Statistics for Business and Finance Assignment: Which Stock Will Perform Better?

You have been asked by your client to recommend which of two available stocks will perform better over time, relative to the market. You will need to compare risk and return relationship of the two stocks over time, and present your findings as a written report detailing your calculations and findings.

The goal of this assignment is to

1. acquaint you with quantitative data analysis skills often required by different organisations

2. estimate the Capital Asset Pricing Model (CAPM)

3. provide you with feedback on your ability to carry out such tasks

4. learn how and when to use different quantitative techniques covered in the second half of this course.

Task 1: Comparison of Stock Returns

1. Obtain the line charts for S&P, IBM and GE series (prices) and comment on your observations.

2. a. Now obtain returns for these three series (ignoring any of the dividends paid) using the transformation: r_t = 100[ln(P_t) - ln(P_t-1)]%.

b. Obtain the summary statistics together with their histograms to further analyse each of the three returns distributions.

c. Interpret your results. In particular, explain risk and average return relationship.

d. Based on your statistics, is IBM relatively riskier than the GE stock?

3. Suppose you are not convinced with your finding about riskiness of the two stocks based on your estimates for sample standard deviations and, therefore, you want to test hypothesis whether both returns are equally volatile (H₀: σ²_IBM = σ²_GE).

Perform an appropriate hypothesis test using 5% significance level and provide all the steps involved. What do you conclude about returns volatility in this case?

4. Before investing in one of the two stocks based on higher risk, you further want to determine whether both stocks have same population average return.

Perform an appropriate hypothesis test given the sample and report your findings. Which stock will you prefer and why?

5. Draw the scatter plot of each of the two returns series against market return. Also, compute the sample covariance and sample correlation between these two stocks and explain your findings.

Task 2: Estimation of CAPM and Hypothesis Testing

6. Now compute excess return on your preferred stock and excess market return by subtracting the 10-year T-Bill rate from both series. That is,

Excess return on preferred stock: y_t = r_t - r_f,t

Excess return on market: x_t = r_M,t - r_f,t

7. a. Estimate the CAPM and report your results.

b. Interpret the estimated coefficients in relation to the profitability of the Stock and its riskiness in comparison with the market.

c. Interpret the value of R².

8. Perform the hypothesis test to determine whether your preferred stock is aggressive (a stock is an aggressive stock if the slope coefficient is greater than 1 and is defensive stock if the slope coefficient is less than 1).

9. Construct 95% confidence interval for the slope coefficient.

10. Estimate AR (1) model (that is, Auto Regressive model of order 1) using either GE stock price or IBM stock price. Report and interpret your result.

Attachment:- Assignment.rar