A Theory of Rational Demand for Index Insurance
Rational demand for hedging products, where there is a risk of contractual nonperformance, is fundamentally different to that for indemnity insurance.� In particular, optimal demand is zero for infinitely risk averse individuals, and is nonmonotonic in risk aversion, wealth and price.� For commonly used families of utility functions, demand is hump-shaped in the degree of risk aversion when the price is actuarially unfair, first increasing then decreasing, and either decreasing or decreasing-increasing-decreasing in risk aversion when the price is actuarially favourable.� For a given belief, upper bound are derived for the optimal demand from risk averse and decreasing absolute risk averse decision makers.� The apparently low level of demand for consumer hedging instruments, particularly from the most risk averse, is explained as a rational response to deadweight costs and the risk of countractual nonperformance.� A numerical example is presented for maize in a developing county which suggests that some unsubsidised weather derivatives, currently being designed for and marketed to poor farmers, may in fact be poor products, in that objective financial advice would recommend�low or zero purchase from all risk averse expected utility maximisers.
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