Capital%20Asset%20Pricing%20Model

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Capital Asset Pricing Model
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Introduction

• The CAPM was developed in the mid 1960s by three
  researchers William Sharp, John Linter and Jan
  Mossin independently.
• CAPM is really the extension of Markowitz
  Portfolio theory.
• The PT is a description how a rational investor
  should build efficient portfolio and select the
  optimal portfolio.
• The CAPM derives the relationship btw the
  expected return and risk of individual securities
  and portfolios in the capital market if every
  one behaved in the way the PT suggest.

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Fundamental notions of PT.

• Risk and return are two important characteristics
  of every investment.
• Risk is measured by the variability in returns
  and investors attempt to reduce the variability
  of returns through diversification of
  investments.
• With a given set of securities, any number of
  portfolios may be created by altering the weight
  of investment in each security.
• Diversification help to reduce risk, but a well
  diversified portfolio does not become risk free.
• Portfolio M is the most diversified portfolio.
• Some variabilities are undiversified e.g
  systematic risk.
• The real risk of a portfolio is the market risk
  which cant be eliminated through
  diversification.
• A rational investor would expect the return on a
  security to be commensurate with the risk.
• The CAPM gives the nature of the relationship btw
  the expected return and the systematic risk of a
  security.

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Assumptions of CAPM

• Investors make their investment decisions on the
  basis of risk- return analysis.
• The purchase and sale of a security can be
  undertaken in infinitely divisible units.
• Purchase and sale by a single investor can not
  effect the prices.
• There is no transaction cost.
• There is no personal income taxes.
• The investor can lend and borrow any amount of
  funds at risk free rate.
• The investor can sell short any amount of any
  share.
• The investors share the homogeneity of
  expectations from the market.

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Efficient frontier with riskless lending and
borrowing.

• The PT deals with the portfolio of risky assets.
• According to the theory, an investor faces an
  efficient frontier containing the set of
  efficient portfolios of risky assts.
• Now it is assumed that there is a riskless asset
  available in the market.
• A riskless asset is one whose return is certain
  e.g. T-bills.
• The investor can invest a certain portion of his
  investment in the riskless assets which would be
  equivalent to lending at the risk free assets
  rate of return namely Rf.

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Efficient frontier with riskless lending and
borrowing

• Similarly it may be assumed that an investor may
  borrow at the risk free rate for the purpose of
  investing in a portfolio of risky assets.
• The EF arises from a feasible set of portfolios
  of risky assets is concave in shape.
• When an investor is assumed to use riskless
  lending and borrowing in his investment activity
  the shape of the EF transforms into a straight
  line.
• Let see the example of portfolio A, B and C.

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Efficient frontier with riskless lending and
borrowing

• Portfolio B is and optimal portfolio with Rp15,
  sp 8 Rf 7 ? 40 in risk free asset and 60
  is risky asset.
• Rc ?Rm (1-?)Rf
• sc ?sm (1-?) sf
• sc ?sm
• Now for borrowing funds by the investor
• ? 1 the investors funds is fully committed to
  the risky portfolio.
• ? lt 1, only a portion of the funds is invested in
  the risky portfolio.
• ? gt 1, it means the investor is borrowing at the
  risk free rate and investing an amount larger
  than his own investments in the risky portfolio.

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Efficient frontier with riskless lending and
borrowing

• Rc ?Rm - (?-1)Rf
• The first term of the equation represents the
  gross return earned by investing the borrowed
  funds as well as investors own funds in the
  risky portfolio.
• The second term of the equation represents the
  const of borrowing funds which is deducted from
  the gross return to obtain the net return of
  levered portfolio.
• sl ?sm

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Efficient frontier with riskless lending and
borrowing

• The return and risk of the levered portfolio are
  larger than those of risky portfolio.
• The risk return of all levered portfolios would
  lie in a straight line to the right of the risky
  portfolio B.
• So the introduction of borrowing and lending
  gives us an efficient frontier that is a straight
  line through line.
• The line segment from Rf to B includes all the
  combinations of the risky portfolios and the risk
  free assets.
• The line segment beyond the point B represents
  all the levered portfolios ( that is combinations
  of the risky portfolio with borrowing)
• Borrowing increase risk and return and lending
  reduces the risk and return of the portfolio.
• Thus the investor can use the borrowing and
  lending the attain the desired level of risk.
• More risk aversor well prefer lending and less
  risk aversor well prefer borrowing.

