Risk Analysis: A Geometric Approach

R isk management and quantitative methods are typically considered to be almost interchangeable, even to the extent that risk management requires or depends on quantitative sophistication. Although a quantitative perspective can certainly be useful in risk management, too often quantitative methods and analytical elegance provide the illusion of control over risk. Such approaches make investors feel as if they have grasped uncertainty and dealt with it simply by the act of quantifying it. But risks, by their very nature, are unexpected. So, quantitative methods should not turn confidence into arrogance; rather, what quantitative methods should do is allow investors (and portfolio managers) to look at risk in new ways-to try to manage risk in ways that they previously could not do, or were not necessarily comfortable doing. This presentation discusses a process that uses Euclidean geometry to visualize risk. Such an approach is somewhat avant-garde for risk management and is decidedly quantitative, but the intent is to illustrate a tool that enables quantitative risk managers to communicate with nonquantitative portfolio managers and nonquantitative clients. Although the approach applies to any investment horizon, this discussion takes a relatively long-term perspective on risk-one that is typical of an investment policy perspective-and allows direct analysis of portfolio risk and portfolio constraints.