# Chicago Booth BUSF 35150 - Empirical methods overheads (7 pages)

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## Empirical methods overheads

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- Pages:
- 7
- School:
- The University of Chicago Booth School of Business
- Course:
- Busf 35150 - Advanced Investments

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12 12 1 Week 4a Empirical methods overheads Motivation and overview 1 Expected return beta model as in CAPM Fama French APT 1 TS regression define 0 1 2 2 Model 0 because the point of the model is that should 0 2 How do we take this to the data Objectives a Estimate parameters b Standard errors of parameter estimates How do vary if you draw new data and try again c Test the model Does 0 Are the 0 Are the that we see due to bad luck rather than real failure of the model d Test one model vs another Can we drop a factor e g size 12 2 Time series regression 1 Time Series Regression Fama French a Method Run and interpret 0 1 2 for each E R ei Slope E f i 1 b Estimates i OLS time series regression 0 173 1 2 for each i ii Mean of the factor 1X 1 c Standard errors independent over time i OLS standard errors ii d Test are jointly zero i Answer look at 0 0 1 Precise forms h i 1 0 1 1 0 1 0 1 2 i 1 h 1 0 1 0 1 Do not memorize Understand look up ii If are also normal then a refinement is valid in small samples i 1 h 1 0 1 0 1 GRS Test iii Distribution of 0 0 1 2 distributions 1 2 1 2 2 0 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 0 5 1 174 1 5 2 2 5 3 3 5 4 4 5 5 12 3 Cross sectional regression 1 Another idea The main point of the model is across assets E Ri Slope i i 0 1 2 Why not fit this as a cross sectional regression 2 Two step procedure a TS over time for each asset to get 1 2 for each b Run CS across assets to get 1 2 3 TS vs CS E Ri Cross section Time Series Rf Factor market for CAPM i 175 4 Estimates a from TS b slope coe cient in CS c from error in CS 1 series regression any more P 1 6 is not the intercept from the time 5 Standard errors a from TS OLS formulas b You can t use OLS formulas c Answer With no intercept in CS 2 d i 1 h 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 1 e See notes for the formula with an intercept in CS 6 Test 0 0 1 2 1 7 Warning Cross section ei E R Time series i 12 4 Fama MacBeth procedure 1 Procedure 176 a Run TS to get betas 0 1 2 for each b Run a cross

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