whether the nut is worth cracking in the first place! How reliable are risk estimates that are based on highly technical estimation methods? If there is a real, stable relationship between the underlying variables it should shine through, whatever the estimation methods employed. If nothing is obvious from a first pass at the data using a method such as OLS, which may not be the best method but which should be good enough to gain some insight, then it is unlikely that any informative relationships are going to be revealed by a more sophisticated analysis.

Value-at-Risk

During the last few years there have been many changes in the way financial institutions evaluate risk. Improvements are continuously being sought to relate the regulatory capital that must be available to the underlying risks that a firm takes. Hence regulations have played a major role in the development of risk measurement techniques. The Basel Committee on Banking Supervision now recommend two types of models for measuring market risk on a daily basis; details of these models are given in the Basel Accord Amendment of 1996.

These internal models have become industry standards for measuring risk not only for external regulatory purposes, but also for internal risk management and control. One approach is to quantify the maximum loss over a large set of scenarios for movements in the risk factors over a certain time horizon. Another approach is to weight scenarios with probabilities and to assess the level of loss that has some low probability of being exceeded over a fixed time horizon.1 This measure is called the portfolio value-at-risk (VaR).2 Both approaches assume the portfolio is not managed during the fixed time horizon.

This chapter is about the VaR approach to measuring market risk, for capital requirements and for internal risk management. The first section looks at the current risky environment in financial markets and gives a brief overview of the developments in risk capital regulation during the last few years. It outlines the limitations with current regulations and discusses how they are being addressed by the new proposals from the Basel Committee that are currently under consultation (Basel 2). The theoretical and practical advantages and limitations of VaR as a measure of portfolio risk are described in §9.2. Here some of the traditional sensitivity-based risk measures and some of the new alternative risk measures are also described.

The next two sections look at the VaR models that have emerged as industry standard during the last few years. The covariance VaR model is described in

1 In our uncertain environment loss is a random variable, so it is only possible to make probabilistic statements about the loss from a portfolio.

-Or more precisely, the market VaR of the portfolio. Although VaR was introduced in the context of market risk, recently the context has been extended to credit VaR and operational VaR.

§9.3, with examples of its application to different types of linear portfolios. Option portfolios have too many non-linear characteristics to be measured by a covariance VaR model; instead one of the simulation methods described in §9.4 will normally be applied.

Section 9.5 describes the methods that are normally used to validate a VaR model and the impact of backtesting results on risk capital requirements. This section also deals with the sensitivity of VaR estimates to assumptions about model parameters, something that deserves careful investigation by both internal and external risk control functions. The chapter concludes by reviewing the methods by which market VaR estimates of current or potential positions can be complemented by stress testing and scenario analysis to control the impact of extreme market movements.

There are three workbooks on the CD to supplement this chapter: covariance VaR, historical VaR and Monte Carlo VaR. The reader can use these to specify portfolios, compute VaR and perform stress tests.

9.1 Controlling the Risk in Financial Markets

Are financial markets more risky than ever? They are certainly more volatile. One of the reasons for this is the increased ability of financial institutions to create leverage. Hedge funds can take extraordinarily highly leveraged positions because their models are supposedly designed to diversify most of the risks. New derivative products are continually being structured to allow companies and banks to increase leverage in more ingenious ways than ever.

Financial activity is unstable and risky by its very nature. As new markets are opened and new products are developed, market liquidity may be insufficient to accommodate our growing appetite for leverage. In young markets for new products sometimes it is just not possible to understand the risks completely. Even when proper pricing models have been developed they may be so new that they are only understood by quants. In established markets that are better understood there can always be an event that has never been experienced before.

Volatility in itself does not imply risk. There does not seem to be a strong connection between crises in financial markets and the risk to the real economy

But volatility in itself does not imply risk. What do we mean by risk anyway? Financial risk should be perceived on three levels: the risks to individual consumers, the risks to a firm, along with its shareholders and investors, and the risks to the markets as a whole. Consider one of the most volatile financial experiences of the twentieth century-the global stock market crash of 1987. All three levels of risk were affected by this event. Firms and individuals suffered immediate and direct financial loss, and the knock-on effect of the crash undermined the fundamental stability of the worlds economy. In more recent years there have been a number of other crises in financial markets around the globe, but it is mainly in