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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
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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