FIN36181- Financial Econometrics - Capital Asset Pricing Model - Finance Report Writing Assessment Answer

Assessment Task:

FIN36181: Finance Report Writing Assessment Answer

1. Follow the steps outlined in Appendices A and B and download the monthly return time series for the following assets:

• U.S. stock market index, and

• U.S. Treasury bills maturing in three months.1 Produce two separate plots:

• First, generate one plot containing the monthly log return time series of both assets from January 1934 to December 2018.

• Second, suppose you invest 1$ at the end of December 1933 in each asset and hold it until the end of December 2018. Generate a plot which shows how your initial investment of 1$ evolves over time. Save both plots (e.g., as pdf file) and put them into your solution paper. Take a close look at both graphs. What do you learn from this about the returns across both asset classes?

2. You are wondering whether a similar relation holds for individual stocks. (a) Follow the steps outlined in Appendix C and download the monthly stock returns for Apple. Calculate log returns and compute, for each year, the average return and the standard deviation. Create a scatter plot in which the standard deviation is on the horizontal axis and the average return on the vertical axis. To take a closer look at the relation between both quantities, use the standard deviation as the independent variable, the average return as the dependent variable, and run the following regression:                                                                    r¯Apple,t = α + β σApple,t + uApple,t.

Report the parameter estimate of β and comment on its statistical significance. Add the corresponding regression line to your scatter plot, save it (e.g., as pdf file), and put it into your solution paper. Are these findings consistent with your results from the first exercise? (15 points) (b) You want to use more stocks and form a portfolio out of those. Follow the steps outlined in Appendix C and download the monthly returns of ten well-known stocks. Add the stocks in alphabetic order step-by-step to the portfolio which ultimately should contain all ten stocks: (1) Apple; (2) Apple and Bank of America; (3) Apple, Bank of America, and Boeing; . . .

(10) Apple, Bank of America, Boeing, . . . , and Walmart. Within each portfolio, stocks are equal weighted. Calculate the simple portfolio returns on a monthly basis. For each of the ten portfolios, determine the standard deviation of its return over the entire sample period. Finally, create a bar plot showing the standard deviation on the vertical axis and the ten different portfolios on the horizontal axis. Save this plot (e.g., as pdf file) and put it into your solution paper. What happens to the standard deviation of the portfolio when the number of stocks in the portfolio increases? Can you provide an explanation for this?

3. You learned in your Finance class that you can form portfolios based on firm characteristics, e.g., firm size (also known as market capitalization or market equity). Follow the steps outlined in Appendix D and download the monthly returns of ten portfolios formed on size, i.e., each portfolio is formed out of those firms which belong to a specific decile of the firm size distribution. Focus on the first and the last size portfolio only. Suppose you invested 1$ at the end of June 1926 in each portfolio and hold it until the end of December 2018. Generate a plot which shows how your initial investment of 1$ evolves over time. Save the plot (e.g., as pdf file) and put it into your solution paper. Would you recommend someone to invest in any of these portfolios? In your answer, you might also refer to additional analyses you consider as useful. In this case, please include the results from your additional analyses in your solution paper. 

4. In your Finance class, you have been introduced to the Capital Asset Pricing Model (CAPM). You want to know whether the CAPM holds for the log return on the Bank of America during the sample period from January 1981 to December 2018 (see exercise part 2.b). You decide to use the time series you already worked with in the first exercises:

• the log return on the U.S. stock market index is your proxy for the market return, and

• the log return on U.S. Treasury bills maturing in three months is your proxy for the risk-free rate. Run the corresponding regression. Summarize the parameter estimates, their standard errors, their t-statistics, and the R2 in a table in your solution paper. Based on these results, does the CAPM hold? In the context of this specific example, illustrate in detail the test of significance approach for a significance level of 5%.

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