Empirical Applications of Capital Market Models

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Empirical Applications of Capital Market Models

• Lecture XXVII

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Capital Asset Pricing Models

• A basic question that must be addressed in the
  application of both CAPM and APT models is
  whether a risk-free asset exists.

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• In the basic Sharpe-Lintner CAPM model

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• Constructing a dataset of 43 stocks from the
  Center for Research into Security Prices (CRSP)
  dataset, using the return on the Standard and
  Poors 500 portfolio and using the 3 month
  treasury bill as the market portfolio

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Sharpe-Lintner Results
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Blacks Model

• An alternative to the model presented by Sharpe
  and Lintner is the zero-beta model suggested by
  Black
• where R0m is the return on the zero-beta
  portfolio, or the minimum variance portfolio that
  is uncorrelated with the market portfolio

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• However, the model can be estimated assuming that
  the zero-beta return is unobserved as
• Which yields the empirical model

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Blacks Results
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Comparison of Betas
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Tests for CAPM Efficiency

• Sharpe-Lintner Model

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Cross-Sectional Regression

• Fama, E. and J. MacBeth Risk, Return, and
  Equilibrium Empirical Tests. 71(1973) 60736.
• Using either set of betas, the question then
  becomes whether the expected returns are
  consistent with their betas.

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Cross-Sectional Results
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• Two Tests
• Sharpe-Lintner test of the constant
• Betas explain the variations in expected returns

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• A little reformulation
• where Di is a dummy variable which is equal to
  one if the stock is an agribusiness stock and
  zero otherwise

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Risk Premium for Agribusinesses
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Arbitrage Pricing Model

• As we discussed in previous lectures, the returns
  in the arbitrage pricing model are assumed to be
  determined by a linear factor model

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• Rt is a vector of N asset returns
• ft is a vector of k common factors
• b is a Nk matrix of factor loadings
• The arbitrage pricing equilibrium implies that
  the expected return on the vector of assets is a
  linear function of the factor loadings

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• Two ways to define the common factors
• Endogenously based on returns
• Exogenously based on macroeconomic variables

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• Given the linear factor model above, the variance
  matrix for the returns on the vector of assets
  becomes
• where ? is a diagonal matrix.

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• Under this specification, we can estimate the
  vector of factor loadings by maximizing

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Factor Loadings
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Estimated Risk Premia
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• Augmenting the model to test for disequilibria in
  the equity market for Agribusinesses

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Estimated Risk Premia