Limit your response to 10 pages (including appendix) and submit a spreadsheet with your calculations.

All VaR and Expected Shortfall calculations, unless otherwise stated, are daily and at the 95%

confidence level.

Please also note: there is an associated Excel File “Allocations.xlsx”

Introduction

You are a junior analyst for GAMBLE – a large, high-risk, high leverage hedge fund that specialises in

long-short global multi-asset strategies.

As part of your role, you have been assigned responsibility over monitoring the risks associated with

a small portfolio of securities, detailed in the allocation file on Canvas.

• UOS US Equity – Oil ETF denominated in USD

• QAN AU Equity – Qantas common stock

Given the prevailing market climate of elevated volatility and global uncertainty stemming from the

Coronavirus pandemic, the portfolio managers of the fund are keen not only to understand the market

risks they currently face, but also the strategies that should be implemented to protect the fund

against adverse market movements. You are to prepare a preliminary report for the risk management

committee. The report should cover short-term risk (1-day risk measures using data up to end of

March, 2020).

Tasks:

Part 1 [5 Marks]: Using the historical data, and assuming the current market value of each investment

is $100,000, calculate the

a) individual VaR of each security assuming a Gaussian (i.e. normal) distribution (2 marks)

b) individual VaR and Expected Shortfall of each security assuming the empirical distribution

provided (3 marks)

Part 2 [9 Marks]: Following on from your initial analysis, the portfolios managers would like to monitor

risk at a portfolio level. Specifically, they are interested in the risk metrics for the two-security

portfolio. Assume the portfolio is valued at $200,000 with equal weight allocated to each security.

a) Calculate the VaR of the portfolio as a whole using a Gaussian (i.e. normal) distribution

(2 marks)

b) Calculate the VaR and Expected Shortfall using the empirical distribution provided

(4 marks)

c) Compare these portfolio level results with your individual security-level results in Part 1. What

conclusions can be drawn around the suitability of the VaR and Expected shortfall as portfolio

risk evaluation metrics? (3 marks)

Part 3 [10 marks]: One of the challenges in risk management is estimating and monitoring volatility.

A more rigorous model for estimating and monitoring volatility using historical data is the generalized

autoregressive conditional heteroscedasticity (GARCH) model. You have been asked by the portfolio

managers to examine the performance of a GARCH(1,1) for calculating VaR.

a) Using the portfolio returns that you have calculated in Part 2, model daily portfolio volatility

using a GARCH(1,1), assuming normally distributed returns. The model parameters should be

estimated by maximum likelihood. Present a graph of your volatility forecast along with actual

volatility for comparison. Discuss the appropriateness of the model. (5 marks)

b) Once you have obtained a series of variances, compute a parametric 95% 1-day VaR for each

trading day assuming zero mean. Days when the actual return exceeds the VaR are known as

exceptions. Calculate the number of exceptions (rt − VaRt) given your daily portfolio return

and VaR. (Make sure that you are using the LOSSES only). Has the GARCH(1,1) model resulted

in over- or underestimation of VaR? Should we reject GARCH (1,1) based on a Binomial test?

Discuss your results. (5 marks)

Part 4 [8 Marks]: As the portfolio is currently levered, you are concerned that the portfolio is too risky

and may be liquidated in accordance with its guidelines. To reduce the potential risk, you consider

using call/put options written on QAN.

• QAN AU 5 C3.5 Equity – Qantas call option with a strike price of $3.50 expiring on 28th May

OR

• QAN AU 5 P2 Equity – Qantas put option with a strike price of $2.00 expiring on 28th May

(see the allocation file)

a) Select an appropriate option (call or put) to reduce the exposure of the portfolio. Using an

appropriate methodology discussed in class recalculate the VaR of the portfolio. (5 marks)

b) Comment on the effectiveness of the hedge (3 marks)

Part 5 [18 Marks]: Given the recent volatility, you are concerned about the stability of estimated

coefficients and distributional assumptions you are making in your analysis. For this question, focus

ONLY on your QANTAS and OIL positions (no options), with $100,000 invested into each security – i.e.

for this question, you will be working with a $200,000, two security portfolio.

a) Stress test the correlations of the portfolio using the copula technique discussed in class. First,

map the empirical returns (PDF) into standard uniform variables (CDF). Then simulate returns

by sampling from either a Gaussian or a Student-t joint distribution using appropriate copula

parameters and then map the simulated returns back into their original empirical marginal

distributions to calculate VaR and ES. (5 marks)

b) Carefully justify any decisions regarding Copula selection and methodology in your report

(3 marks)

c) Discuss why detailed study of correlations is relevant to your portfolio. (2 marks)

d) Using appropriate justifications, estimate appropriate copula parameters across high and low

correlation market scenarios (hint: see how the correlation changes through time. You can

define “high” and “low” correlation market structures as above/below median or use another

threshold). (2 marks)

e) Using the above copula parameters, recalculate VaR and ES across these high and low

correlation market scenarios. What observations and conclusions can you draw from your

results? (6 marks)

Additional Hints

• This assignment is deliberately open ended. Do not panic.

• Although 10 pages are allocated for this assessment, we encourage you to answer succinctly – and

wisely utilise the generous page limit for setting out your calculations and methodology.

Specifically, we would like to see clear discussion around the models and formulae used, as well

as the use of tables and charts to clarify your results.

• A substantial proportion of marks will be awarded for discussion around the insights gained from

your analysis, not just descriptive recollections of your methodology. We encourage you to think

about what you are doing, why and the implications of your results.

• There is no limit on what methodologies or analytical frameworks may or may not be applied in

this assignment. It is recommended that full reference to all relevant materials covered in the

course.

• Additional research is not essential even to get full marks, but the task is flexible if students do

want to attempt to go the extra mile. Additional research in the form of plagiarism will result in a

fail.

• Clearly state all your assumptions.

• VaR needs to be stated in AUD

• Mechanical application of various techniques, or discussion that patently lacks understanding

around the underlying methodology is the fastest and most efficient way to fail this assignment.