A Two–Dimensional Risk Measure

The measurement of “risk” is a critical component of enterprise risk management, insurance pricing and reserving, and strategic and operational decision making. Some commonly used measures attempt to quantify risk by considering volatility or downside “potential.” Other measures examine ratios of upside versus downside potential, or upside potential versus volatility. A general characteristic of such measures is that they describe risk in a single dimension—placing risk along a number line and providing a single quantitative value. In this paper, we suggest that risk is too complex to quantify with a single number. We suggest a two-dimensional risk measure and introduce the concept of iso-risk curves.