The estimation of potential losses that could arise from adverse changes in market conditions is a key element of risk management. For financial institutions and corporate treasuries across the world, Value at Risk (VaR) is rapidly emerging as the dominant methodology for estimating precisely how much money is at risk each day in the financial markets. However, the communication and application of VaR is a field in which the signal to noise ratio is not high. there is neither a widespread intuitive understanding of VaR in the market, nor an appreciation of the practicalities of its implementation and limitations. Mastering Value at Risk will close that knowledge gap, introducing this potentially powerful methodology to those most in need of its benefits, and helping all those who encounter VaR to use it wisely.
1. An Outline of Value at Risk.
Introduction. What is Value at Risk? Volatility and how to exploit it profitably. Correlation—its role in risk reduction. Conclusion.
Regulation: what it is and why it's necessary. Capital adequacy and the Basle Accord—what it is trying to achieve. Should regulators recognize diversification? Conclusion.
A profile of VaR methods. How matrices are used to calculate VaR. Comparison of the variance covariance approach with other methods, or which VaR method is best? Variance covariance with a three-asset portfolio. Constructing the weighting matrix. Mapping. Appendix 3.1. Appendix 3.2.
The range of fixed income products. Interest rate conventions. VaR on forward rate agreements. How swaps work. Conclusion.
Interest rate sensitivity. Calculating duration and convexity. The unique risk characteristics of convexity. The role of delta gamma in VaR measurement. Conclusion. Appendix 5.1.
The risk sensitivities of options. Reducing the risk of option portfolios. Exploiting volatility smiles profitably. Conclusion.
Which option strategies work? Volatility trading: straddles, strangles, butterflies, and ratio spreads. Time spread strategies. Conclusion.
Monte Carlo simulation and its applications. Generating the share prices. Applying Monte Carlo simulation to VaR. Conclusion.
Measuring credit risk more accurately. Reducing credit risk. Using credit derivatives to reduce credit risk. Conclusion.
Volatility and its measures. Exponentially weighted moving average (EWMA) vs time series. GARCH: changing variance and correlation between current and past events. Conclusion.
Should we rely on VaR? Over-the-counter options. Criticisms of VaR methods. Conclusion. Appendix 11.1. Appendix 11.2.
There is little doubt that, over the past four years, the profession of Financial Risk Management has grown considerably. Banks have set up specialist risk divisions whose function is not only to measure risk, but also to control it. Value at Risk has an important role to play here. Those who have a sound grasp of its principles, and who understand the unique nature of derivative risk, are in a better position not only to trade properly, but also to avoid contributing to the huge losses that many major banks have suffered in the last few years. Value at Risk is not only of interest to risk practitioners, but also to traders who want to trade profitably and, of course, to graduate and post-graduate students who want to become derivative traders, or who want to specialize in risk management. Recently, the Futures and Options Association has recommended that directors of major banks become actively involved in policies of risk management, rather than to delegate them, which is the current practice of many banks. A good grasp of VaR is, therefore, essential for this sector as well.
Mastering VaR is designed for the practitioner. Today, most practitioners recognize the importance of an interactive book, which encourages active as opposed to passive learning. Mastering VaR uses Excel spreadsheets to achieve this. If you have Excel available, you will be guided toward setting up a simple but illustrative VaR system. If you do not have Excel, the examples are designed so that you can follow them with relative ease and so at least understand how VaR systems operate.
A common complaint among practitioners is that, although there are many books on VaR, few are accessible to the non-academic. As one colleague put it, "It seems as though all writers in risk management are academic professors trying to impress more senior academic professors." In a practical world, many of the articles and books on VaR will lose the attention span of busy traders and practitioners who do not have a post-graduate degree in mathematics or statistics. Clearly, there is a gap in the market for a book which sets out, in digestible blocks, what VaR is, its limitations, and how to apply it.
The book is designed to give readers a practical insight into VaR and what this latest risk-measurement system is trying to achieve. In the first chapter, the concept of VaR is explained. You will be introduced to the concepts of volatility, normal distribution, and correlation. There are a number of practical but simple examples of each of these concepts. By the end of the chapter, you will have an intuitive understanding of the basics of VaR.
In Chapter 2, we examine why regulators and banks have found it necessary to develop a VaR system. We give you the regulators' perspective and the need for banks to "self-assess" their own risk with a view to calculating capital adequacy. We examine the role of the capital adequacy and why the existing framework is not the most suitable for measuring risk. The chapter also gives some insight into the Basle Committee and the evolution of self-assessment in terms of risk measurement.
In Chapter 3 we get down to the practical issues of risk measurement and build your knowledge of volatility and correlation (already introduced in Chapter 1). The idea behind this is to show you various approaches to the measurement of VaR and to illustrate the computational challenges of dealing with large portfolios. This chapter is to a large extent an interactive chapter where you can (if you have spreadsheets) build up a VaR measuring system which almost incorporates the broad features inherent in real VaR packages. Those who do not have spreadsheets will nevertheless to be able to follow the examples without any difficulty. Although the chapter appears very mathematical, we assume only a basic knowledge and direct nonmathematical readers to two small appendices which explain in simple terms how matrices operate.
In Chapters 4 and 5 we illustrate how fixed income products are "decomposed" and mapped onto weighting matrices for the purpose of risk measurement. Swaps, swaptions, and forward rate agreements are discussed in detail, in order to illustrate the complexities and how we can exploit natural hedging. We also compare VaR risk measurement with the more traditional forms of risk measurement, such as duration and convexity.
Chapters 6, 7, and 8 concentrate on risk measurement for options. In Chapter 6 we illustrate the unique risk nature of options and emphasize the "Greeks". In Chapter 7 we outline some of the popular strategies in which option traders engage and their risk implications. Chapter 8 then illustrates the weaknesses with the standard variance covariance approach and introduces a new method of risk measurement: Monte Carlo simulation. The principles of VaR are not just confined to market risk. In Chapter 9, we show how we can apply VaR principles to the estimation of credit risk. In particular, we look at CreditMetrics and the growth in the use of credit derivatives.
In Chapter 10, we concentrate on volatility forecasting and estimation. We illustrate the unique nature of volatility and the various models used by practitioners In particular, we talk about GARCH and compare this method to the exponentially weighted moving average method, as adopted by RiskMetrics. Finally, in Chapter 11, we look at the particular problems with modeling risk in general and in, particular, the pitfall of overreliance on models to measure risk.
Questions & answers
We have launched a new website,
answerback.org, to deal with the most popular questions and queries that readers have raised, after reading Mastering Value at Risk. If you are stuck on any area, please send your question to us via the website. You will also see questions and answers from other readers.