Description

Instructions: 

The maximum length for this assessment is five single-sided A4 paper (Times New Roman, 1.5 spacing, 12 point). If you are required to make a decision while conducting a hypothesis test, use a 5% significance level (unless otherwise specified). Be sure to state your null and alternative hypotheses, rejection criterion and your decision. Do not answer questions with a simple ”yes” or ”no”, but carefully justify your answers. 

Furthermore, you should upload only one single PDF format file. This PDF file should consist of both your analysis and codes. In Particular, you should combine both PDF files into one PDF file. The first PDF file contains your written answer that includes your discussion and data analysis, while the other PDF file contains the code that you required to generate the figures and graphs in your first PDF file. Note: Watch the Panopto video that shows you how to convert your analysis, discussion, and figures and codes into a single PDF file.

Part One: Estimating and Testing the Capital Asset Pricing Model (CAPM)

In this exercise, we use monthly data to estimate the ‘betas’ of stocks (equities) traded on the New York Stock Exchange. We study equations of the from: 

rjt = αj + βj rmt + ujt

where rjt represents the actual return to holding company j’s stock in month t, rmt is the return on the market portfolio in month t (i.e., the portfolio consisting of all stocks, held in the same proportions as the market as a whole) and ujt represents other influences on returns of the stock j. 

The strict form of the capital asset pricing model (CAPM) predicts that this equation fully ‘explains’ stock returns. Specifically, this means that ujt depends only on random effects particular to company j, and is not predictable by macroeconomic variables. According to the CAPM, when markets operate efficiently in response to complete information, market equilibrium implies that rmt contains all such information, relevant to individual stock returns. In this exercise you will be required to test empirically all your doubts and assumptions you had about the financial data given to you using econometric techniques learned in your lectures and tutorials. 

The parameter β (the ‘beta’) is an indicator of the risk and return associated with the stock. When βj = 1, the expected net return is the same as that of the market portfolio. When βj > 1, the expected return exceeds that of the market portfolio, but there is correspondingly greater risk. When βj < 1 there is lower return, but also less risk. Thus, market equilibrium ensures the existence of a risk-return trade-off. The CAPM model also predicts that αj = 0 i.e. it is not widely believed that one entity in the stock market can outperform the market.