Please use the data in the "Data-Part2" tab of homework data file for this exercise.
1. Assume the Hang Seng Index returns follow an i.i.d. normal distribution. Given the index data in the "DataPart2" tab, construct 95% and 99% confidence intervals for the population mean of the Hang Seng Index returns. Explain what distribution you should use to construct the confidence interval (Student-t or normal distribution)? Explain how to interpret the confidence intervals.
2. Following the assumptions in Q1, construct a hypothesis testing to evaluate whether the variance of HSI returns is less than 1% per month. Choose 10% level of significance.
Hint: You can use excel function CHISQ.INV to calculate the critical point for hypothesis testing.
Please use the data in the "Data-Part5" tab of homework data file for this exercise. Read the following background information first.
Background: The most important economic release in the US is the job report. At 8:30 pm of every first Friday of every month, the US Labor Department reports the previous month's unemployment rate and number of jobs (payroll) gained or lost. About one week before the release, economists from dozens of big financial institutions submitted their forecasts to the media (i.e., Bloomberg). The median of these forecast payroll numbers form the so called market consensus. In the Friday morning, if actual payroll number released is significantly different from the consensus, the stock market, bond market, and foreign exchange market could move significantly. In this exercise we are going to see how this payroll surprise may impact the bond market through 10 year treasury rate. We will organize data to run the following regression:
Delta (10 year treasury rate) = alpha + beta*payroll surprise + error term
Delta (10 year treasury rate)= 10 year treasury rate of the release date - 10 year treasury rate of the date prior the release date;
Payroll surprise = actual payroll release – consensus
Intuitively, payroll surprise > 0 implies that job market and the general economy is stronger than economists have expected, and so market would expect the Fed to have more reasons to raise interest rate forward, this implies that beta>0.
The excel file “part3_data.xls” includes four variables: “date”, “treasury_10y_dif”, “payroll_surprise”, and
"payroll_revision_previous_month". “treasury_10y_dif” represents delta (10 year treasury rate) which is Delta_treasury_10y below.
Now please work out the following questions (please use 1% level of significance as reference):
1. Run the regression model and discuss briefly your results based on the above background information:
Delta_treasury_10y = b0 + b1*payroll_surprise + error term.
2. Run another regression by adding payroll_revision_previous_month as an independent variable and discuss briefly your result:
Delta_treasury_10y = b0 + b1*payroll_surprise + b2*payroll_revision_previous_month + error term.