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Empirical Financial Economics

Empirical Financial Economics. New developments in asset pricing. Where does m come from?. Stein’s lemma If the vector f t+1 and r t+1 are jointly Normal. Modeling m directly. Typically assume power utility Equity Premium Puzzle: Habit persistence: These models imply

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Empirical Financial Economics

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  1. Empirical Financial Economics New developments in asset pricing

  2. Where does m come from? • Stein’s lemma • If the vector ft+1and rt+1 are jointly Normal

  3. Modeling mdirectly • Typically assume power utility • Equity Premium Puzzle: • Habit persistence: • These models imply • Lettau and Ludvigson (2001)

  4. Multivariate Asset Pricing • Consider • Unconditional means are given by • Model for observations is • Shanken result: Shanken, J., 1987, Multivariate proxies and asset pricing relations: Living with the Roll critique Journal of Financial Economics 18, 91-110.

  5. McElroy and Burmeister • Consider • Unconditional means are given by • Model for observations is • Can estimate this model using NLSUR, GMM McElroy, M., and E. Burmeister, 1988, Arbitrage pricing theory as a restricted nonlinear regression model Journal of Business and Economic Statistics 6(1), 29-42.

  6. Black, Jensen and Scholes Jensen, Michael C. and Black, Fischer and Scholes, Myron S., The Capital Asset Pricing Model: Some Empirical Tests. Michael C. Jensen, STUDIES IN THE THEORY OF CAPITAL MARKETS, Praeger Publishers Inc., 1972. Available at SSRN: http://ssrn.com/abstract=908569

  7. Fama and MacBeth procedure 30 10 15 20 25 0 5 t

  8. Fama and MacBeth procedure 30 10 15 20 25 0 5 t

  9. Fama and MacBeth procedure 30 10 15 20 25 0 5 t

  10. Attributes of two pass procedure • Use portfolio returns • Lintner (1968) used individual securities • Black, Jensen and Scholes (1972) used portfolios • Fama and MacBeth (1973) used portfolios out of sample • Motivated by concern about errors in variables • Inference uses time series of cross section estimates • Use of Ordinary Least Squares in second pass

  11. The Likelihood Function

  12. The market model regression

  13. The Fama MacBeth cross section regression

  14. Updating market model

  15. Full Information Maximum Likelihood

  16. Modeling mdirectly • Typically assume power utility • Equity Premium Puzzle: • Habit persistence: • These models imply • Lettau and Ludvigson (2001)

  17. The geometry of mean variance

  18. OLS or GLS? • Out of sample cross section regression • Regress average excess returns against factor loadings • Estimate expected excess returns so • The covariance matrix of is proportional to • OLS: Estimate • GLS: Estimate • Can use GLS R2 for non-nested model comparison

  19. Lewellan, Nagel and Shanken (2010) Results Lewellen, Jonathan, Sefan Nagel and Jay Shanken 2010 A skeptical appraisal of asset pricing tests Journal of Financial Economics 96, 175-194.

  20. Choice among alternative benchmarks • Disenchantment with empirical asset pricing models • Fallen out of favor in corporate finance and other applications • Growing popularity of firm characteristics and industry controls • Limited theoretical or empirical support • These controls can be interpreted in a risk-class framework • Approach has a sound asset pricing justification • New results in asset pricing literature provide basis for a horserace • Strong asset pricing justification for industry controls Brown, Stephen J. and Handley, John C. and Lajbcygier, Paul, Choice Among Alternative Benchmarks: An Asset Pricing Approach (April 17, 2014). Available at SSRN: http://ssrn.com/abstract=2426277

  21. Modigliani and Miller Risk Classes • An asset pricing rationale for MM risk classes: "This process of understanding how the economy allows investors to duplicate the risky return of any individual company should be understood as an expansion of the original MM notion of a risk class. The "risk class" played an important role in the original arbitrage analysis, as Miller explains, but it has subsequently passed from favor. However, I think that it might be time for a revival of a modern perspective on the older views. This is particularly so given the sorry empirical state of our asset pricing theories". Ross, Stephen A., 1988. “Comment on the Modigliani–Miller propositions” Journal of Economic Perspectives, 2 pp.127–133.

  22. Risk classes • Risk classes imply model for the observations • Consistent with a broad class of asset pricing models • Justifies use of risk class benchmarks • How should we determine affiliation ? • Factor sensitivity? (Fama and French 1992) • Financial characteristics? (Daniel & Titman 1997) • Industrial affiliation? (Modigliani and Miller 1958) • Basis assets? (Conrad Ahn and Dittmar 2009)

  23. Basis Asset Approach • Consider the following model for the observations • Membership classes are ‘basis assets’ (Conrad et al 2007) • Corresponds to k-means model (Hartigan 1975) • Modified Hartigan procedure • Use daily data for a calendar year • Start with an initial allocation to risk classes • Iteratively reassign securities to minimize sum of squares (SS) • Allow for clustering by date and security (Brown and Goetzmann 1997)

  24. The horse race Factor loadings Characteristics Industries Basis Assets

  25. The horse race • For every year 1980 – 2010 • Determine the category membership in prior year • Regress excess returns against category membership • Compare models on basis of resulting R2 • A valid non-nested model comparison

  26. Attributes of our procedure • Use individual security returns, not portfolios • No concern about errors in variables • Regress on category membership, not factor loadings • Inference uses time series of cross section estimates • Use of Generalized Least Squares in second pass

  27. Generalized Least Squares? • Sample covariance matrix is singular for • Is GLS infeasible for individual security regressions? • k-factor covariance matrix is nonsingular for • is a better estimator of than is (Fan et al. 2008) • is simple to compute: for

  28. Individual security characteristics do not beat risk factor loadings -- OLS

  29. Individual security characteristics DO beat risk factor loadings -- GLS

  30. Out of sample cross section regression results

  31. Out of sample cross section regression results

  32. Out of sample cross section regression results

  33. Out of sample cross section regression results

  34. Out of sample cross section regression results

  35. Out of sample cross section regression results

  36. Out of sample cross section regression results

  37. Kruskal Tau Average Value

  38. Theil U Average Value

  39. Conclusion • Firm specific characteristics commonly used in matched samples • Can be interpreted as basis assets • Approach consistent with many asset pricing models • Can be applied on an individual security basis • Out of sample, industry classifications explain returns • Superior to risk factor or firm characteristics-based methods • Simpler to apply than empirically estimating basis assets • Easy to interpret • More stable than other classification schemes • Strong endorsement of MM (1958) risk class conjecture

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