Chapter 5

Quantifying Portfolio Risks

… to pursue mathematical analysis while at the same time turning one's back on its applications and on intuition is to condemn it to hopeless atrophy.

Richard Courant, Differential and Integral Calculus

5.1. THE NATURE OF RISK

Risk is ultimately an impalpable and, to a large degree, subjective concept, reflecting a multitude of tangible and intangible factors, perceptions, and sentiments, some measurable, some observable, some quantifiable, and some identifiable, but many more not. Risk management and investment activity in general strive to accomplish an epistemologically dubious task of predicting, and anticipating, the future using the past as a guide.

Of course, projecting past behavior into the future as a portfolio management approach is unavoidable, if only because there are few alternatives. This projecting relies on the persistence of the statistical properties of capital market observables (prices, trading volumes, interest rates, foreign exchange rates), both individually, as captured, for example, by the probability distribution of past returns and its cumulants, and in relation to each other, as measured, for instance, by pair-wise correlations of returns. It also assumes the similarity of past and future responses of market and economic indicators to discontinuous events, such as government and central bank policy announcements, legal actions, or terrorist attacks. In reality, both statistical properties and responses to shocks ...

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