02 May ASSIGNMENT DETAILS (Topics include: Statistical Inference, Simple Regression Analysis
ASSIGNMENT DETAILS
(Topics include: 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).
Which stock should I invest in?
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 the Standard and Poor index of 500 companies and will be used as a market portfolio. (You would use the return from this series as Market Return rM,t)
http://finance.yahoo.com/quote/%5egspc/history?p=^gspc
PB = Boeing Company- BA’s 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/
PGD = General Dynamics- GD’s Stock Price
A particular stock we are interested in to determine how it behaves in response to market changes.
http://finance.yahoo.com/quote/GD/
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 GD) and Market excess returns.
http://finance.yahoo.com/quote/%5ETNX/
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, using 5% significance level.
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 the same population average return. Perform an appropriate hypothesis test using information in your sample of 60 observations on returns, using 5% significance level. 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 (CAPITAL ASSET PRICING MODEL) 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?
Include 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.
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