Quantitative Business Analysis
The data collected for Task 1 will be used for Task 2 and 3 for further analysis. Use the link http://au.finance.yahoo.com/q?s=^AORD to download All Ordinaries Index data for the period from 2/January/2009 to 30/April/2013. This period is hereafter called the study period.
The data contains information of Date, Open, High, Low, Close, Volume, and Adjust Close. Use Date, Volume, and Adjust Close data for this assignment.
– The first trading day of the study period is date 1. The prior trading day to date 1 is date 0. Index the date using the first trading day of the study period as date 1 and the next trading day as date 2, ect. To compute the daily return for date 1, you need to find the Adjust Close of date 0. But the data of date 0 is not used in Task 2 and 3.
– Compute the daily return for the All Ordinaries Index using the following formula: , where Xt is the All Ordinaries Index at date t and Rt is the daily return.
– Obtain relevant descriptive statistics for the daily return during the study period.
– Use an appropriate chart (one chart only) to display the distribution of the daily return.
Task 2 (10 points)
Separate the data into two groups. Group 1: Rt is positive. Group 2: Rt is negative. Compute the sample mean and sample standard deviation of the volume for each group. Perform a statistical test to investigate the hypothesis that “on the trading day when the All Ordinaries Index increases (i.e., Rt is positive), the trading volume is larger than the trading day when the All Ordinaries Index decreases.”
Task 3 (25 points)
Use the data of Adjust Close and Date to perform a regression analysis. Run a regression using the time index t as the independent variable and the All Ordinaries Index (Xt) as the dependent variable.
– Show your regression results, which should include the regression equation and R-square.
– Interpret the regression coefficient.
– Perform the Durbin-Watson test with a=0.05 and state your conclusions. (The relevant critical values are dL=1.899 and dU=1.904.)
– Perform relevant tests or procedures to verify whether the assumptions of regression are satisfied.
– Compute the 90% prediction interval for all trading days in the study period.
– Display the data of Xt, the fitted line based on the regression model, the lower and upper bounds of the prediction interval on a time-series plot.
Task 4 (5 points)
Write a summary (no more than 500 words) about what you find from the analysis of Tasks 1, 2, and 3.