The Stochastic Nature of Risk Aversion

An aspect often missing from risk analysis discussion is the stochastic nature of risk aversion. In calibrating a financial model, the resulting implied values are the ones that would prevail, in that they are risk-adjusted. The expected cash flows are discounted at a rate that takes risk aversion into account. Should the risk aversion vary stochastically over time, the knowledge that some unknown (and possibly unknowable) future degree of risk aversion will prevail tomorrow, such that the future prices will be accurately determined, is of little comfort. It is the unknowing that carries a hidden cost.

Typically, financial models tend to price future risk either as a constant, or as a deterministic function of time. Unfortunately, there is evidence that risk aversion changes. And it changes in an unpredictable way over time. The risk analyst cannot be confident that today’s calibration will be valid in the future. We need only to examine commodities markets over the last few years to see how volatility risk has affected prices and behaviors in a variety of markets. Estimates do appear, if we hold out a long enough historical time horizon, to offer at least a provisional distribution for the future market prices. Once we have an estimate, we can create a time series Monte Carlo simulation of the distribution to represent that history and obtain, through the simulated scenarios, a future joint probability distribution of the variable and of the traditional observable risk factors. The Monte Carlo simulation generates the data we need to perform the statistical analysis, assisting in our estimates needed for effective valuation and decision analysis.

Thompson Terry
Palisade Training Team

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