hypothesis testing, portfolio optimisation

MICROSOFT: mean=0.07321 median=0 mode=0 variance=4.8317 st. deviation=2.1981 kurt=5.1873 skew= -0.0442

APPLE: mean=0.0479 median=0 mode=0 variance=10.0336 st. deviation=3.1675 kurt=56.7055 skew= -2.1590

INTEL: mean=0.0526 median=0 mode=0 variance=7.0372 st. deviation=2.6527 kurt=5.3823 skew= -0.4118

HP: mean=0.03762 median=0 mode=0 variance=6.0895 st. deviation=2.4676 kurt=6.2304 skew= -0.0182

1. 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.

2. Assume the stock returns from each asset are independent from each other, are the mean returns statistically different from each other?

3.Calculate the correlation matrix of the stock returns.

4. Is the assumption of independence realistic? If not, re-test the hypotheses in Question 2 using appropriate test statistics. Compare the results to the results obtained in Question 2.

5. 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

6. Why is it not realistic to assume these stock prices follow a normal distribution?

PLEASE SHOW WORKINGS FOR MY UNDERSTANDING