Investment Theory and Risk Management, + Website

Taxonomy of Risk

Investment decisions are intertemporal choices that trade off present and future consumption. Because the future can only be anticipated, then these choices must rest upon some expectation of uncertain future payoffs. If we admit the possibility that future payoffs are state-dependent (for example, the asset pays a dollar on a rainy day and zero otherwise), then we allow, in principle, the possibility that an uncertain future can be modeled as a set of contingent claims whose payoffs (receiving a dollar) depend on whether certain future conditions are met (a rainy day) with respect to a set of related factors (humidity, barometric pressure). This suggests that there is a distinction, a la Frank Knight, between uncertainty and risk with risk as a refined state of uncertainty in the sense that although future outcomes may not be known, their probabilities are.

Knight didn't mean that the difference between risk and uncertainty was an arbitrary set of probabilities. Markets, after all, are not card decks whose outcomes, though uncertain, can be modeled with a well-defined probability distribution and whose risks are perfectly known. Instead, market models will necessarily contain model risk in varying degrees, depending on our inability to model the problem's structure precisely. Attempts to model risk in market environments must therefore incorporate an awareness of this additional source of risk. Value at Risk (VaR), for example, is a flawed model, and to the extent ...