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Capital Market Line

• All investors are assumed to have identical
  expectations.
• Every investor will seek to combine the same
  risky portfolio B with different levels of
  lending or borrowing according to his desired
  level of risk.
• Because all investors hold the same risky
  portfolio, then it will include all risky
  securities in the market.
• This known as market portfolio M.
• Each security will be held in the proportion
  which the market value of the security bears to
  the total market value of all risky securities in
  the market.
• All investors will hold combination of only two
  assets, Market portfolio and a riskless security.

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CML

• All the combination will lie along the straight
  line representing the EF.
• This line is formed by the action all investors
  mixing the market portfolio with the risk free
  asset is known as the CML.
• Re Rf (Rm Rf)/sm se
• Where the subscript e denotes an efficient
  portfolio.
• The risk free return Rf represents the reward for
  waiting. In the other words the price of time.
• The term (Rm Rf)/sm represents the price of
  risk or risk premium.

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CML

• When the risk of the Efficient Portfolio se
• is multiplied with this term, we get the risk
  premium available for the particular efficient
  portfolio under consideration.
• (Expected return) (Price of time) (Price of
  risk) ( Amount of risk)
• So the CML provides the risk return relationship
  and a measure of risk for efficient portfolio.

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Security market line

• The CML shows the risk and return relationship
  and would all lie along the capital market line.
• All portfolios other than the efficient ones will
  lie below the capital market line.
• The CAPM specifies the relationship between
  expected return and risk for all securities and
  all portfolios, whether efficient or inefficient.
• Only relevant risk is systematic risk measure by
  beta ß.
• It follows that the expected return of a security
  or of a portfolio should be related to the risk
  of that security or portfolio measured by ß.
• ß is the measure of sensitivity of the security
  to changes in the market.
• ß of the market is one.
• The relationship between the expected return and
  ß can be determined graphically.
• The straight line joining these two points is as
  SML.

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Security market line

• Mathematically this relationship can be written
  as
• Ri Rf ßi(Rm Rf)
• The risk premium is directly proportional the ß.
• Expected return on a security risk free rate
  ( beta x risk premium of market)

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CAPM

• A model that describes the relationship between
  risk and expected return and that is used in the
  pricing of risky securities.
•  
• The general idea behind CAPM is that investors
  need to be compensated in two ways time value of
  money and risk. The time value of money is
  represented by the risk-free (rf) rate in the
  formula and compensates the investors for placing
  money in any investment over a period of time.
  The other half of the formula represents risk and
  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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Short Comings of CAPM

• The model assumes that either asset returns are
  (jointly) normally distributed random variables
  or that investors employ a quadratic form of
  utility. It is however frequently observed that
  returns in equity and other markets are not
  normally distributed. As a result, large swings
  (3 to 6 standard deviations from the mean) occur
  in the market more frequently than the normal
  distribution assumption would expect.3
• The model assumes that the variance of returns is
  an adequate measurement of risk. This might be
  justified under the assumption of normally
  distributed returns, but for general return
  distributions other risk measures (like coherent
  risk measures) will likely reflect the investors'
  preferences more adequately. Indeed risk in
  financial investments is not variance in itself,
  rather it is the probability of losing it is
  asymmetric in nature.
• The model assumes that all investors have access
  to the same information and agree about the risk
  and expected return of all assets (homogeneous
  expectations assumption).
• The model assumes that the probability beliefs of
  investors match the true distribution of returns.
  A different possibility is that investors'
  expectations are biased, causing market prices to
  be informationally inefficient. This possibility
  is studied in the field of behavioral finance,
  which uses psychological assumptions to provide
  alternatives to the CAPM such as the
  overconfidence-based asset pricing model of Kent
  Daniel, David Hirshleifer, and Avanidhar
  Subrahmanyam (2001)4.
• The model does not appear to adequately explain
  the variation in stock returns. Empirical studies
  show that low beta stocks may offer higher
  returns than the model would predict. Some data
  to this effect was presented as early as a 1969
  conference in Buffalo, New York in a paper by
  Fischer Black, Michael Jensen, and Myron Scholes.
  Either that fact is itself rational (which saves
  the efficient-market hypothesis but makes CAPM
  wrong), or it is irrational (which saves CAPM,
  but makes the EMH wrong indeed, this
  possibility makes volatility arbitrage a strategy
  for reliably beating the market).

