Reference no: EM132003730 , Length: word count:2000

Which stock should I invest in?
(Topics included: Statistical Inference, Simple 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, and

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 20% of the total assessment in this subject. This assignment is based on topics including; Sampling and Estimation, Hypothesis Testing, and Regression Analysis.

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 a market portfolio. (You would use return from this series as Market Return rM,t)

- PB = Boeing Company- BA's Stock Price

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

- PGD = General Dynamics- GD's Stock Price

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

- 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.

Now perform the following tasks.

Task A: Downloading the data

Download the data for S&P 500 index, Boeing Stock Price, General Dynamics Corp. 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.

Task B: Perform the following.

1. Calculate returns for these three series in Excel or any software of your choice using the transformation: rt = 100*ln(Pt / Pt-1) and perform the Jarque-Berra test of normally distributed returns for each of Boeing and GD. What do you infer about the distribution of the two stock returns series? Describe also the risk and average return relationship in each of the two stocks.
Hints:

- We have performed a similar task in Workshop 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. But you would not put a percentage sign in your data. For example, returns for two periods are 0.35% and 0.41% but we would use 0.35 and 0.41 after omitting % sign in our excel
worksheet.

2. Test a hypothesis that the average return on GD stock is different from 2.8%. Which test statistic would you choose to perform this hypothesis test and why? Also, specify the distribution of the test statistic under the null hypothesis.

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

4. Besides, you want to determine whether both stocks have same population average return. Perform an appropriate hypothesis test using information in your sample of 60 observations on returns. Report your findings and also mention which stock will you prefer and why?

5. Compute excess return on your preferred stock as yt = rt - rf,t and excess market return as xt = rM,t - rf,t and perform the following tasks.

a. Estimate the CAPM using linear regression by regressing the excess return on your preferred stock (yt) on excess market return (xt) and properly report your regression results.
b. Interpret the estimated CAPM beta-coefficient in terms of the stock's riskiness in comparison with the market.
c. Interpret the value of R2.
d. Interpret 95% confidence interval for the slope coefficient.

6. 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 test a hypothesis)

7. One of the assumptions of ordinary least squares (OLS) method is; normally distributed error term in the model. Perform an appropriate hypothesis test to determine whether it is plausible to assume normally distributed errors.

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.

Attachment:- STATS.rar