# Statistics for business

#### Statistics for business

Referencing Styles : Chicago | Pages : 6

Calculate the returns of each stock price using the following: rt = 100 ln Pt Pt−1 where Pt is the stock price at time t. Plot the returns for each stock price. 3. Create a histogram for each of the returns series and report their descriptive statistics including mean, median, mode, variance, standard deviation, skewness and kurtosis. What conclusion can you draw by examining the kurtosis in each case? 4. Under the assumption that the stock returns of each asset are drawn from an independently and identically distributed normal distribution, are the expected returns statistically different from zero for each asset? State clearly the null and alternative hypothesis in each case. 5. Assume the stock returns from each asset are independent from each other, are the mean returns statistically different from each other? 6. Calculate the correlation matrix of the stock returns. 7. Is the assumption of independence realistic? If not, re-test the hypotheses in Question 5 using appropriate test statistics. Compare the results to the results obtained in Question 5. 8. If you can only choose maximum of two stocks into a portfolio, which will you choose? What are the optimal weights and the optimal expected returns? State clearly your objective function and provide step-by-step derivations. 9. Bonus question: Why is it not realistic to assume these stock prices follow a normal distribution?