Market Risk Quantification of the Equity Portfolio by Applying VaR

Rong Huang

Master's thesis

Abstract:

The main purpose of this thesis is to quantify and explain the maximum expected loss of a portfolio where the selected underlying asset is a stock by using a VaR model. More precisely, this paper examines a portfolio of seven stocks publicly traded in the U.S. and still available, and measures equity risk, i.e., calculates the maximum expected loss, based on daily returns from stock price changes over a cross-sectional period of four years, and a specified confidence level. All stock markets are approximated by their daily major stock indices. This thesis is divided into five chapters, which are structured as follows. Chapter 1 is the introduction, focusing on the main purpose of this thesis and the structure. In the second chapter, we will learn about the basic characteristics of the selected seven stocks and the global stock market as they are the most important part of the economy from the beginning. Particularly highlighted in the subchapter on global stock markets are three events that have occurred during the last four years, 2016-2020, that have affected global stock prices. Chapter 3 will introduce the three most famous and widely used models for quantifying VaR in market risk, while the normal distribution as the basis of VaR will also be introduced. Specifically, this chapter will introduce the basics of VaR models, the calculation of extended VaR models, the basics of the normal distribution and the sensitivity analysis of the three VaR results. In Chapter 4, based on the models mentioned in Chapter 3, we will apply the normal distribution calculation, the historical simulation VaR, the variance-covariance VaR method and the Monte Carlo VaR approach to study the expected maximum loss of the portfolio. The outcomes of each method will be presented graphically. Finally, we will compare and interpret the results of each model and summarize the obtained results. In the final chapter, the full conclusion will be given.

Abstract:

The main purpose of this thesis is to quantify and explain the maximum expected loss of a portfolio where the selected underlying asset is a stock by using a VaR model. More precisely, this paper examines a portfolio of seven stocks publicly traded in the U.S. and still available, and measures equity risk, i.e., calculates the maximum expected loss, based on daily returns from stock price changes over a cross-sectional period of four years, and a specified confidence level. All stock markets are approximated by their daily major stock indices. This thesis is divided into five chapters, which are structured as follows. Chapter 1 is the introduction, focusing on the main purpose of this thesis and the structure. In the second chapter, we will learn about the basic characteristics of the selected seven stocks and the global stock market as they are the most important part of the economy from the beginning. Particularly highlighted in the subchapter on global stock markets are three events that have occurred during the last four years, 2016-2020, that have affected global stock prices. Chapter 3 will introduce the three most famous and widely used models for quantifying VaR in market risk, while the normal distribution as the basis of VaR will also be introduced. Specifically, this chapter will introduce the basics of VaR models, the calculation of extended VaR models, the basics of the normal distribution and the sensitivity analysis of the three VaR results. In Chapter 4, based on the models mentioned in Chapter 3, we will apply the normal distribution calculation, the historical simulation VaR, the variance-covariance VaR method and the Monte Carlo VaR approach to study the expected maximum loss of the portfolio. The outcomes of each method will be presented graphically. Finally, we will compare and interpret the results of each model and summarize the obtained results. In the final chapter, the full conclusion will be given.

Keywords

Value at Risk, Monte Carlo simulation, historical approach, variance-covariance approach, confidence level, market risk

Keywords

Value at Risk, Monte Carlo simulation, historical approach, variance-covariance approach, confidence level, market risk

Language used: English

Date on which the thesis was submitted / produced: 23. 4. 2021

Thesis defence

• Date of defence: 24. 5. 2021
• Supervisor: Miroslav Čulík
• Reader: Petr Gurný

VSB – Technical University of Ostrava

Ekonomická fakulta

Master programme:
Finance