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# Value at Risk: A Comparative Analysis - PowerPoint PPT Presentation

Value at Risk: A Comparative Analysis. Filip Iorgulescu. Introduction. Why is VaR a challenging subject for me?. - scientific but also practical - easy to understood, difficult to determine - a benchmark with certain shortcomings.

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Presentation Transcript

Filip Iorgulescu

### Introduction

Why is VaR a challenging subject for me?

- scientific but also practical

- easy to understood, difficult to determine

- a benchmark with certain shortcomings

VaR - the number that measures risk, so popular it may not need an introduction

The objective: to develop a comparison between different approaches to VaR by the means of a portfolio consisting of three stocks traded at BSE

### The Methodology

• The analysis focuses on two aspects that are taken into account when computing VaR:

- the volatility models

- the distributional approaches

It was considered that T = 1 day and p = 1%

Mainly based on Christoffersen (2002) and Codirlasu (2007)

Therefore, I set out from 1-day, 1% VaR formula

VaR1% = - (Q1%σ + μ)S

• Historical volatility

• EWMA volatility model for the three stocks

• GARCH volatility model for the portfolio

• GARCH volatility models for the three stocks

• GARCH volatility models for the stocks along with a dynamic conditional correlation model

• Standard N distribution

• Historical quantile (last 750 days)

• t-Student, NIG and GH distributions

• CF approximation

• Extreme Value Theory. ES measure was also considered

The following approaches were considered:

### Welcome to the Championship of VaR measures!!!

The pitch is ready… all the tickets are sold…

The computed VaR measures were examined according to the following criteria:

- precision

- level of capital coverage

- calculation requirements

### Meet the players – The Data

Period: 5 Jan 2001 – 9 May 2008

• Main features:

- Volatility clustering => conditional volatility models are recommended

- Non-normality => other distributional approaches are needed

- No unit roots

A portfolio consisting of three stocks with equal weights: ATB, AZO and TLV. Arguments:

quoted at Category 1 at BSE

diversification across industries

### Group 1 – Historical volatility

Historical volatility approach

VaR GHD seems to be the most appropriate choice under historical volatility approach.

• Simplest volatility approach

• Good precision results

• Strictly dependent on these portfolio allocations

• Rather high capital coverage levels

### Group 2 – EWMA volatility historical volatility approach.

ES EVT seems to be the most appropriate choice under EWMA volatility approach.

• Lower capital coverage

• No estimations for λ

• No strict dependence on current allocations

• Very weak precision results

• Carries the limitations of EWMA model

### Group 3 – GARCH for the portfolio historical volatility approach.

VaR GHD seems to be the most appropriate choice under GARCH (portfolio) volatility approach.

• Lower capital coverage

• Very good precision

• No difficult calculations required

• Strictly dependent on these portfolio allocations

### Group 4 – GARCH for the stocks historical volatility approach.

VaR NIG seems to be the most appropriate choice under GARCH (stocks) volatility approach.

• Lower capital coverage

• No strict dependence on current allocations

• Weak precision results

• For large portfolios many estimations are needed

### Group 5 – GARCH DCC historical volatility approach.

VaR GHD seems to be the most appropriate choice under GARCH DCC volatility approach.

• Lower capital coverage

• Good precision results

• No strict dependence on current allocations

• For large portfolios the estimation of the variance and correlation models is very difficult

### Conclusions – The Semifinals

• GARCH portfolio has the advantage of precision and smaller calculation effort, but is strictly dependent on current portfolio allocations.

• GARCH DCC has the advantage of lower capital coverage but requires many estimations

### Conclusions – The Final useful

• VaR GHD under GARCH DCC volatility approach may be considered the “best” risk measure for the analyzed portfolio and the chosen period. Yet, is the effort of estimating a DCC model worth the decrease from 5.21% to 5.07%?

• Using more improved volatility models tends to reduce the level of capital coverage

• It is recommended to use other distributional approaches to deal with the non-normality of the returns

• CF approximation tends to overestimate risk leading to very high levels of capital coverage

• NIG and GHD seem to be reasonable distributional approaches

• VaR under the EVT approach does not perform very well, while ES leads to nice precision results but at the cost of high levels of capital coverage. Other threshold values should be also considered.