Risk Management and Derivatives AFIN806

Australian Expert Writers

Group Assignment worth 20%

Due 15thjune 2019

Download the Bloomberg financial data provided on the Macquarie ilearn web page to help prepare responses to these short answer questions about VaR, the VIX and options.

Notes about the Bloomberg data:

The PX_LAST column contains the last price which is the closing price at the end of the trading day.

The PX_LAST data contains errors on dates such as 11 September 2001 and a handful of other dates. To clean the data, sort by PX_LAST then delete the rows which contain erroneous data. Then re-sort the data by date so it’s back to normal and now cleaned. Then you are ready to make another column for continuously compounded daily returns which can be used to answer Question 2 and those that follow.

Question 1a (2 marks, half page): Make a graph of the United States’ VIX (use the series that’s spliced with the old VXO) together with the S&P500 capital and accumulation indices with the two indices on the left hand side (LHS) axis and the VIX on the right hand side (RHS) axis. Index the price and accumulation indices to 100 on 4 Jan 1988. Do not index the VIX. Show the full history of each series in your graph, so your x-axis dates should begin on 30 Dec 1927. For an example of how an indexed graph should look, see this graph, but ignore the log scale:

http://www.rba.gov.au/chart-pack/share-markets.html

Question 1b (1 mark, half page): Make another graph like that above, but use a logarithmic scale on the LHS for the price and accumulation indices. Be sure to crop the vertical axes so that the variation in the series is apparent.

Question 2 (3 marks, half page): Make one graph showing 3 lines:

– Rolling annual historical standard deviations of the S&P500 capital index over the past year at each point in time. Use an equal weight (1/n where n is the days in the year) for each observation.

– Exponentially weighted moving average (EWMA) historical standard deviations per annum of the S&P500 capital index over the past at each point in time. Use a weight of 6% on the newest observation so Lambda is 0.94.

– The VIX.

Show the full history of each series in your graph, so your x-axis dates should begin on 30 Dec 1927. Make sure that the rolling annual standard deviations and EWMA lines are of the past year at each date, not the future year which is obviously unknown at that date.

Question 3a (2 mark, one or two sentences): Provide an interpretation of what the VIX number means. Be as specific as possible.

For example: “The VIX is measured in basis points (bps) per six months and is the historical variance over the past year of a deeply out of the money call option on the S&P500 accumulation index that matures in six months, annualized by multiplying by 2.”

Note that this description is not correct for many reasons, but this level of detail should be aimed for.

Question 3b (2 mark, half page): Find the implied volatility one month ahead using a recent (post-1st Jan 2019) S&P500 index option and briefly describe your calculation. Explain any difference between your estimate and the VIX on that same date. Use sources to justify your answer. State all assumptions.

Question 4ai (1 mark, one sentence): Find the 99.9% parametric absolute daily value-at-risk (VaR) of continuously compounded daily returns on the S&P500 capital index, where the parameters are the daily mean and historical variance over the whole sample of S&P500 daily data.

Question 4aii (1 mark, one sentence): Find the 99.9% parametric absolute daily expected shortfall (ES) of continuously compounded daily returns on the S&P500 capital index, where the parameters are the daily mean and historical variance over the whole sample of S&P500 daily data.

Question 4bi (1 mark, one sentence): Find the 99.9% non-parametric absolute daily value-at-risk (VaR) of continuously compounded daily returns on the S&P500 capital index. The non-parametric VaR is also called the cut-off or percentile method of finding the VaR. Use the whole sample of S&P500 historical data. Interpolate between points for maximum accuracy.

Question 4bii (1 mark, one sentence): Find the 99.9% non-parametric absolute daily expected shortfall (ES) of continuously compounded daily returns on the S&P500 capital index. Use the whole sample of S&P500 historical data. Interpolate between points for maximum accuracy.

Question 4c (1 mark, one sentence): Find the 99.9% non-parametric absolute daily expected shortfall (ES). Use the whole sample of S&P500 historical data. Don’t bother interpolating between points.

Question 5 (5 marks, 2 pages): Estimate the real-world (risk-averse world, not risk neutral world) probability that the S&P500 falls by more than 25% over the next year. State all data, sources and assumptions used in your calculations and explain your reasoning.

Administrative requirements

This report is worth 20% of the course’s marks.

The limit is 5 pages using 1.5 line spacing and default margins, just like this page. The page guide given in each question is just a suggestion, you can go above or below, but you must observe the overall limit.

Supporting images, graphs, tables and so on should be placed in-text next to the paragraph where the figure is discussed. There’s no need for an appendix and if you have one it’s not likely to be marked. You may use any common referencing style you like. Bibliographies are not included in the page count. Items listed in the bibliography but not actually referred to in the report will have marks deducted.

The assignment should be submitted in electronic form to Turnitin which will be made available as a link online.

Assignments that are not proof-read will be marked down. Grammar and sentence structure is important. Business writing should be clear, succinct and front-focused, which means putting the most important points at the very start.

Answer the questions in the order that they are asked. Be sure to include sub-headings that contain the question number.

There’s no need for an introduction or conclusion. This assignment is a collection of short answer questions.

There’s no need to write the whole question in your assignment if you’re struggling to fit everything into the page limit. You may write the question number as a subtitle to show where each question begins. For example:

Question 1: Write answer here.

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