Aalto University School of Science and Technology Faculty of Information and Natural Sciences Timo Pekkala, 63016P Value at Risk in Bank Risk Management Mat-2.4108 Independent Research Projects in Applied Mathematics Helsinki, June 6, 2010 Contents 1 Introduction3 2 Value at Risk Methodology3 2.1 A Case for Holistic Risk Management..............5 2.2 Quantifying Tail Events.....................6 2.3 Practical Implementations of Value at Risk...........7 2.4 Common Criticism........................9 2.5 Improving on the RiskMetrics Value at Risk.......... 12 2.5.1 Accurate Market Models................. 12 2.5.2 Sophisticated Metrics................... 13 2.5.3 Computational Efficiency................. 13 3 Performance and Role of Value at Risk in Banks 14 3.1 Goodnes of the Value at Risk Figures.............. 15 3.2 Benchmarking Value at Risk................... 16 3.3 Value at Risk Deficiencies.................... 17 4 Conclusions and Future Outlook 18 2 1 INTRODUCTION 3 1 Introduction This research project discusses a popular risk measurement methodology known as Value at Risk and its use in bank risk management. Value at Risk is an approach to risk management that gained popularity rapidly as the method was introduced and formalized by RiskMetrics in the middle of the 1990's. The methodology is introduced here in the extent that is necessary in order to assess its the suitability and performance in risk management. An emphasis is placed on assessing the method's suitability for bank risk management. Its strengths are introduced and a fair account of publicly presented criticism is given. We also take note of how VaR methods have withstood the recent financial crisis. 2 Value at Risk Methodology Value at Risk (VaR) methodology aims to quantify the level of the worst case outcomes in a situation where the future is uncertain. VaR is defined as a threshold value that the losses should not exceed in a given time period and a given confidence level. This principle is laid out in figure1. The figure represents schematically the distribution of possible outcomes of a stochastic process. The VaR threshold value limits the left tail of the distribution. The outcome of the process hits the grayed out portion only in 5% of cases. This general approach can be applied to uncertain returns of financial assets as well as to different physical processes whose risks need to be quantified. The definition of the VaR measure is theoretical in that VaR is agnostic to the underlying process. One can calculate a VaR value for many different things: a manufacturing company might asses its operations by estimating VaR of the yield of an important key process, for instance. Employing VaR requires a certain degree of stochastic modeling regarding the underlying process. Modeling complex real-world phenomena can therefore be a daunting task. In finance, however, the processes are often simpler, data is readily available and it is relatively easy to analyze. It is therefore natural that VaR methods 2 VALUE AT RISK METHODOLOGY 4 0,2 VaR 95% 0,1 -4 -3 -2 -1 0 1 Figure 1: A graphical presentation of the VaR measure. have found wide adoption in the banking and finance industry, and in risk management departments of those organizations in particular. As for using VaR in finance, many approaches exist. In this study we concen- trate on methods used to determine VaR for the trading book of a commercial bank. Use of VaR in the financial industry has its roots in the developments of the 20th century. VaR can be seen as a logical continuation of the growing complexity of financial instruments and the tightening regulatory environ- ment of the last century. Damodaran(2008) gives a short history of VaR noting that \the impetus for the use of VaR measures [...] came from the crises that beset financial service firms over time and the regulatory responses to these crises". Damodaran has an emphasis on the US regulatory environment. The first of the crises is said to be the Great Depression, during which bank failures led to regulations limiting the level of borrowing in terms of the banks equity capital. The next step of the development of the current regulatory environment came through in the 1970's, when exchange rates were allowed to float and the derivatives market started to operate in a significant scale. This led to a refinement of capital requirements by dividing financial assets into different classes, each with different capital requirements. Different asset classes would from then on require different risk management practices. Damodaran places the first VaR-like regulatory measure to he 1980's, when \the [Securities Exchange Commission (SEC)] tied the capital requirements 2 VALUE AT RISK METHODOLOGY 5 of financial service firms to the losses that would be incurred [] with 95% con- fidence over a thirty-day interval". According to the author, this approach spurred the development of bank internal measurement techniques that re- sembled that introduced by the SEC. The term Value at Risk was not used to describe these techniques. Not until 1995, when J.P. Morgan published their internal results of analyses \accross various security and asset classes". They coined the term Value at Risk to describe the new metric. The method was widely accepted, in part because of the collapse of the British invest- ment bank Barings (Damodaran, 2008; Wikipedia, 2010a). The failure of Barings made the need for more effective risk management measures even more apparent. 