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Investment Analysis and Portfolio Management. Lecture 7 Gareth Myles. The Capital Asset Pricing Model (CAPM). The CAPM is a model of equilibrium in the market for securities.

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the capital asset pricing model capm
The Capital Asset Pricing Model (CAPM)
  • The CAPM is a model of equilibrium in the market for securities.
  • Previous lectures have addressed the question of how investors should choose assets given the observed structure of returns.
  • Now the question is changed to:
    • If investors follow these strategies, how will returns be determined in equilibrium?
the capital asset pricing model capm3
The Capital Asset Pricing Model (CAPM)
  • The simplest and most fundamental model of equilibrium in the security market
    • Builds on the Markowitz model of portfolio choice
    • Aggregates the choices of individual investors
  • Trading ensures an equilibrium where returns adjust so that the demand and supply of assets are equal
  • Many modifications/extensions can be made
    • But basic insights always extend
  • The CAPM is built on a set of assumptions
  • Individual investors
    • Investors evaluate portfolios by the mean and variance of returns over a one period horizon
    • Preferences satisfy non-satiation
    • Investors are risk averse
  • Trading conditions
    • Assets are infinitely divisible
    • Borrowing and lending can be undertaken at the risk-free rate of return
    • There are no taxes or transactions costs
    • The risk-free rate is the same for all
    • Information flows perfectly
  • The set of investors
    • All investors have the same time horizon
    • Investors have identical expectations
  • The first six assumptions are the Markowitz model
  • The seventh and eighth assumptions add a perfect capital market and perfect information
  • The final two assumptions make all investors identical except for their degree of risk aversion
direct implications
Direct Implications
  • All investors face the same efficient set of portfolios
direct implications8
Direct Implications
  • All investors choose a location on the efficient frontier
  • The location depends on the degree of risk aversion
  • The chosen portfolio mixes the risk-free asset and portfolio M of risky assets
separation theorem
Separation Theorem
  • The optimal combination of risky assets is determined without knowledge of preferences
    • All choose portfolio M
    • This is the Separation Theorem
  • M must be the market portfolio of risky assets
    • All investors hold it to a greater or lesser extent
    • No other portfolio of risky assets is held
    • There is a question about the interpretation of this portfolio
  • The only assets that need to be marketed are:
    • The risk-free asset
    • A mutual fund representing the market portfolio
    • No other assets are required
  • In equilibrium there can be no short sales of the risky assets
    • All investors buy the same risky assets
    • No-one can be short since all would be short
    • If all are short the market is not in equilibrium
  • Equilibrium occurs when the demand for assets matches the supply
    • This also applies to the risk-free
    • Borrowing must equal lending
  • This is achieved by the adjustment of asset prices
  • As prices change so do the returns on the assets
  • This process generates an equilibrium structure of returns
the capital market line
The Capital Market Line
  • All efficient portfolios must lie on this line
  • Slope =
  • Equation of the line
  • rf is the reward for "time"
    • Patience is rewarded
    • Investment delays consumption
  • is the reward for accepting "risk"
    • The market price of risk
    • Judged to be equilibrium reward
    • Obtained by matching demand to supply
security market line
Security Market Line
  • Now consider the implications for individual assets
  • Graph covariance against return
    • The risk on the market portfolio is
    • The covariance of the risk-free asset is zero
    • The covariance of the market with the market is
security market line15
Security Market Line
  • Can mix M and the risk-free asset along the line
    • If there was a portfolio above the line all investors would buy it
    • No investor would hold one below
  • The equation of the line is


security market line16
Security Market Line
  • Define
  • The equation of the line becomes
  • This is the security market line (SML)
security market line17
Security Market Line
  • There is a linear trade-off between risk measured by and return
  • In equilibrium all assets and portfolios must have risk-return combinations that lie on this line
market model and capm
Market Model and CAPM
  • Market model uses
  • CAPM uses
  • is derived from an assumption about the determination of returns
    • it is derived from a statistical model
    • the index is chosen not specified by any underlying analysis
  • is derived from an equilibrium theory
market model and capm19
Market Model and CAPM
  • In addition:
    • I is usually assumed to be the market index, but in principal could be any index
    • M is always the market portfolio
  • There is a difference between these
  • But they are often used interchangeably
  • The market index is taken as an approximation of the market portfolio
estimation of capm
Estimation of CAPM
  • Use the regression equation
  • Take the expected value
  • The security market line implies
  • It also shows
capm and pricing
CAPM and Pricing
  • CAPM also implies the equilibrium asset prices
  • The security market line is
  • But

where pi(0) is the value of the asset at time 0 and pi(1) is the value at time 1

capm and pricing22
CAPM and Pricing
  • So the security market line gives
  • This can be rearranged to find
  • The price today is related to the expected value at the end of the holding period
capm and project appraisal
CAPM and Project Appraisal
  • Consider an investment project
  • It requires an investment of p(0) today
  • It provides a payment of p(1) in a year
  • Should the project be undertaken?
  • The answer is yes if the present discounted value (PDV) of the project is positive
capm and project appraisal24
CAPM and Project Appraisal
  • If both p(0) and p(1) are certain then the risk-free interest rate is used to discount
  • The PDV is
  • The decision is to accept project if
capm and project appraisal25
CAPM and Project Appraisal
  • Now assume p(1) is uncertain
  • Cannot simply discount at risk-free rate if investors are risk averse
  • For example using

will over-value the project

  • With risk aversion the project is worth less than its expected return
capm and project appraisal26
CAPM and Project Appraisal
  • One method to obtain the correct value is to adjust the rate of discount to reflect risk
  • But by how much?
  • The CAPM pricing rule gives the answer
  • The correct PDV of the project is