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EFB344 Assignment - Part A

Due: Wednesday the 18^th of October, 2023 at 11:59pm

Weight: 30% of the overall unit

Note: This is an individual assignment.

Overview

The task you are given is to estimate the market risk for a hypothetical holding of 1,000 Coles shares (ticker code COL.ax), held on September 4, 2023 (you are working out the risk position assuming that you own these shares at the open of trading that day).  You will do this by estimating the Value-at-Risk for the stock using historical data.  

Description

You will be asked to calculate the following;

-  10 day VaR for the portfolio of shares at a confidence level of 99%.

Note: This risk estimate applies to the next 10 trading days from September 4, 2023 until September 15, 2023 (i.e. – it should be a forecast of risk).

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

a) the normal distribution using a 252 day rolling window,

b) the normal distribution using a 66  day rolling window,

c) the normal distribution using the EWMA (lambda = 0.94),

d) historical simulation based on a window of 252 days, or

e) historical simulation based on a window of 66  days.

To aid in the decision of which to use, you are going to consider the recent historical performance of the five models in calculating 1 day VaR at the confidence level of 99%.  You will do so by first examining the frequency of instances when the VaR was exceeded by the observed return using the last five years of data.  

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 September 4, 2023.

Presenting your results

- You are to conduct your analysis in a copy of the Excel file “Assignment_Part_A – Data and Results.xlsx” provided on the Canvas page.  This file contains a tab with the raw for historical Coles share prices as well as a front page for you to summarize your results.  All working is to be contained in the subsequent tabs.

- The front tab asks you to provide the following

o Your name and Student number

o The exceedance probabilities for the five models above.

o A graph summarizing the Basel Traffic Light results (such as the one shown in lecture 3).

o Which of the models above is your preferred model based on the backtesting results.

o The final VaR(10,99%) for the stock based on your preferred model.

o An evaluation of the relative performance of the five models and a clear justification of which model is superior based on your backtesting.  This is essentially a discussion of how you should interpret the backtesting results in order to select the most appropriate model.  This should be no more than 300 words.

- Your excel file should be formatted in a reasonably clear way, so that someone who was given the same job after you would be able to understand your working and replicate what you have done.

Details of Submission

- Submit the Excel file through the assignment portal that is available on the EFB344 Risk Management and Derivatives Canvas site. Please include your name and student number in the file name of your document.  

Additional Notes and Instructions

- I have sourced the raw data for you from Yahoo finance.  You will need to make it suitable for analysis.

- Your excel spreadsheet must contain the formulas that you have used for all calculations (i.e. – don’t paste the values for the calculations).  

- There is an Excel file available on Canvas (called “Excel guide.xlsx”) that includes instructions for how to do several useful things in excel.  It also includes some informative examples which might be of interest.  Please look at this file.

- A few hints that will help stop people going down the wrong path;

o In theory, you should use arithmetic returns as you are constructing a portfolio, but I don’t mind if you use log returns (the results will be very similar).

o You can assume that the mean returns are zero as discussed in the lectures.  Alternatively, you can estimate them from the data.  However, you should not use a time-varying estimate of the mean.  The reason is that we don’t think the true value changes over time in the same way the volatility does, so any variation is likely to be random noise.

o You should initialise your EWMA using the sample variance/covariance of the first 252 daily returns.  This will enable you to produce the same number of potential exceedances for both models.

o While you have around five years of data, you will only be able to produce around four years of VaR estimates, and your Basel Traffic lights can only be calculated for around three years.  This should become clear as you go through the process of calculating what is asked for

If you have any questions about any of this, please ask them!!!!