The task you are given is to estimate the market risk for a hypothetical holding of 1,000 BHP shares, held on August 2, 2017 (you are working out the risk position assuming that you own these shares at the close of trading that day). You will do this by estimating the Value-at-Risk for the stock using historical data. You will then analyse two hedging strategies using derivatives that will alter the risk of holding these shares.
You will be asked to calculate the following;
- 10 day VaR for the portfolio of shares at a confidence level of 99%.
Based on what you have learnt from EFB344, you realized that you have several options for how to compute this risk measure. You are considering using a VaR based on
- the normal distribution using a 252 day rolling window,
- the normal distribution using the EWMA (lambda = 0.94), or
- historical simulation based on a window of 252 days.
data model is finished
You will then evaluate the appropriateness of these frequencies over time relative to the Basel traffic light levels discussed in lectures. Based on this performance, and any other factors you want to discuss, select the best model and report the required VaR(10, 99%) for August 3, 2017.
Next, you will look at the possibility of hedging your downside risk over the subsequent three months using a portfolio of American put options written on BHP shares that expire in exactly three months.
The current stock price for each is to be taken as the closing price on August 2, 2017. Your portfolio consists of 1,000 shares. Assume that the risk-free rate is currently 2% p.a. continuously compounding. The annual variance can be estimated from historical data using whichever method seems most effective from the VaR analysis above (i.e. – Rolling window vs EWMA).
- Noting that each put option covers 100 shares, determine how many BHP put options you would need to buy to eliminate your downside risk. Next, determine the appropriate price for each of these put options if they are at-the-money. Use a five-step binomial tree for this task.
- Repeat the repricing of all the options if the strike price is 10% below the current market price for each share.
- Determine how much cheaper each of the hedges above would be if you were able to use European options instead.
Presenting your results
- You will then write a brief report of no more than twelve pages including graphs that present your results. A rough outline of what your report could include is
- Present the final VaR(10, 99%) for August 3 2017 based on your preferred model. You must also include some explanation of how these final estimates should be interpreted (what does this VaR number mean).
- A brief description of the final/preferred VaR model you used. This includes the length of any subsamples of data or selection of any fixed parameters.
- Presentation of the main results in the back-testing study. The results should be accompanied with an evaluation of the relative performance of the various models and a clear justification of which model is superior. With this should be a brief description of data (start/end dates, number of observations and details of where you got the data, what the data was (g. – closing prices?), how the data was cleaned (e.g. – non-trading days) and how you calculated returns.
Additional Notes and Instructions
- You will need to source the data yourself. I recommend using Yahoo Finance as was outlined in lecture 2 using the ticker code BHP.ax.
- For the backtest, you will start with the five years of data specified above when you begin your analysis. This is does not mean that you will have five years of VaR numbers and exceedances to compare (you will have less than this). That is ok, you only need to use the data specified.
- Your excel spreadsheet must contain the formulas that you have used for all calculates (e. – don’t paste the values of the main calculations).
Two corrections to the task sheet for the group assignment.
– You are working out the risk as though you hold the 1000 BHP shares at the close of business on August 2. The first sentence of the assignment description has been altered to reflect this.
– You are to assume the options in the second half of the assignment expire in exactly 3 months. The first sentence of the second part of the assignment (below the line) has been altered to reflect this.
Finally, I have decided to upload the solutions for the next tutorial now so as to give everyone a chance to check there work over the break and get going on the second part of the assignment. They are up on Blackboard now.
Criteria and Standards Sheet for Assignment Part A (30 marks)
|Marking Criteria||High Distinction||Distinction||Credit||Pass||Fail||Mark|
|KS (1.1): Demonstrate and apply integrated discipline (including technical) knowledge|
|Demonstrates comprehensive understanding of relevant finance and risk management concepts and techniques.||Demonstrates a developed understanding of relevant finance and risk management concepts and techniques.||Demonstrates a developed understanding of relevant finance and risk management concepts and techniques but with a few errors.||Demonstrates an adequate understanding of relevant finance and risk management concepts and techniques.||Insufficient or inaccurate understanding of relevant finance and risk management concepts and techniques.||/16|
|KS (1.2): Apply technical and technological skills appropriate and effective for real world business contexts|
|Excel Use and Formatting||Document prepared and formatted according to standards required by the subject.||Document generally prepared and formatted according to standards required by the subject, but with a small number of minor errors||Document generally prepared and formatted according to standards required by the subject, but contains some errors||Frequent errors, but displays an ability to prepare and format the document according to standards required by the subject.||Fails to format the document to an appropriate standard required by the subject||/ 5|
|HO (2.2): Exercise independent judgement and initiative in adapting and applying knowledge and skills for effective problem solving|
|Critical Analysis||Provides a clear and well-reasoned justification for the choice of superior risk management model that fully considers the empirical findings.||Provides a strong justification for the choice of superior risk management model that is supported by the empirical findings.||Provides a solid justification for the choice of superior risk management model which is generally consistent with the empirical findings.||Provides only weak justification for the choice of superior risk management model which barely takes account of the empirical findings.||Fails to provide a justification for the choice of superior risk management model and/or the arguments are at odds with the empirical findings.||/4|
|TS (4.2): Apply teamwork knowledge and skills for effective collaboration|
|Work effectively in a team on a finance project||Students will assess their team peers on how effectively they performed in the team and on their contribution to the team product via an online survey. Each student will assess every member of their own team and themselves. Students’ score out of 5 marks on this criterion will reflect the average of the ratings received from their peers and their own rating.||/5|
Overall Grade: HD, D, C, P, F Overall Mark: ________
Comments: An overall mark is awarded to the group, but can be adjusted for individuals at the discretion of the unit coordinator.