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Expected Shortfall and VaR--Complementary or Substitute

Author: SunYang
Tutor: ZhouLiZuo
School: Southwestern University of Finance and Economics
Course: Finance
Keywords: Expected shortfall VAR Subadditivity Fat tail risk Portfolio Optimization Economic capital Monte Carlo simulation
CLC: F830
Type: Master's thesis
Year: 2009
Downloads: 70
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Abstract

The purpose of this paper is to discuss two VAR and ES risk metrics in theoretical completeness and select the relationship in dealing with specific risk management issues - complementary or alternative. The VAR the concept first appeared in the 1980s, that time, the number of large financial institutions for holding some portfolio risk assessment. Since then, the VAR method in the field of financial risk management began rapid promotion. The VAR first use just to assess and manage the market risk of derivative financial instruments. In October 1994, JPMorgan exposed to the industry they RiskMetrics system, this event is a great promotion VAR method further application in the field of risk management. Various types of financial institutions and financial regulators caught VAR approach to risk measurement and management purposes. In the recent ten years, VAR range of applications in the field of risk management to continue to expand, and achieved great success, and has been very widely accepted and recognized. However, the criticism of the VAR this risk metrics and questioned almost simultaneously, and the concept was born. Much appreciated, while the merits of the VAR VAR implied by the concept itself, but also had to bear the risk. Theorists admit VAR is an imperfect concept, a result, a number of scholars have been seeking and developing new, able to compensate for the the VAR defect risk measure. For these problems, many scholars from both theoretical and practical aspects of certain remedy, from which a series of new risk metrics (alternative risk measure) Conditional-VAR Expected shortfall, the Relative-VAR Worst conditional expectation, Tail conditional expectation and more. We believe that all these new indicators, Expected shortfall is most worthy of attention because of the following four points: First, the good physical properties of ES number to meet the requirements of consistency Risk Measures \ES definition is simple, easy to understand, and relatively simple calculation and practical application; once again, the VAR problems faced in practical applications, the most abundant ES supplementary means of settlement; Finally, do not give up in the industry the VAR as mainstream risk under the premise of metrics, ES emerging indicators VAR relationship recently, most intuitive, therefore, it is more likely to be accepted by the industry and the application. We first begin from the mathematical definition of the VAR and ES, discuss and study its mathematical properties. VAR's lack of consistency this problem, theorists have a more consistent view this article for discussion of this issue is only intended as a general reference to results of previous studies. For the the ES risk metrics generation and development process, we have the following observations: theoretical circles for the study conducted by the ES clutter, the lack of a clear context. Therefore, should this problem be solved at least to be done to improve. We have access to a lot of literature, trying to proceed from the most classic, most mainstream literature, seize ES emergence and development of the main line, and its relatively accurate definition, and its better than the characteristics of the VAR-depth explanations, so as to The next step, that the basis for discussion of the choice of the VAR deal with practical problems and ES. On the basis of a comparative study of the mathematical properties of the VAR and ES, we further efforts to deal with the other problems exist in financial risk management theorists, ES as a new generation of risk than the VAR metrics, and how should it look at it, That actually worked, how to deal with it and VAR relationship? Currently, the major debate is whether thoroughly with ES alternative VAR, thus becoming the new risk measure, risk management work; Or as species complement and improve the means used in conjunction with the VAR, and their respective merits. In this regard, our attitude is very clear: ES only as VAR complement, rather than radical alternative. Following three reasons: First, VAR inherently flawed, but not under all conditions can cause serious problems, so it still has a certain theoretical value; followed VAR is easy to apply, and the feature that makes it easy to interpret in the actual work has incomparable superiority; Finally, after years of development and promotion, VAR has been in the industry to establish a strong hardware and software infrastructure, which in itself is an achievement in the field of risk management, and on this basis should continue to improve and innovation, there is no reason to completely reject (that will bring a huge, unexpected costs). In view of the above, the paper tries to solve a problem that has practical significance, that is, in the circumstances in which we can feel at ease using the VAR measure risk, without having to worry too much about it \on VAR will lose its function, and ES can effectively solve the problem, which in turn is due to the ES of which the features of its own. For different situations in the text of a specific problem (case) study, trying to give readers an overall, comprehensive understanding of these issues. Involved in the risk management issues, including fat tail risk, portfolio optimization and the calculation of economic capital three representative problems. The thick tail risks faced in the discussion VAR measure risk, we have chosen the ES and VAR used in conjunction with the ideas. Statistical indicators to build the \Based on the Monte Carlo simulation method, we design a a data simulation test. The simulation experiments show that ES / VAR ratio can be used to determine portfolio return distribution characteristics of the tail. This ratio can not be given on the tail of the thickness of the absolute value, However, the unknown distribution ES / VAR ratio with some known distribution ES / VAR ratio comparison, we have at least the thickness thereof can be determined within a certain range, which risk management has a certain significance. For example, if we first calculate the tail thickness of a series of known distribution in different confidence level ES / VAR ratio, and the result is made into table. Then inspect the tail risk of a portfolio of income distribution unknown, we can be the unknown distribution the ES / VAR ratio compared with ES / VAR ratio previously calculated table to determine the unknown distribution the tail thickness should range between which two known distribution to make appropriate judgments, and thus their tail risk profile. In the discussion of the mean-VAR or the mean-ES portfolio optimization problem for theoretical reasons, we think that the mean-ES are better able to deal with such problems, especially in dealing with the loss distribution for non- normal distribution, portfolio and risk concentration, mean-ES method compared to the mean-VAR method can ensure the accuracy of the results and the global optimality. In order to verify the practical operability of the mean-ES method, optimization method based on the Rockafelar et al, introduced copula function to deal with the internal dependence structure of the portfolio, to design a more effective set of simulation methods used The probability distribution of portfolio losses. Based on this method, we have instances of a specific credit portfolio optimization problem to be solved, and eventually come to a satisfactory result. This is enough to prove that the process portfolio optimization problem, ES is fully alternative to VAR, at the same time to ensure the reliability of the theoretical, the actual operation is also very simple. Discussion VAR or the ES calculation of economic capital, we discuss the VAR and ES in addressing this issue, the pros and cons. However, the problem of calculating the economic capital, we can not draw firm conclusions to support the the ES method or VAR approach. Intuitively ES economic capital means more conservative, more sound business strategy, of course, will improve the credit quality of the bank, but will reduce the profitability of the banks. VAR economic capital is more convenient in operation, and standardized methods provided by the regulatory authorities, the industry's mainstream. Through appropriate stress testing and back-tested VAR inherent defects can be solved to a certain extent.

Expected Shortfall and VaR--Complementary or Substitute

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