Empirical Financial Economics - New York Universitypeople.stern.nyu.edu/sbrown/NIPE/Lecture...
Transcript of Empirical Financial Economics - New York Universitypeople.stern.nyu.edu/sbrown/NIPE/Lecture...
Empirical Financial Economics
New developments in asset pricing
Where does m come from?
Stein’s lemmaIf the vector ft+1 and rt+1 are jointly Normal
Modeling m directly
Typically assume power utility
Equity Premium Puzzle:
Habit persistence:
These models imply
Lettau and Ludvigson (2001)
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.
McElroy and Burmeister
Consider
Unconditional means are given by
Model for observations is
Can estimate this model using NLSUR, GMMMcElroy, M., and E. Burmeister, 1988, Arbitrage pricing theory as a restricted nonlinear
regression model Journal of Business and Economic Statistics 6(1), 29-42.
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
Fama and MacBeth procedure
0 5 10 15 20 25 30 t
Fama and MacBeth procedure
0 5 10 15 20 25 30 t
Fama and MacBeth procedure
0 5 10 15 20 25 30 t
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
The Likelihood Function
The market model regression
The Fama MacBeth cross section regression
Updating market model
Full Information Maximum Likelihood
Modeling m directly
Typically assume power utility
Equity Premium Puzzle:
Habit persistence:
These models imply
Lettau and Ludvigson (2001)
The geometry of mean variance
OLS or GLS? Out of sample cross section regression Regress average excess returns against factor loadingsEstimate expected excess returns soThe covariance matrix of is proportional to
OLS: Estimate
GLS: Estimate
Can use GLS R2 for non-nested model comparison
Lewellan, Nagel and Shanken (2010) Results
Empirical Asset Pricing Model FF 25 Size - B/M portfolios
FF 25 plus 30 industry portfolios
Data from 1963-2004 k OLS R2 GLS R2 OLS R2 GLS R2
CAPM 2 3% 1% 2% 0%
Consumption CAPM 2 5% 1% 2% 0%
Yogo (2006) 4 18% 4% 2% 5%
Santos and Veronesi (2006) 3 27% 2% 8% 2%
Lustig and Van Nieuwerburgh (2004) 4 57% 2% 9% 0%
Lettau and Ludvigson (2001) 4 58% 5% 0% 1%
Fama-French 4 78% 19% 31% 6%
Li, Vassalou, and Xing (2006) 4 80% 26% 42% 4%
Lewellen, Jonathan, Sefan Nagel and Jay Shanken 2010 A skeptical appraisal of assetpricing tests Journal of Financial Economics 96, 175-194.
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 controlsBrown, 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
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.
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)
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)
The horse race
Factor loadingsCharacteristics
IndustriesBasis Assets
The horse race
For every year 1980 – 2010Determine the category membership in prior yearRegress excess returns against category membership
Compare models on basis of resulting R2
A valid non-nested model comparison
Attributes of our procedure
Use individual security returns, not portfolios
No concern about errors in variablesRegress on category membership, not factor
loadings
Inference uses time series of cross section estimates
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
Individual security characteristics do not beat risk factor loadings -- OLS
Out of sample OLS regressing annual returns on factor loadings and characteristics
125 FF Loadings 125 Characteristics Difference
Year N k Rsq Rbar k Rsq Rbar Rsq Rbar
1980 2708 125 9.71% 5.37% 115 12.86% 9.03% 3.15% 3.66%
1981 2907 125 11.43% 7.48% 115 11.84% 8.24% 0.41% 0.75%
1982 3019 125 9.50% 5.62% 124 7.69% 3.77% -1.81% -1.85%
… … … … … … … … … …
2010 4396 125 8.53% 5.87% 125 6.41% 3.70% -2.11% -2.17%
2011 4499 125 9.05% 6.06% 125 4.52% 1.81% -4.54% -4.25%
