Risk measurement and diversification

Measuring and controlling risks is now a major concern in many modern human activities. The financial markets, which act as highly sensitive (probably over sensitive) economical and political thermometers, are no exception. One of their rôles is actually to allow the different actors in the economic world to trade their risks, to which a price must therefore be given.

The very essence of the financial markets is to fix thousands of prices all day long, thereby generating enormous quantities of data that can be analysed statistically. An objective measure of risk therefore appears to be easier to achieve in finance than in most other human activities, where the definition of risk is vaguer, and the available data often very poor. Even if a purely statistical approach to financial risks is itself a dangerous scientists' dream (see e.g. Fig. 1.1), it is fair to say that this approach has not been fully exploited until the very recent years, and that many improvements can be still expected in the future, in particular concerning the control of extreme risks. The aim of this chapter is to introduce some classical ideas on financial risks, to illustrate their weaknesses, and to propose several theoretical ideas devised to handle more adequately the ‘rare events’ where the true financial risk resides.