Risk Preferences in Small and Large Stakes: Evidence from Insurance Contract Decisions

Abstract

We examine risk preferences using the flood insurance decisions of over 100,000 households. In each contract, households make a small stakes decision, the deductible, and a large stakes one, the coverage limit. Over 94 percent of household choose one of the two lowest deductibles out of six options, and 77 percent fully insure, select a coverage limit of at least their home’s replacement cost. Households must be extremely risk averse to explain each of these choices with standard expected utility models. Households’ deductible choices imply a median relative risk aversion of 108. Households’ coverage limit choices require a median relative risk aversion of at least 112. Their substantial risk aversion over large stakes is due to households’ tendency to fully insure despite paying premiums well above their contracts’ expected value. Allowing for probability distortions improves our models and explains the small and large decisions of most households in our data. Assessing rank dependent utility models, we find that households follow two tenets of prospect theory: overestimation of small probabilities and diminishing sensitivity to losses.