Rating criteria, risk measures, and risk consistency

Abstract

Categorical ratings are widely used by investors to screen financial products, such as defaultable securities and investment funds. We model rating criteria as discrete transforms of risk measures, and introduce and study several natural notions of risk consistency that promote prudent investment decisions. Three closely related notions of risk consistency are considered: with respect to risk aversion, the asset pooling effect, and the benefit of portfolio diversification. These notions can be formulated under multiple probability measures. For both the monetary and positive homogeneous (MPH) and state-dependent expected utility (SEU) classes, we show how these properties translate between rating criteria and their corresponding risk measures, and establish a hierarchical structure among the properties. These findings lead to full characterizations for the Choquet subclass of MPH criteria and for SEU criteria. Illustrated by case studies on collateralized loan obligations and investment funds, some classes of risk-consistent scenario-based criteria can serve as useful alternatives to the probability of default and expected loss criteria used in practice for rating financial products.

73 pages, 5 figures and 5 tables