Excerpt

## Contents

1. Why should we measure risk?

2. Understanding the concept ofValue at Risk

2.1 How to define risk

2.2 Defining the Value at Risk concept

2.3 Calculating the Value at Risk

2.4 Critical view on the concept of Value at Risk

3. Using Value at Risk in practice

3.1 Value at Risk in banking regulation

3.2 Value at Risk in internal risk management processes

4. Further development of the concept

Reference List II

## 1. Why should we measure risk?

Higher volatility in exchange markets, credit defaults, even endangering countries, and the call for more regulation drastically changed the circumstances in which banks have to perform. Such situations of uncertainty are called risks and managing them is one of the main tasks of banks, either taking them themselves or transferring them through the market. But not only banks are interested in managing their risks, regulators also want to force the banks to minimize their risks to prevent them from failing. Furthermore, investors also want to compare different banks in case of their risk-performance relation for their investment decision. Nowadays even ordinary companies are forced by law, the so called “Gesetz zur Kontrolle und Transparenz”, in short “KonTraG”, to implement a risk management.

But how is it possible to manage or measure such a hard to defining term like „risk“? To solve this problem and giving the stakeholders above a tool to measure their individual risk or to compare it, an empirical risk measurer called „Value at Risk“ is used in practice. The main task of this work is to introduce the concept of Value at Risk and giving an overview about the concept itself, its problems and its use in practice.

At first in chapter 2 an introduction into the definition of risk itself and the Value at Risk concept is given, closing with a critical view on it. Afterwards, chapter 3 will show you how the Value at Risk is used in practice, first from an external view from the perspective of a bank, the view of the regulators. In a next step we will have a look on the internal view of a bank and how the Value at Risk is used to evaluate their own performances. Finally Chapter 4 will give you a small insight of further development of the concept.

## 2. Understanding the concept of Value at Risk

### 2.1 How to define risk

Before introducing the concept of Value at Risk, we have to define what risk actually means. In a general way risk can be defined as a danger to the goals and strategies of a company because of decisions and actions made under uncertainty.^{[1]} In banking practice it is possible to categorize risk in four different kinds, namely market risk, credit risk, operational risk and business risk.^{[2]} Market risk can be defined as the change in the financial situation of a company because of the volatility of stock exchange prices, interest rates, exchange rates or commodity prices.^{[3]} Especially the market risk created by the volatility of share prices will be a main focus in the next chapters, when introducing the Value at Risk concept. Of course it can also be applied on other market risks. Managing market risks is especially important for banks, because they endanger the value of their portfolio of securities. Credit risk can be defined as the change in value of a credit portfolio because of unexpected losses and credit defaults.^{[4]} Especially commercial banks are interested in measuring credit risk because of their main function in giving loans to companies and individuals. That is why they use rating agencies to check the credit-worthiness of those stakeholders.^{[5]} The third risk category contains operational risk. It describes risks that endanger the daily operational businesses, e.g. in the production process. Reasons are mostly human errors or fraud, as seen in the financial crisis.^{[6]} Business risk results from changing sales prices and sales volumes. Atypical example is the change in demand in the producing sector.^{[7]} In banks they refer to the changes in profit based on fees, e.g. from advisory, asset management or payment services.^{[8]} This should have given you an short overview about the risks that face banks. In a next step we will introduce the concept ofValue at Risk and apply it to the market risk.

