Reference no: EM132311386

Task A: Hypothesis Testing of Means and Variances Equality

1. Returns computation Calculate returns for these three series in Excel or any software of your choice using the transformation: r_t = 100*ln(P_t/P_t-1) and perform the Jarque-Berra test of normally distributed returns for each of Boeing and GD stocks. What do you infer about the distribution of the two stock returns series? Specify the sampling distribution of the average returns of the two stocks.

Hints:
o We have computed stock returns in Workshop 02.
o If there are say 11+1' observations on prices, then the return series would have 'n' observations.
o These numbers would represent percentages after multiplication with 100 in the formula above. But you would not include a percentage sign in your data. For example, returns for two periods are 035% and 0.41% but we would use 0.35 and 0.41 after omitting % sign in our excel worksheet.

2. Hypothesis testing of a single population mean 0.0: 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 a 5% significance level.

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

4. Hypothesis testing of two population means: Besides, you want to determine whether both stocks have the same population average return. Using the confidence interval approach, perform an appropriate hypothesis test given the information in your sample of 60 observations on returns at a 5% significance level. Report your findings and also mention which stock will you prefer and why? Note: You will not be given marks if you do not follow the confidence interval approach to test the hypothesis

Task B: Regression Analysis and Inference

5. 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 and perform the following tasks.

a. Estimate the Capital Asset Pricing Model (Use the link below for the CAPM details) by regressing the excess return on your preferred stock (yr) on excess market return (x) 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 a 95% confidence interval (CI) for the slope coefficient.

6. Perform a hypothesis test to infer whether your preferred stock is an aggressive stock.

7. One of the assumptions of the linear regression model is: Random errors are normally distributed. Perform an appropriate hypothesis test to determine whether it is plausible to assume normally distributed errors.

Model in equation (1) is called economic model since it describes the relationship between excess stock return and the excess market return based on financial theory.

Why is CAPM important?

The CAPM beta is important to investors since it discloses the stock's volatility. In particular, this beta measures the sensitivity of given security's return to variation in the whole stock market. Value of beta determines whether the stock is a defensive, a neutral, or an aggressive stock.

Defensive stock A stock is known as defensive stock if its beta value is less than 1. A defensive stock has its variation less than the market's and therefore is considered as less risky than the market is.

Neutral Stock A stock with beta equal to 1 is called neutral stock because it is as volatile as the market is.

Aggressive stock A beta with a value greater than 1 is known as an aggressive stock since it has variation larger than the market's and therefore is considered as more risky/volatile than the market is.

Since beta is an unknown parameter, therefore, investors usually require an estimate of a stock's beta before purchasing it. However, the statistical model can be obtained by including an intercept (Po) and an error term (ut) in the model, so that we have a simple linear regression model as

r_t - r_f,t = β_o+ β_M (r_M,t - r_f,t) + u_t

By defining y_t = r_t - r_f,t and x_t = rM,t - r_f,t, we can express CAPM model in above equation as

Y_t = β_o + β₁xt + u_t

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 in the report to be submitted in a pdf file.

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
numerical measures, undertake inappropriate tests or discuss irrelevant matters.