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.

Comparison of stock returns (Boeing vs IBM)

Variable and Data source

• P_S&P = S&P 500 Price Index

This is standard and poor index of 500 companies and will be used as market portfolio. (Return on this variable would be use as market return rM5)

• P_B = Boeing Company stock Price

A particular stock we are interested in to determine how it behave in response to market changes.

• P_IB = IBM(International business machine) stock Price

A particular stock we are interested in to determine how it behave in response to market changes.

• Rr = 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 return on our preferred stock (either) Boeing or IBM) and Market excess return.

Now perform the following tasks.

Task A: Downloading the data

Download the data for S&P index Boeing stock price and US TN (10 year), using the links provided above and choosing monthly historical data for all variable covering the period related to a group your student ID belongs to

Data Group         Data Period                                Students with ID between

                              Start Data           End Date

(Inclusive)

Group o1             1/03/2012            31/08/2017         17308727             19116305

Group 02             1/10/2011            31/03/2017         19116806             19163288

Group 03             1/05/2011            31/10/2016         19163289             19194892

Group 04             1/12/2010            31/05/2016         19194893             19215128

Group 05             1/07/2010            31/12/2015         19215129             19245497

Group 06             1/02/2010            31/07/2015         19245498             19531208

Example: Suppose my student ID is 9778800 This ID falls in group 03 and I would download monthly data covering the period 01 May 2017 to 37 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 r_t = 100 ln(P_t/P_t-1)

Hints
we performed a stony task in Tutorial 01

If there are say n+1 observations on paces, then the return series would have 'n' observations

These numbers would represent percentages after multiplication vain 100 in the formula above However, you would not put a percentage sign in your data For example, returns for two periods are 035% and 041% 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 lest and why? Also specify the distribution of the test statistic under the null.

4. Before investing in one of the two stocks is at least 3%. Which test statistics would you use to perform this 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 repot your findings. Also which stock will you prefer and why?

6. Compute excess return on your preferred stock as y_t = r_t- r_f,t and excess market return as x_t = r_M,t - r_f,t (that is you subtract the 10-year T-Bit rate from return on your preferred stock and the market return that is the return on S&P 500).

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 as 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.

Attachment:- bsf.rar