Investment Analysis 107 August 2011
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Investment Analysis 107 August 2011



primer for asset managers

primer for asset managers



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Investment Analysis 107 August 2011 Investment Analysis 107 August 2011 Presentation Transcript

  • Investment Analysis and Portfolio Management August 2011 MCR
  • 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 (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
  • Assumptions
    • 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
  • Assumptions
      • 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
  • Assumptions
    • 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
    • All investors face the same efficient set of portfolios
  • 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
    • 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
  • Equilibrium
    • 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
    • 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
    • All efficient portfolios must lie on this line
    • Slope =
    • Equation of the line
  • Interpretation
    • r f 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
    • 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 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 Line
    • D efine
    • The equation of the line becomes
    • This is the security market line (SML)
  • 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 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 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
    • Use the regression equation
    • Take the expected value
    • The security market line implies
    • It also shows
  • CAPM and Pricing
    • CAPM also implies the equilibrium asset prices
    • The security market line is
    • But
    • where p i (0) is the value of the asset at time 0 and p i (1) is the value at time 1
  • 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
    • 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 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 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 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