Abstract
This paper proposes a decomposition of the cost of risk (as measured by a risk premium) across intervals/quantiles of the payoff distribution. The analysis is based on general smooth risk preferences. While this includes the expected utility model as a special case, the investigation is done under a broad class of non-expected utility models. We decompose the risk premium into additive components across quantiles. Defining downside risk as the risk associated with a lower quantile, this provides a basis to evaluate the cost of exposure to downside risk. We derive a local measure of the cost of risk associated with each quantile. It establishes linkages between the cost of risk, risk preferences and the distribution of risky prospects across quantiles (as measured by quantile variance and skewness). The analysis gives new and useful information on how risk aversion, exposure to downside risk and departures from the expected utility model interact as they affect the risk premium.
Highlights
For risk-averse decision makers, the cost of risk can be measured by the risk premium reflecting the willingness-to-pay to replace a risky outcome by its mean
This paper has developed a quantile-based analysis of the cost of risk reflecting risk exposure across different intervals of the risk distribution
Using a quantile-based analysis of the cost of risk, we show how the risk premium can be decomposed into additive components across the range of stochastic outcomes
Summary
For risk-averse decision makers, the cost of risk can be measured by the risk premium reflecting the willingness-to-pay to replace a risky outcome by its mean. Our quantile-based measures generalize previous literature on local risk premium in two directions: 1) they rely on quantile moments across quantiles; and 2) they hold under non-expected utility models (in contrast with many previous analyses of local risk premium that have been obtained under the expected utility model; see [10] [12] [14] [16] [17]) In this context, we show how quantilevariance and skewness associated with relevant quantiles capture the role of risk located in different intervals of the payoff distribution. Our fourth contribution is to use our local quantile-based measures to examine how departures from the expected utility model affect the risk premium This is of particular interest when such departures occur for low probability events located in the lower tail of distribution. It shows how departures from expected utility and exposure to downside risk can interact to increase the cost of risk
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