2012 4501 124 3.87% 0.80% 125 4.12% 1.40% 0.25% 0.60%
Mean 6.36% 3.30% 6.23% 3.28% -0.13% -0.02%
t-value (13.27) (7.03) (10.16) (5.39) (-0.27) (-0.04)
Individual security characteristics DO beat risk factor loadings -- GLS
Out of sample GLS regressing annual returns on factor loadings and characteristics
125 FF Loadings 125 Characteristics Difference
Year N k Rsq Rbar k Rsq Rbar Rsq Rbar
1980 2708 125 6.20% 1.65% 115 10.58% 6.61% 4.38% 4.96%
1981 2907 125 14.65% 10.81% 115 15.16% 11.66% 0.51% 0.85%
1982 3019 125 11.24% 7.40% 124 12.58% 8.83% 1.34% 1.43%
… … … … … … … … … …
2010 4396 125 7.06% 4.34% 125 8.89% 6.23% 1.83% 1.89%
2011 4499 125 19.05% 16.36% 125 10.10% 7.53% -8.95% -8.83%
2012 4501 124 10.97% 8.11% 125 8.22% 5.60% -2.75% -2.51%
Mean 12.24% 9.35% 13.58% 10.84% 1.34% 1.49%
t-value (9.42) (7.03) (9.71) (7.57) (2.59) (2.82)
Out of sample cross section regression results
Ordinary Least Squares Generalized Least Squares
Risk class methodology R2 Adjusted R2 R2 Adjusted R2
125 Basis Assets13.00% 10.23% 16.64% 13.96%
(14.67) (11.29) (11.43) (9.20)
48 Fama French industry groups7.27% 6.15% 14.20% 13.14%
(10.48) (8.84) (10.49) (9.63)
125 risk classes based on characteristics6.23% 3.28% 13.58% 10.84%
(10.16) (5.39) (9.71) (7.57)
125 risk classes based on loadings6.36% 3.30% 12.24% 9.35%
(13.27) (7.03) (9.42) (7.03)
Out of sample cross section regression results
Ordinary Least Squares Generalized Least SquaresDifference between methods R2 Adjusted R2 R2 Adjusted R2
Basis Assets - 48 Industry groups5.74% 4.09% 2.44% 0.81%
(8.04) (5.53) (2.50) (0.79)
Basis Assets - Characteristics groups6.77% 6.96% 3.06% 3.11%
(8.58) (8.48) (3.28) (3.22)
Basis Assets - Loadings groups6.64% 6.94% 4.40% 4.61%
(11.02) (11.01) (6.79) (6.85)
48 Industry - Characteristics groups1.04% 2.87% 0.62% 2.30%
(1.62) (4.43) (1.25) (4.52)
48 Industry - Loadings groups0.91% 2.85% 1.96% 3.79%
(1.99) (6.23) (3.30) (6.30)
Characteristics - Loadings groups-0.13% -0.02% 1.34% 1.49%
(-0.27) (-0.04) (2.59) (2.82)
Basis Assets – Hoberg-Phillips 100 industries3.33% 2.82% 1.68% 1.18%
(2.30) (1.91) (1.20) (0.83)
Characteristics – Hoberg-Phillips 100 industries-3.37% -4.08% -2.36% -3.00%
(-2.20) (-2.62) (-2.35) (-2.96)
Out of sample cross section regression results
Ordinary Least Squares Generalized Least SquaresDifference between methods R2 Adjusted R2 R2 Adjusted R2
Basis Assets - 48 Industry groups5.74% 4.09% 2.44% 0.81%
(8.04) (5.53) (2.50) (0.79)
Basis Assets - Characteristics groups6.77% 6.96% 3.06% 3.11%
(8.58) (8.48) (3.28) (3.22)
Basis Assets - Loadings groups6.64% 6.94% 4.40% 4.61%
(11.02) (11.01) (6.79) (6.85)
48 Industry - Characteristics groups1.04% 2.87% 0.62% 2.30%
(1.62) (4.43) (1.25) (4.52)
48 Industry - Loadings groups0.91% 2.85% 1.96% 3.79%
(1.99) (6.23) (3.30) (6.30)
Characteristics - Loadings groups-0.13% -0.02% 1.34% 1.49%
(-0.27) (-0.04) (2.59) (2.82)
Basis Assets – Hoberg-Phillips 100 industries3.33% 2.82% 1.68% 1.18%
(2.30) (1.91) (1.20) (0.83)
Characteristics – Hoberg-Phillips 100 industries-3.37% -4.08% -2.36% -3.00%
(-2.20) (-2.62) (-2.35) (-2.96)
Out of sample cross section regression results
Ordinary Least Squares Generalized Least SquaresDifference between methods R2 Adjusted R2 R2 Adjusted R2
Basis Assets - 48 Industry groups5.74% 4.09% 2.44% 0.81%
(8.04) (5.53) (2.50) (0.79)
Basis Assets - Characteristics groups6.77% 6.96% 3.06% 3.11%
(8.58) (8.48) (3.28) (3.22)
Basis Assets - Loadings groups6.64% 6.94% 4.40% 4.61%
(11.02) (11.01) (6.79) (6.85)
48 Industry - Characteristics groups1.04% 2.87% 0.62% 2.30%
(1.62) (4.43) (1.25) (4.52)
48 Industry - Loadings groups0.91% 2.85% 1.96% 3.79%
(1.99) (6.23) (3.30) (6.30)
