QBUS2810

Statistical Modelling for Business

Individual Assignment Task 2

This individual assignment task 2 will contribute 10% towards your final re-sult in the unit. The deadline is Sunday, May 2 nd by 11:59pm. Submission is via Canvas and Turnitin.

Key requirements:

• It is encouraged for you to create your entire assignment in a Jupyter note-book, including your Python code and with Markdown sections for your writ-ten answers, and to submit the resulting downloaded html file as your entire assignment. Care must be taken with presentation for this option, however un-avoidable error messages and page formatting issues will be ignored in marking, as discussed in class.

• Alternatively, you can write/type your answers and copy and paste relevant outputs into a text editor and prepare a pdf file for submission; if you take this latter option then you must include the Python code you developed as an appendix in your report. Failure to provide your Python code will result in penalty and significant loss of marks.

In both cases, only relevant analysis outputs (graphs, tables, etc) should appear in the assignment file, while all output should appear together with, or very close to, the discussion of that output, in the file. Less relevant outputs may be placed in an optional (extra) appendix.

Business problem:

This assignment is a continuation of the analysis conducted in tutorial week 3 regarding financial volatility and how it might change with seasonal effects, e.g. day of the week. In tutorial in week 3 we (mostly) found that realized volatility was not significantly different on Mondays, compared to the rest of the trading week. The framework of ANOVA allows us to investigate if for realized volatility any day of the week is different to any of the other days, and simultaneously also assess other (e.g. season of the year) effects, via a two-way ANOVA model. These are the goals of this assignment. Investors and financial institutions are greatly interested in assessing and measuring risk. The increase in the availability of intra-day data has only increased the focus for these groups in how to measure, model and predict financial risk. Volatility of financial returns plays a major role here, and it is commonplace to report and use daily financial return volatility measures to assess risk. One of the most popular daily measures is called “Realized Volatility” (RV). The RV on any day is the sum of the squared intra-day returns, over a specific time interval; the most common interval employed is 5 minutes, giving the so-called “5 min RV”. Such measures are widely and publicly available, for both individual assets and various financial indices. Here we focus on the 5 min RV series from the ASX 200 index on the Australian Stock Exchange. The data are in the file “ASX Data Final 2000 2016.xlsx” which was provided in tutorial week 3.

Seasonal effects are commonly theorized in finance for financial returns and volatility. So-called “day of the week” effects are commonly analyzed, as are theories such as the “Spring effect”, the “”sunshine effect”, etc. We consider two such theories in this assignment:

• that volatility is different on different trading days of the week; and

• that volatility is different over the seasons of the year: Summer, Spring, Au-tumn, Winter.

You will examine and assess these theories for the ASX market using the daily 5 min RV data from July, 2000 - June, 2016 provided.

Data:

The data to be used in this assignment is “Mydata.csv” provided. This data was created from the data file ”ASX Data Final 2000 2016.xlsx” provided in tutorial week 3 that contains three columns:

• ’Date’, which gives the date the data correspond to;

• ’r data’, which is the log-return on that day;

• ’rv data not scaled’, which is the calculated 5 min RV for that day. Each day’s 5 min RV is meant to be an accurate proxy of return volatility on that day and on the daily scale, i.e. 5 min RV for day t is an estimate of σt2 = V (rt|It−1), where It−1 is the information available at end of day t−1 and rt is the financial (log-) return on day t.

Additional columns were created: (i) Square root of RV on the percentage return scale; (ii) A day of the week indicator; (iii) Dummy variables for each day of the week; (iv) A season indicator and (v) Dummy variables for each season; to create a unique, randomly thinned data set “Mydata.csv” provided.

Questions:

1. Conduct an appropriate exploratory analysis to informally assess the two primary questions: whether the square root of 5 min RV (you may also use the log of the RV as log(Square root of RV)) could be affected by two categorical variables; day of the week and season of the year. Discuss any cleaning or manipulation of the data you did, including why and how you did it. (4 marks)

2. Conduct the two ANOVA tests (α = 0.05), separately, to formally assess the two primary questions here. Show the ANOVA tables, assess/discuss whether the assumptions made could be satisfied, and then formally assess and discuss where any differences lie. (6 marks)

3. Discuss any data cleaning or manipulation of the data you did in Questions 1 and 2, including why and how you did it. (2 marks)

4. Conduct a formal two-way ANOVA (α = 0.05) analysis to assess the effect of day of week and season of year on volatility. Interpret and explain your results. (6 marks)

5. Write a brief (e.g. 0.5 page) report summarising and discussing your findings and conclusions. Include an assessment of how financial volatility levels are affected by the factors you have considered for the ASX. (4 marks)