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Short Comings of CAPM

• The model assumes that given a certain expected
  return investors will prefer lower risk (lower
  variance) to higher risk and conversely given a
  certain level of risk will prefer higher returns
  to lower ones. It does not allow for investors
  who will accept lower returns for higher risk.
  Casino gamblers clearly pay for risk, and it is
  possible that some stock traders will pay for
  risk as well
• The model assumes that there are no taxes or
  transaction costs, although this assumption may
  be relaxed with more complicated versions of the
  model
• The market portfolio consists of all assets in
  all markets, where each asset is weighted by its
  market capitalization. This assumes no preference
  between markets and assets for individual
  investors, and that investors choose assets
  solely as a function of their risk-return
  profile. It also assumes that all assets are
  infinitely divisible as to the amount which may
  be held or transacted
• The market portfolio should in theory include all
  types of assets that are held by anyone as an
  investment (including works of art, real estate,
  human capital...) In practice, such a market
  portfolio is unobservable and people usually
  substitute a stock index as a proxy for the true
  market portfolio. Unfortunately, it has been
  shown that this substitution is not innocuous and
  can lead to false inferences as to the validity
  of the CAPM, and it has been said that due to the
  inobservability of the true market portfolio, the
  CAPM might not be empirically testable. This was
  presented in greater depth in a paper by Richard
  Roll in 1977, and is generally referred to as
  Roll's critique

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Short Comings of CAPM

• The model assumes just two dates, so that there
  is no opportunity to consume and rebalance
  portfolios repeatedly over time. The basic
  insights of the model are extended and
  generalized in the intertemporal CAPM (ICAPM) of
  Robert Merton, and the consumption CAPM (CCAPM)
  of Douglas Breeden and Mark Rubinstein.
• CAPM assumes that all investors will consider all
  of their assets and optimize one portfolio. This
  is in sharp contradiction with portfolios that
  are held by individual investors humans tend to
  have fragmented portfolios or, rather, multiple
  portfolios for each goal one portfolio

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SML Vs CML

• 1. The CML is a line that is used to show the
  rates of return, which depends on risk-free rates
  of return and levels of risk for a specific
  portfolio. SML, which is also called a
  Characteristic Line, is a graphical
  representation of the markets risk and return at
  a given time.
• 2. While standard deviation is the measure of
  risk in CML, Beta coefficient determines the risk
  factors of the SML.
• 3. While the Capital Market Line graphs define
  efficient portfolios, the Security Market Line
  graphs define both efficient and non-efficient
  portfolios.
• 4. The Capital Market Line is considered to be
  superior when measuring the risk factors.
• 5. Where the market portfolio and risk free
  assets are determined by the CML, all security
  factors are determined by the SML.

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Pricing of Securities with CAPM

• The CAPM provides a framework for assessing
  whether the a security is under priced,
  overpriced or correctly priced.
• Under priced when the estimated return is more
  than the expected return.
• Over priced when the estimated return is less
  than the expected return.
• Correctly price when the estimated return is
  equal to expected retun.