Overview

The task you are given is to estimate the market risk for a 5 year Commonwealth government bond, held on September 2 , 2019 (you are working out the risk position assuming that you own the bond at the close of trading the previous day). You will do this by estimating the Value-at-Risk for the bond. This will require you to choose the best VaR model by backtesting several methods to determine the most reliable for the task at hand.

Description

You will be asked to calculate the following;

• 10 day VaR for the bond at a confidence level of 99%.

Note: This risk estimate applies to the next 10 trading days from September 2, 2019 until September 13, 2019 (i.e.- it should be a forecast of risk).

Based on what you have learnt from EFB344, you are considering several options for how to compute this risk measure,a)the normal distribution using the EWMA for volatility, orb)a normal distribution based on a rolling window for volatility. Both methods require choosing parameters to assign weight to past data,for the EWMA and the window length for the rolling window. You will consider the following;

Normal Distribution (EWMA)

=0.94

Normal Distribution (RW)

Rolling window with 252 trading days.

This leaves you with two possible models that could be used to provide the VaR measure asked for above. You must choose the most appropriate model and report the associated 10 day VaR. To inform your decision of which to use, you are going to consider the recent historical performance of both 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 loss over the period for which you are provided with historical data (approximately five years).

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, select the best model and report the required VaR(10, 99%) for September 2, 2019.

Bond Pricing details and Risk management assumptions

The bond you are dealing with has five years to maturity, with semi-annual coupons at a rate of 4% per annum. The face value of the bond is $1,000,000. When pricing the bond you are to assume that you use a single discount rate for all cash flows (you are provided with data for this rate). This is equivalent to assuming a flat yield curve that always moves in parallel shifts.

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 Blackboard. This file contains a tab with the raw data for the discount rate 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
• Your name and Student number
• The exceedance probabilities for the two models above.
• A graph summarizing the Basel Traffic Light results (such as the one shown in lecture 3).
• Which of the models above is your preferred model based on the backtesting results.
• The final VaR(10,99%) for the portfolio based on your preferred model.
• Anevaluationof the relative performance of the two 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.