Characteristics - Loadings groups-0.13% -0.02% 1.34% 1.49%
(-0.27) (-0.04) (2.59) (2.82)
Basis Assets – Hoberg-Phillips 100 industries3.33% 2.82% 1.68% 1.18%
(2.30) (1.91) (1.20) (0.83)
Characteristics – Hoberg-Phillips 100 industries-3.37% -4.08% -2.36% -3.00%
(-2.20) (-2.62) (-2.35) (-2.96)
Out of sample cross section regression results
Ordinary Least Squares Generalized Least SquaresDifference between methods R2 Adjusted R2 R2 Adjusted R2
Basis Assets - 48 Industry groups5.74% 4.09% 2.44% 0.81%
(8.04) (5.53) (2.50) (0.79)
Basis Assets - Characteristics groups6.77% 6.96% 3.06% 3.11%
(8.58) (8.48) (3.28) (3.22)
Basis Assets - Loadings groups6.64% 6.94% 4.40% 4.61%
(11.02) (11.01) (6.79) (6.85)
48 Industry - Characteristics groups1.04% 2.87% 0.62% 2.30%
(1.62) (4.43) (1.25) (4.52)
48 Industry - Loadings groups0.91% 2.85% 1.96% 3.79%
(1.99) (6.23) (3.30) (6.30)
Characteristics - Loadings groups-0.13% -0.02% 1.34% 1.49%
(-0.27) (-0.04) (2.59) (2.82)
Basis Assets – Hoberg-Phillips 100 industries3.33% 2.82% 1.68% 1.18%
(2.30) (1.91) (1.20) (0.83)
Characteristics – Hoberg-Phillips 100 industries-3.37% -4.08% -2.36% -3.00%
(-2.20) (-2.62) (-2.35) (-2.96)
Out of sample cross section regression results
Ordinary Least Squares Generalized Least SquaresDifference between methods R2 Adjusted R2 R2 Adjusted R2
Basis Assets - 48 Industry groups5.74% 4.09% 2.44% 0.81%
(8.04) (5.53) (2.50) (0.79)
Basis Assets - Characteristics groups6.77% 6.96% 3.06% 3.11%
(8.58) (8.48) (3.28) (3.22)
Basis Assets - Loadings groups6.64% 6.94% 4.40% 4.61%
(11.02) (11.01) (6.79) (6.85)
48 Industry - Characteristics groups1.04% 2.87% 0.62% 2.30%
(1.62) (4.43) (1.25) (4.52)
48 Industry - Loadings groups0.91% 2.85% 1.96% 3.79%
(1.99) (6.23) (3.30) (6.30)
Characteristics - Loadings groups-0.13% -0.02% 1.34% 1.49%
(-0.27) (-0.04) (2.59) (2.82)
Basis Assets – Hoberg-Phillips 100 industries3.33% 2.82% 1.68% 1.18%
(2.30) (1.91) (1.20) (0.83)
Characteristics – Hoberg-Phillips 100 industries-3.37% -4.08% -2.36% -3.00%
(-2.20) (-2.62) (-2.35) (-2.96)
Out of sample cross section regression results
Ordinary Least Squares Generalized Least SquaresDifference between methods R2 Adjusted R2 R2 Adjusted R2
Basis Assets - 48 Industry groups5.74% 4.09% 2.44% 0.81%
(8.04) (5.53) (2.50) (0.79)
Basis Assets - Characteristics groups6.77% 6.96% 3.06% 3.11%
(8.58) (8.48) (3.28) (3.22)
Basis Assets - Loadings groups6.64% 6.94% 4.40% 4.61%
(11.02) (11.01) (6.79) (6.85)
48 Industry - Characteristics groups1.04% 2.87% 0.62% 2.30%
(1.62) (4.43) (1.25) (4.52)
48 Industry - Loadings groups0.91% 2.85% 1.96% 3.79%
(1.99) (6.23) (3.30) (6.30)
Characteristics - Loadings groups-0.13% -0.02% 1.34% 1.49%
(-0.27) (-0.04) (2.59) (2.82)
Basis Assets – Hoberg-Phillips 100 industries3.33% 2.82% 1.68% 1.18%
(2.30) (1.91) (1.20) (0.83)
Characteristics – Hoberg-Phillips 100 industries-3.37% -4.08% -2.36% -3.00%
(-2.20) (-2.62) (-2.35) (-2.96)
Kruskal Tau Average Value
Basis assets 48 FF industry 125 characteristics 125 loadings 100 HP industries
Basis assets 1 0.155 0.058 0.045 0.25
48 FF industries 0.155 1 0.023 0.024 0.107
125 characteristics 0.058 0.023 1 0.058 0.394
125 loadings 0.045 0.024 0.058 1 0.427
100 HP industries 0.25 0.107 0.394 0.427 1
Serial dependence 0.175 0.955 0.13 0.067 0.16
Theil U Average Value
Basis assets 48 FF industry 125 characteristics 125 loadings 100 HP industries
Basis assets 1 0.307 0.31 0.289 0.533
48 FF industries 0.307 1 0.197 0.196 0.326
125 characteristics 0.31 0.197 1 0.365 0.695
125 loadings 0.289 0.196 0.365 1 0.724
100 HP industries 0.533 0.326 0.695 0.724 1
Serial dependence 0.426 0.967 0.509 0.406 0.478
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