# 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.

## Comparison of stock returns

Variables and Data Sources:

• PS&P = S&P 500 Price Index

This is Standard and Poor index of 500 companies and will be used as market portfolio. (You would use return from this series as Market Return rM,t)
http://finance.yahoo.com/quote/%5egspc/history?p=^gspc

• PB = Boeing Company Stock Price

A particular stock we are interested in to determine how it behaves in response to market changes.
http://finance.yahoo.com/quote/BA/

• PIB = IBM (International Business Machines) Stock Price

A particular stock we are interested in to determine how it behaves in response to market changes.
http://finance.yahoo.com/quote/IBM/

• rf =Interest rate on 10 year US-Treasury Note

This variable is given in percentage (with % sign omitted) and will serve as a risk-free interest rate. We will use this variable to compute excess returns on our preferred stock (either Boeing or IBM) and Market excess returns.
http://finance.yahoo.com/quote/%5ETNX/

#### Now perform the following tasks.

Download the data for S&P 500 index, Boeing Stock Price, IBM Stock Price, and US TN (10 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.

 Data Group Data Period Students with ID Between (inclusive) End Date Start Date Group 01 31/08/2017 1/03/2012 16539787 19112537 Group 02 31/03/2017 1/10/2011 19112538 19164460 Group 03 31/10/2016 1/05/2011 19164461 19200552 Group 04 31/05/2016 1/12/2010 19200553 19225500 Group 05 31/12/2015 1/07/2010 19225501 19245537 Group 06 31/07/2015 1/02/2010 19245538 19534916

Example: Suppose my student ID is 19178800. This ID falls in group 03 and I would download monthly data covering the period  01 May 2011 to 31 October 2016.

#### 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*ln(Pt / Pt-1)
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 – rf,t    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 market return).
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.

### Analyse Data & Submit Report

Prepare your written report in two Parts:
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.

Marks Distribution

 Description Total Marks Task A Downloaded correct data 9 Task B 1. Line charts 6 2. a Returns computation 6 2. b Summary statistics 6 2. c Jarque-Berra test of normality 10 3. 0 Hypothesis testing of single population mean 5 4. 0 Hypothesis testing to compare equality of risk in both stocks 5 5. 0 Hypothesis Testing-Two Population Means 10 6. 0 Computing excess returns 5 7. a CAPM estimation 6 7. b Interpretation of Coefficients 6 7. c Interpretation of R2 3 7. d Interpretation of Confidence interval for beta 3 8. 0 Confidence Interval approach to Hypothesis test 5 9.0 Testing the assumption of normally distributed errors 5 Organisation of the report (Word Document) 10 Grand Total 100