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(a) Use the appropriate diagrams and summary tables to discuss briefly the behavior of the excess returns on Bank of America and the market index (e.g., showing the time series of the excess returns of Bank of America and the market index in a unique graph, presenting histograms, scatter plots and summary statistics of the two excess returns).

Financial Econometrics Coursework

Introduction

In finance, it is customary to explain the changes in the extra return on an asset as a linear function of the extra returns on the market portfolio, i.e. 𝑅𝑡 = 𝛼 + 𝛽 × 𝑅𝑀𝑡 + 𝑢𝑡 (1) Where 𝑅𝑡 is the excess return on a stock (with respect to the risk free rate), 𝑅𝑀𝑡 is the excess return on a market index (with respect to the risk free rate). The main aim of this exercise is to learn regression techniques by applying them to the estimation of equation (1) in the presence of (possible) anomalies in the stock market. You will analyze the monthly data for Bank of America Corporation (BAC) for the period April 1996-March 2014. On Moodle, you will find Excel file with the returns on the stock price of Bank of America, the excess return on the market portfolio, the HML portfolio, the SML portfolio and the risk free rate. The numbers in the five columns are all in percentage points.

Assignment

(a) Use the appropriate diagrams and summary tables to discuss briefly the behavior of the excess returns on Bank of America and the market index (e.g., showing the time series of the excess returns of Bank of America and the market index in a unique graph, presenting histograms, scatter plots and summary statistics of the two excess returns).

(b) Estimate the model described in equation (1). What is the estimate of the intercept and slope? Please interpret them. Briefly interpret also the ‘R-squared’ and the ‘Adjusted R-squared’.

(c) Use your empirical findings in part (b) to test the two null hypotheses: (i) 𝛼 = 0 and 𝛽 = 1 and (ii) 𝛽 = 0.54. Concerning point (ii), please interpret your findings using the intuitions linked to the CAPM and considering that 0.54 is the beta of the entire banking industry.

(d) Test the stability of the estimated parameters of equation (1) between two sub-samples: April 1996-September 2008 and September 2008-March 2014. Interpret your findings.

(e) Modify equation (1) to test for the January effect and interpret your findings.

(f) Augment equation (1) with the size (SMB) and book‐to‐market (HML) factors to estimate the Fama‐French model. Comment on your results.

(g) Provide an overall assessment of your findings in parts from (b) to (f) regarding the most suitable model to explain the returns of your chosen company. Discuss, in particular, the goodness of fit


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