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Empirical Applications of Capital Market Models

Empirical Applications of Capital Market Models. Lecture XXVII. 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. In the basic Sharpe-Lintner CAPM model.

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Empirical Applications of Capital Market Models

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  1. Empirical Applications of Capital Market Models Lecture XXVII

  2. 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.

  3. In the basic Sharpe-Lintner CAPM model

  4. 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

  5. Sharpe-Lintner Results

  6. Black’s 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

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

  8. Black’s Results

  9. Comparison of Betas

  10. Tests for CAPM Efficiency • Sharpe-Lintner Model

  11. Cross-Sectional Regression • Fama, E. and J. MacBeth “Risk, Return, and Equilibrium: Empirical Tests.” 71(1973): 607–36. • Using either set of betas, the question then becomes whether the expected returns are consistent with their betas.

  12. Cross-Sectional Results

  13. Two Tests • Sharpe-Lintner test of the constant • Betas explain the variations in expected returns

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

  15. Risk Premium for Agribusinesses

  16. 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:

  17. Rt is a vector of N asset returns • ft is a vector of k common factors • b is a N*k 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

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

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

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

  21. Factor Loadings

  22. Estimated Risk Premia

  23. Augmenting the model to test for disequilibria in the equity market for Agribusinesses

  24. Estimated Risk Premia

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