Although Hong Kong market had experienced large extend of uncertainty, often such things can also provide opportunities for investors. As a first step, an investor considering the Hong Kong share market, examines the long term continuous returns for the Hang Seng. Use Excel's Data Analysis/Descriptive Statistics to find the Hang Seng monthly returns from start of 1991 until March 2021.

(a)Calculate the 95% confidence interval for the monthly returns for the Hang Seng over this period.

(b)As the investor is concerned about the possibility of negative returns, test to see whether the average monthly returns for the Hang Seng are less than or equal to zero.[1] Making reference to this hypothesis test, briefly discuss whether the investor should be worried about the possibility of negative returns if they invest in the Hong Kong share market. Discuss type 1 and type 2 error and how they may relate to this hypothesis test.

(c)Test to see whether the monthly returns on the Hang Seng over this period are normally distributed using the Jarque-Bera test. This should be done in Excel, by calculating the Jarque-Bera statistic using the formulas from the notes and Data Analysis/Descriptive Statistics.^[2] Using the results of this test, comment on the accuracy of the probabilities calculated in parts (a) and (b) of this question.

(d)Calculate and comment the skewness of the Hang Seng monthly returns over the sample period. Explain why this is the case and the implications for investment decisions.

(e)Using the continuous returns on the Hang Seng, determine whether the rises and falls are independent using a runs test. What are the implications of your findings?

[1] Use a level of significance of a = 0.05 for this and all other tests in this assignment.

[2] Note that when Excel calculates kurtosis it subtracts 3 from the value.