first four variables.


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The default risk is measured by the difference between the

return on long term government bonds and the return onlong term bonds issued by corporate plus one half of one %.

Time premium is measured by the return on long term

government bonds minus one month treasury bill rate one

month ahead.

Deflation is measured by expected inflation at the beginning

of the month minus actual inflation during the month.

Contn.


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Salomon Brothers identified 5 factors in their fundamental factor model.

Growth rate in gross national product

Rate of interest

Rate of change in oil prices

Rate of change in defence spending.


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Arbitrage Pricing TheoryONE FACTOR MODEL

Assume, there is only one factor which generates returns on asset i, APT Model boils down

to

E(ri) = Fio +FijP1

Fio = Risk Free Return or Zero Beta Security

Slope of arbitrage price line is P and intercept is Fio. The arbitrage price line shows the

equilibrium relation between an assets systematic risk and expected return.

In a single factor model, the linear relationship between the return Ri and

sensitivity bi can be given in the following form.

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The risk is measured along the horizontal axis and the return on the vertical axis.

The A, B and C stocks are considered to be in the same risk class. The arbitrage

pricing line interests the Y axis on lamda 0, which represents riskless rate of

interest i e the interest offered for the treasury bills. Here, the investments involve

zero risk and it is appealing to the investors who are highly risk averse.

Lamda i stands for the slope of arbitrage pricing line. It indicates market price of

risk and measures the risk return trade off in the security markets. The beta i is thesensitivity coefficient or factor beta that shows the sensitivity of the asset or stock

A to the respective risk factor.


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APT and CAPM


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In APT model, factors are not well specified . Hence investors finds it difficult to

establish equilibrium relationship.

The well defined market portfolio is a significant advantage of the CAPM leadingwide usage in the stock exchange.

Lack of consistency in the measurements of the APT model.

Further , the influence of factor are not independent to each other because it is

difficult to identify the influence that corresponds exactly to each factor.

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