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CHAPTER TEN. THE CAPITAL ASSET PRICING MODEL. THE CAPM ASSUMPTIONS. NORMATIVE ASSUMPTIONS expected returns and standard deviation cover a one-period investor horizon nonsatiation risk averse investors assets are infinitely divisible risk free asset exists no taxes nor transaction costs.

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Chapter ten l.jpg

CHAPTER TEN

THE CAPITAL ASSET PRICING MODEL


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THE CAPM ASSUMPTIONS

  • NORMATIVE ASSUMPTIONS

    • expected returns and standard deviation cover a one-period investor horizon

    • nonsatiation

    • risk averse investors

    • assets are infinitely divisible

    • risk free asset exists

    • no taxes nor transaction costs


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THE CAPM ASSUMPTIONS

  • ADDITIONAL ASSUMPTIONS

    • one period investor horizon for all

    • risk free rate is the same for all

    • information is free and instantaneously available

    • homogeneous expectations


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THE CAPITAL MARKET LINE

  • THE CAPITAL MARKET LINE (CML)

    • the new efficient frontier that results from risk free lending and borrowing

    • both risk and return increase in a linear fashion along the CML


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THE CAPITAL MARKET LINE

CML

THE CAPITAL MARKET LINE

rP

M

rfr

sP


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THE CAPITAL MARKET LINE

  • THE SEPARATION THEOREM

    • James Tobin identifies:

      • the division between the investment decision and the financing decision


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THE CAPITAL MARKET LINE

  • THE SEPARATION THEOREM

    • to be somewhere on the CML, the investor initially

      • decides to invest and

      • based on risk preferences makes a separate financing decision either

        • to borrow or

        • to lend


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THE MARKET PORTFOLIO

  • DEFINITION: the portfolio of all risky assets which contains

    • complete diversification

    • a central role in the CAPM theory which is the tangency portfolio (M) with the CML


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THE SECURITY MARKET LINE (SML)

  • FOR AN INDIVIDUAL RISKY ASSET

    • the relevant risk measure is its covariance with the market portfolio (si, M)

    • DEFINITION: the security market line expresses the linear relationship between

      • the expected returns on a risky asset and

      • its covariance with the market returns


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THE SECURITY MARKET LINE (SML)

  • THE SECURITY MARKET LINE

    or

    where


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THE SECURITY MARKET LINE (SML)

  • THE SECURITY MARKET LINE

    • THE BETA COEFFICIENT

      • an alternative way to represent the covariance of a security


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THE SECURITY MARKET LINE (SML)

  • THE SECURITY MARKET LINE

    • THE BETA COEFFICIENT

      • of a portfolio

        • is the weighted average of the betas of its component securities


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THE SECURITY MARKET LINE (SML)

THE SECURITY MARKET LINE

SML

E(r)

rM

rrf

b

b =1.0


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THE MARKET MODEL

  • FROM CHAPTER 7

    • assumed return on a risky asset was related to the return on a market index


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THE MARKET MODEL

  • DIFFERENCES WITH THE CAPM

    • the market model is a single-factor model

    • the market model is not an equilibrium model like the CAPM

    • the market model uses a market index,

    • the CAPM uses the market portfolio


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THE MARKET MODEL

  • MARKET INDICES

    • the most widely used and known are

      • S&P 500

      • NYSE COMPOSITE

      • AMEX COMPOSITE

      • RUSSELL 3000

      • WILSHIRE 5000

      • DJIA


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THE MARKET MODEL

  • MARKET AND NON-MARKET RISK

    • Recall that a security’s total risk may be expressed as


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THE MARKET MODEL

  • MARKET AND NON-MARKET RISK

    • according to the CAPM

      • the relationship is identical except the market portfolio is involved instead of the market index


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THE MARKET MODEL

  • MARKET AND NON-MARKET RISK

    • Why partition risk?

      • market risk

        • related to the risk of the market portfolio and to the beta of the risky asset

        • risky assets with large betas require larger amounts of market risk

        • larger betas mean larger returns


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THE MARKET MODEL

  • MARKET AND NON-MARKET RISK

    • Why partition risk?

      • non-market risk

        • not related to beta

        • risky assets with larger amounts of seIwill not have larger E(r)

      • According to CAPM

        • investors are rewarded for bearing market risk not non-market risk