### 2.2 Defining the Value at Risk concept

Historically, the concept of Value at Risk was developed by J.P. Morgan as a concept to simplify the risk measurement and management processes. Before the introduction of the concept, they used a great amount of different risk measurers, enlarging the daily riskreports, but not providing any significant management uses. By using Value at Risk, it was possible to aggregate the risks providing a single number for the top management.^{[9]} The basic question behind the concept is always „How much can we lose at a given certainty in a given time by our trading portfolio?“. So it describes the possible loss at a certain confidence level with a certain time horizon.^{[10]} The confidence level is the probability that the loss will not exceed the Value at Risk. Value at Risk is a downside risk measurer based on a statistical model. It is calculated from the probability distribution of gains, e.g. from a portfolio. Downside means that Value at Risk simply considers negative gains, the losses, but not extremely high yields. Volatility on the other side measurers both, up- and downside risk. At first we will have a closer look on the different parameters this concept is existing of. These are the assumption about the distribution of the change in value of the portfolio, the confidence level and the time horizon. A common assumption about the distribution of the changes in value of the portfolio is the normal distribution N~(p; o2) with a standard deviation of o, a variance of 02 and a mean of p. The mean shows the value that can be expected in average over a large number of random variables. The standard deviation shows the variability of the change in value of the portfolio.^{[11]} It should be kept in mind, that the normal distribution is just an approximation and sometimes other distributions are better approximations. But using such a parametric concept simplifies the process in calculating Value at Risk.^{[12]} Next part is the confidence level. It has to be chosen by the user of the concept. It shows the risk appetite of a bank, because if the loss exceeds the Value at Risk, the bank would be bankrupt.^{[13]} Common levels that are used are a 99% confidence level, because it is also used by regulators, and a 95% level.^{[14]} This means, that with a 99% certainty, a potential loss in the time horizon won' t exceed the Value at Risk. Third part is the time horizon. The user of the concept has to choose the time horizon he wants to calculate the Value at Risk on. The choice of the time horizon depends on the application of the concept. For actively and daily managed portfolios it makes sense to calculate a daily Value at Risk. Less actively managed portfolios e.g. pension funds can also be calculated on a monthly base.^{[15]} In the following chart you can see a normal distribution of earnings of a portfolio. The grey area shows the certainty, that the losses exceed the Value at Risk, which is a, because the confidence level is calculated by 1- a.^{[16]}

Abbildung in dieser Leseprobe nicht enthalten

Image 1:example of normal distribution (see Bessis [Risk Management] 93, slightly changed)

Summarized we are getting the following formula on calculating Value at Risk:

VaR — market value * a* z*4t

where the market value is the actual value of the position on the market, о is the standard deviation, z is the factor of the normal distribution at a setted confidence level with a probability of a and t is the setted time horizon.^{[17]} In the next section we will use this model step by step and show how Value at Risk can be calculated in practice.

### 2.3 Calculating the Value atRisk

Calculating the Value at Risk in practice follows the next steps. At first the portfolio will be valuated, which is done by multiplying the number of assets with their respective market prices, calling this process „mark to market“. Next the variability о will be measured. The user of the concept will set the time horizon he wants to calculate the Value at Risk on, as well as his preferred confidence level. By using the above formula we will get the Value at Risk.^{[18]} For example: estimate a portfolio consisting of 50 shares A and 100 shares B, with market prices of 10€ and 5€ respectively, with normal distributed change in earnings. So the value of the portfolio is 1000€. Estimate the portfolio standard deviation is 2% and we want to calculate the Value at Risk for a time horizon of 10 days with a confidence level of 99%. So we have a market value of 1000€, a о of 0,02, an a of 0,01, which leads to a 2,33 factor of the normal distribution and a tof10.By using the above formula we get:

VaR—1000 € *0,02 *2,33*410 —147,36 €

As a solution we can say: „With a 99% certainty we will not lose more than 147,36€ in the next ten trading days. Now that we know the basics of this concept, we can continue with a critical view on it, checking the benefits and problems.

### 2.4 Critical view on the concept of Value at Risk

That the concept of Value at Risk is nowadays a widely used tool for calculating economic capital and is also acknowledged by regulators must have its reasons.^{[19]}

**[...]**

^{[1]} See Reichmann [Controlling] 623.

^{[2]} See Fricke [VaR] 8.

^{[3]} See Jorion [Value at Risk] 76 and Fricke [VaR] 8.

^{[4]} See Saita [Bank Capital Management] 67.

^{[5]} See Fricke [VaR] 9.

^{[6]} See Saita [Bank Capital Management] 115.

^{[7]} See Fricke [VaR] 10.

^{[8]} See Saita [Bank Capital Management] 115.

^{[9]} See Hull [Risk Management] 158.

^{[10]} See Hull [Risk Management] 157.

^{[11]} See Jorion [Value at Risk] 107.

^{[12]} See Jorion [Value at Risk] 110.

^{[13]} See Bessis [Risk Management] 86.

^{[14]} See Völker [Value-at-Risk-Modelle] 70.

^{[15]} See Hull [Risk Management] 166.

^{[16]} See Völker [Value-at-Risk-Modelle] 72.

^{[17]} See Hager [Cash Flow] 55.

^{[18]} See Jorion [Value at Risk] 107.

^{[19]} See Fricke [VaR] 16.

- Quote paper
- Fabian Kremer (Author), 2013, Concept of Value at Risk (VaR), Munich, GRIN Verlag, https://www.grin.com/document/232538

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