Homework Assignment No. 3: due April 30, 2008

This will introduce you to the idea of time variation in expected returns and betas. You should use the Fama-French factors you downloaded for homework 2 [a proxy for the market risk premium (R_M-R_f), the HML portfolio (book-to-market factor), the SMB portfolio (size factor), and the monthly T-bill return (R_f) from 1964 until 2007], along with the monthly returns of 10 equal-weighted portfolios formed on Dividend to price (D/P). Use the Excel spreadsheet that contains several variables that are frequently used to predict stock returns, including a measure of default premium (DEF), a term premium (TERM), the dividend yield (DIV), and the risk-free rate (R_f). You may use any statistical package to do your work. Your report should include tables of results, not copies of computer output. All tables and charts should have legends and explanations. Answers (excluding tables and figures) should be typed and a maximum of four pages long (Times New Roman 11p font or larger, 1.5 line spacing, 1 inch margins).

a) (20 points)
Test the Fama-French factors are related to these predictor variables.

b) (20 points)
Test whether the returns to the D/P portfolios are related to these predictor variables.

c) (20 points)
Test whether the Fama-MacBeth risk and return factors γ_0t and γ_Mt that you estimated in homework 1 are related to these predictor variables.

d) (40 points)
Using all ten D/P portfolios, estimate a time series regression of the form,

(R_pt - R_ft) = a_pt + b_pMt (R_Mt - R_ft) + e_pt

where the constant a_pt and the slope b_pMt are explained exactly by linear functions of these predictor variables:

a_pt = a₀ + a₁ def_t + a₂ div_t + a₃ R_ft + a₄ term_t

b_pMt = b₀ + b₁ def_t + b₂ div_t + b₃ R_ft + b₄ term_t

Is there evidence that these predictor variables help explain time series variation in a_pt and b_pMt? If so, what does this imply for tests of the CAPM?

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Some sample calculations from Eviews related to this homework are available in an Excel spreadsheet f532hw308A.xls.

Some sample Eviews programs and workfiles used for this problem are contained in this ZIP file.

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