2.1 A Case for Holistic Risk Management The growing trading book of banks and the ever-growing use of derivative products in both commercial banks and investment banks has been the prominent trend in the 1990's and in the 21st century. The case of Long Term Capital Management (LTCM) is indicative of this trend in that it tells the tale of a hedge fund's use of aggressive trading strategies in an envi- ronment that lacks sufficient regulation. The consequences shook the whole industry and were a catalyst for even wider penetration of the VaR model in the financial industry. LTCM was a hedge fund founded in 1993 by John Meriwether and a team of prestigious partners. The funds goal was to seek funds from few high net worth individuals and institutions, which enabled it to operate without much financial regulation and to use very aggressive trading strategies to achieve high returns. The fund did amass capital quickly. Its trading strategies included different sorts of arbitrage trading and investment in developing regions. Specifically the fund seeked to take advantage of arbitrage opportunities between certain equity and fixed income pairs by taking both long and short positions and betting on the future development of the correlation of that pair. 2 VALUE AT RISK METHODOLOGY 6 Such strategies did indeed generate a hefty profit in the first years of the funds operations. In the late 1990's the fund started making losses, which was aggravated by the Russian Government bonds defaulting in 1998. In order to survive these initial losses LTCM had to liquidate important positions, thus further worsening the situation. This liquidation spree demolished several of the betting strategies the fund had built on certain asset pairs. The situation LTCM had gotten itself into was severe from the standpoint of the total industry. Therefore the fund was bailed out by other prominent industry participants and the Federal Reserve Bank of New York in order to avoid a total melt down of the market possibly induced by the fund liqui- dating all of its assets. At the end, the new shareholders of the fund were successful at liquidating the fund over a longer period of time with minimal losses. The case of LTCM shows the potentially detrimental effect of betting on the dynamics of the market | and on the correlations of assets in particular. The expected returns from these kinds of strategies are minuscule in relation to the potential losses. Quantifying the risks associated with such strategies properly could have made the situation more apparent to all stakeholders involved with LTCM, and the market at whole. And indeed, VaR models were seen as an improvement after the demise of LTCM and they gained in popularity quickly (Damodaran, 2008). The problems LTCM caused were severe on a industry level scale. The losses would not have harmed the shareholders alone, but could have potentially caused havoc in Wall Street. That, although no regulation was imposed on a fund operating with the clientele LTCM was operating with. The failure of the fund led eventually to SEC mandating banks to use their own VaR models in assessing the banks' capital requirements. 2.2 Quantifying Tail Events As noted in the previous section, VaR gives a value for a certain quantile of the distribution that is being investigated. This section specifies some 2 VALUE AT RISK METHODOLOGY 7 methods that are commonly used to achieve this. 2.3 Practical Implementations of Value at Risk The definition of VaR is indifferent in terms of the underlying market model or means of calculation. There are many different approaches to calculating the threshold value that defines the chosen quantile. These methods differ in terms of whether an empirical or a theoretical distribution is used, and on how the underlying measure is calculated. Let us now concentrate on the value of portfolio of financial assets for the remainder of this study. More accurately, let the return of that portfolio be the value of interest. The most basic approach is to analyze the historical values of the returns. Say, take the 1.000 most recent daily returns and determine the 99% VaR over a one day period. This task is taken care by simply putting the daily return observations in order and choosing the 990th value.