Computing the limits of risk aversion

Utility theory can be used to model the decision process involved in evaluating the cost-effectiveness of systems that protect against a risk to assets. A key variable in the model is the coefficient of relative risk aversion (or simply “risk-aversion”) which reflects the decision maker's reluctance to invest in such safety systems. This reluctance to invest is the scaled difference in expected utility before and after installing the safety system and has a minimum at some given value of risk-aversion known as the “permission point”, and it has been argued that decisions to sanction safety systems would be made at this point. As the cost of implementing a safety system increases, this difference in utility will diminish. At some point, the “point of indiscriminate decision”, the decision maker will not be able to discern any benefit from installing the safety system. This point is used to calculate the maximum reasonable cost of a proposed safety system. The value of the utility difference at which the decision maker is unable to discern any difference is called the “discrimination limit”.By considering the full range of accident probabilities, costs of the safety system and potential loss of assets, an average risk-aversion can be calculated from the model. This paper presents the numerical and computational techniques employed in performing these calculations. Two independent approaches to the calculations have been taken, the first of which is the derivative-based secant method, an extension of the referred derivative method employed in previous papers. The second is the Golden Bisection Method, based on a Golden Section Search algorithm, which was found to be more robust but less efficient than the secant method. The average risk-aversion is a function of several key parameters: the organisation's assets, the probability and maximum cost of an incident, and the discrimination limit. An analysis of the sensitivity of the results to changes in these parameters is presented. An average risk-aversion of 0.8–1.0 is found for a wide range of parameters appropriate to individuals or small companies, while an average risk-aversion of 0.1 is found for large corporations. This reproduces the view that large corporations will be risk neutral until faced with risks that pose a threat to their viability.