Quantitative Risk Management: A Practical Guide to Financial Risk, + Website

2.1 What Is Risk?

Before asking, “What is risk management?” we need to ask, “What is risk?” This question is not trivial; risk is a very slippery concept. To define risk, we need to consider both the uncertainty of future outcomes and the utility or benefit of those outcomes. When someone ventures onto a frozen lake, that person is taking a risk not just because the ice may break but because if it does break, the result will be bad. In contrast, for a frozen lake upon which no one is trying to cross on foot, we would talk of the chance of ice breaking; we would use the word risk only if the breaking ice had an impact on someone or something. Or, to paraphrase the philosopher George Berkeley, if a tree falls in the forest but there is nobody there for it to fall upon, is it risky?

The word risk is usually associated with downside or bad outcomes, but when trying to understand financial risk, limiting the analysis to just the downside would be a mistake. Managing financial risk is as much about exploiting opportunities for gain as it is about avoiding downside. It is true that, everything else held equal, more randomness is bad and less randomness is good. It is certainly appropriate to focus, as most risk measurement texts do, on downside measures (for example, lower quantiles and VaR). But upside risk cannot be ignored. In financial markets, everything else is never equal and more uncertainty is almost invariably associated with more opportunity for gain. Upside risk might be better ...