Determine whether the monthly returns for the 96 months of the data (January 2001 to December 2008 in Tab 5) for BHP and TLS are from the same population (i.e. whether the sample data is drawn from underlying populations that have the same mean and standard deviation) by conducting the following tests:
(i) Test if the mean of paired differences between the two series of returns is zero. Use the Excel function TTEST(BHP,TLS,2,1) for this test.
Do you reject the null hypothesis at 5% level of significance based on a two-sided t-test (from your test result)? Explain your decision.
Identify the sample mean of the paired differences between the two series of returns.
Identify the standard error of the sample mean of the paired differences between the two series of returns.
(ii) Test if the difference between the means of the two series of returns is zero. (Assume that BHP and TLS have the same population of price returns.) Use the Excel function TTEST(BHP,TLS,2,2) for this test.
Do you reject the null hypothesis at 5% level of significance based on a two-sided t-test (from your test result)? Explain your decision.
What is the difference between the means of the two series of returns?
What is the standard error of the difference between the means of the two series of returns?
(b) (i) Compute the mean (μ) and standard deviation (σ) of monthly returns (x) for the BHP stock price between January 2001 and December 2008. Express your answers as percentages.
(iii) Using your sample estimates of the mean and standard deviation in part (i) above, what is the probability of observing positive monthly returns for BHP?
(c) Using the monthly returns for the year 2008 as a random sample for any 12-month period, calculate the following:
(i) the sample mean
(ii) the standard deviation of the sample mean
(iii) the probability that the average monthly returns for BHP over any 12-month period will be positive.