Money, Banking

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Money, Banking FinanceLecture 5

• The Capital Asset Pricing Model CAPM

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Aims

• Analyse the determinants of the equilibrium
  expected return on an individual security.
• To show how the risk premium on an asset is
  determined.
• Explain the capital asset pricing model.
• Show that the riskiness of an individual asset is
  given by its beta.

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The Capital Market Line

• Assume once again that the investor can borrow
  and lend at the same rate.
• The transformation line that is tangential to the
  efficient set is the capital market line CML
• This defines the single composition of risky
  assets the investor wants to hold. This is called
  the market portfolio M
• The CML is the transformation line that is
  tangential to the efficient frontier.

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CML

• The market portfolio represents the point on the
  efficient frontier which maximises the slope of
  the CML.
• The optimal proportions of risky assets at M
  maximise expected return E(Rm)-Rf.
• If all investors are at M then they earn the same
  excess return per unit of risk.
• The slope of the CML represents the market price
  of risk.

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Capital Market Line

• The CML provided a linear relation between
  expected return and risk that describes the
  proportion of a risk-free asset and an efficient
  portfolio of assets (market portfolio) that an
  investor can hold.
• The same basic function can be used to derive an
  expression for the expected return on an
  inefficient investment other than the market
  portfolio.
• Or indeed for a single stock

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Individual stock return

• At the Market portfolio M all the risky assets
  are held in the optimal proportions by all
  investors. This represents a market equilibrium.
• Since all n assets are held at M, there is a
  set of expected returns E(Ri) corresponding to
  point M on the efficient frontier.
• The equation representing the equilibrium returns
  for asset i recognises that when held as part
  of a wider portfolio it could reduce the risk of
  the total portfolio depending on the covariance.
• The riskiness of asset i when considered as
  part of a diversified portfolio is not its own
  variance but the covariance between Ri and the
  market return Rm.

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CML and the market portfolio
CML
E(Rp)
M
E(Rm)
E(Rm)-Rf
Rf
a
sm
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Slope of CML
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So to recap - The Capital Market Line

• The transformation line that is tangential to the
  efficient set and has intercept at the risk-free
  rate Rf is the capital market line CML
• This defines the single composition of risky
  assets the investor wants to hold. This is called
  the market portfolio M
• The CML is the transformation line that is
  tangential to the efficient frontier.

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CML and SML

• CML E(Rp) Rf ?sp, where ? is the slope.
• Interpretation of the CML is that it represents
  the return available to an investor with no risk
  or the additional return that can be expected as
  a reward for holding the investments risk this
  is ?sp and is known as the risk premium.
• The risk premium is the product of the market
  price of risk ? and the amount of risk taken
  given by sp.
• The amount of market risk at M is sM

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SML

• The SML is similar to the CML.
• The individual expected return of a share
  consists of 2 elements. The risk-free return and
  a risk premium.
• The risk premium for an individual share is not
  the product of the market price of risk ? and the
  risk of the share si but the covariance
  relationship between the share and the market
  portfolio which is defined by - Beta

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Beta

• Beta represents an assets systematic (market or
  non-diversifiable) risk
• The CAPM at the point M on the efficient
  frontier gives the risk adjusted equilibrium
  return on asset i
• E(Ri) Rf ßiE(Rm) Rf
• ßi Cov(Ri,Rm)/s2m
• The risk premium is ßiE(Rm) Rf and represents
  the reward for taking risk above that of the
  risk-free rate

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Deriving the SML

• The covariance between the returns of an
  individual share return and the market return
  will tell us how much the inclusion of that asset
  in the portfolio will reduce the risk on the
  portfolio as a whole.
• To derive the SML let us look at a 2-asset
  portfolio an asset A and the market M
• E(Rp) ?E(RA) (1 ?)E(Rm)

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Two-asset portfolio
E(Rp)
CML
E(Rm)
M
Rf
A
sp
sm
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The expected return from a marginal investment in
the inefficient portfolio is
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The marginal risk produced by a marginal
investment in A is
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At the point M ?0
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Tangent at point M on the frontier AM is
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The CML is also tangent to frontier at M. So
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Security Market Line
E(Rp)
SML
E(Rm)
Rf
ß
1
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Interpreting Beta
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Beta

• The numerator represents the systematic risk of
  asset A
• The denominator represents the total risk of the
  market portfolio
• Beta is an index of the amount of share As
  systematic risk relative to the market portfolio
• The beta value will tell us how much the expected
  return on a share should rise or fall relative to
  the market.

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If the expected return on the market rises by 10

• E(Ri) will rise gt 10 if ß gt 1
• E(Ri) will rise lt 10 if ß lt 1
• E(Ri) will rise 10 if ß 1
• Higher beta shares will outperform the market in
  a bull run and lower beta shares will
  under-perform
• Conversely high beta shares will fall faster in a
  bear market.

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Measurement of beta

• Plot the risk premium of the asset against the
  risk premium of the market slope is beta
• Regress risk premium of the asset against the
  risk premium of the market beta is the
  regression coefficient
• (Ri Rf) ai ßi(Rm Rf) ui ai 0
• ai 0 means that when the market risk premium is
  zero so should the individual shares that make up
  the portfolio have zero risk premium.
• So what if ai ? 0?

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Alpha

• Over a long period alpha values should be zero.
• But if not it can used to provide investor
  advice.
• ai lt 0 shares should be sold and ai gt 0 should be
  bought. Meaning share price of i is mispriced.
• Negative alpha means that returns are below the
  equilibrium predicted by the CAPM, therefore
  share prices will fall until yields rise to the
  equilibrium. The act of selling will drive down
  the price.
• Vice versa for positive alpha

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Summary

• We have examined the CAPM framework
• The CAPM is used to measure the systematic risk
  of an individual share.
• The beta value measures the degree of
  responsiveness of the expected return on the
  share relative to movements in the expected
  return of the market.
• Alpha is interpreted as an indication of
  mispricing and has been used as justification for
  investment strategy