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Assignment - Details

Which stock should I invest in? (Statistical Inference and Regression Analysis)

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

The goal of this assignment is to

1. give you practice in performing the different types of quantitative analysis tasks often undertaken by Business graduates

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

3. learn how and when to use different quantitative techniques covered in the last six (6) modules of the subject.

This is an individual assignment, worth 30% of the total assessment in this subject. This assignment is based on topics including; Sampling and Estimation, Hypothesis Testing, and Regression Analysis.

Use the marking rubric as a guide when working on your assignment.

Now perform the following tasks.

Task A: Downloading the data

Download the data for S&P 500 index, Boeing Stock Price, IBM Stock Price, and US TN (70 year), using the links provided above and
choosing Monthly Historical Data for all variables covering the period related to a group your Student ID belongs to.

Task B: Perform the following.

1. Create the line charts for each of S&P, Boeing and IBM series using Close prices against time in Excel and comment on your observations (focusing on different features a time series can exhibit)

2. a. Calculate returns for these three series in Excel using the transformation: rt = 100 In[Pt/Pti]

Hints:

- We performed a similar task in Tutorial 01.

- If there are say "n+1" observations on prices, then the return series would have "n" observations.

- These numbers would represent percentages after multiplication with 100 in the formula above. However, you would not put a percentage sign in your data. For example, returns for two periods are 0.35% and 0.41% but we omit % sign in our excel worksheet and use 0.35 and 0.41.

b. Obtain the summary statistics for returns series in your sample and briefly discuss the risk and average return relationship in each stock. Which stock (Boeing or IBM) is relatively riskier than the other?

c. Perform the Jarque-Berra test of normally distributed returns for each of Boeing and IBM. Discuss your findings and also explain why do you test normality test.

3. Test the hypothesis that average return on Boeing stock is at least 3%. Which test statistic would you use to perform this hypothesis test and why? Also, specify the distribution of the test statistic under the null.

4. Before investing in one of the two stocks, you first want to compare risk associated to each of the two stocks. Perform any appropriate hypothesis test using 5% significance level and interpret your results.

5. You further want to determine whether both stocks have same population average return. Perform an appropriate hypothesis test using information in your sample of 65 observations on returns and report your findings. Also, which stock will you prefer and why?

6. Compute excess return on your preferred stock as yt = rt - rft and excess market return as xt = rm,t - rf,t (that is, you subtract the 10-year T-Bill rate from return on your preferred stock and the

7. a. Estimate the CAPM using linear regression where the dependent variable is excess return on your preferred stock while the independent variable is excess market return (computed as return on S&P 500 minus the risk fee rate) 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.

d. Interpret 95% confidence interval for the slope coefficient.

8. Using the confidence interval approach to hypothesis testing, perform the hypothesis test to determine whether your preferred stock is a neutral stock. (Note: You would not be given any marks if you do not use CI approach to hypothesis testing)

9. One of the assumptions of ordinary least squares (OLS) method is; normally distributed error term in the model. Verify that the error term follows normal distribution using any appropriate test.

Your written report must

include:

Part A: Calculations
- Set out all your calculations for each of the tasks (listed above) using Data Analysis Tool in Excel. Present your results in graphs and charts as appropriate

Part B: Interpretation

- Explain what your results mean, in language that your client can understand. For example, what conclusions can you draw from each of your findings?

- Your written report must be no more than TWELVE (12) pages in total, including all appendices, graphs, tables and written answers.
Answer the questions directly. Do not present unnecessary graphs or numerical measures, undertake inappropriate tests or discuss irrelevant matters.