Question (20 marks):

The Fama-MacBeth regression output provided on the following page originates from Fama and French (1992). Utilize this output to answer the following questions:

Part 1: Interpretation of Slope Coefficients for Beta (6 marks):

a.    Interpret the slope coefficient for beta (β) with a value of 0.15 in the first row of the Fama- MacBeth regression. Accompany your interpretation with a diagram illustrating the relationship between X and Y variables corresponding to this regression.

b.    Similarly, interpret the slope coefficient for beta (β) with a value of -0.37 in the third row of the Fama-MacBeth regression. Discuss the evidence presented in the table and assess its consistency with the key predictions of the Capital Asset Pricing Model (CAPM).

Part 2: t-Statistic Calculation and Time-Series Standard Error (10 marks):

a.    The description in the table claims that the t-statistic of the slope estimates are equal to the average slope divided by its time-series standard error. Provide an intuitive explanation of     this procedure to calculate the Fama-MacBeth t-statistic (2 marks).

b.    Determine the time-series standard error of the average slope for the beta coefficient with a value of 0.15 in this table (3 marks).

c.    Offer a mathematical expression explaining how this standard error would be computed, detailing all components of the expression (3 marks).

d.    Propose a correction that should be applied to calculate this standard error in the scenario of autocorrelated returns (2 marks).

Part 3: Usage of Fama-MacBeth Regressions for Portfolio Construction (4 marks):

Consider the information in the first and second columns of the table, representing beta (β) and ln(ME) in the Fama-MacBeth regression.

Assess whether this regression implies a strategy for constructing tradable portfolios that can generate alpha concerning the market portfolio. If yes, outline the strategy and explain the expected rationale behind its effectiveness. If not, provide a rationale for why no such strategy is implied. Base your response on the information presented in the table and your knowledge of Fama-McBeth regressions.