First-order risk aversion and non-differentiability

We use Kőszegi and Rabin's (2006) model of reference-dependent utility, and an extension of it that applies to decisions with delayed consequences, to study preferences over monetary risk. Because our theory equates the reference point with recent probabilistic beliefs about outcomes, it predicts specific ways in which the environment influences attitudes toward modest-scale risk. It replicates “classical” prospect theory—including the prediction of distaste for insuring losses—when exposure to risk is a surprise, but implies first-order risk aversion when a risk, and the possibility of insuring it, are anticipated. A prior expectation to take on risk decreases aversion to both the anticipated and additional risk. For large-scale risk, the model allows for standard “consumption utility” to dominate reference-dependent “gain-loss utility,” generating nearly identical risk aversion across situations. (JEL D81)

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Optimal Dynamic Portfolio Risk with First-Order and Second-Order Predictability

Contributions in Theoretical Economics ◽

10.2202/1534-5971.1070 ◽

2004 ◽

Vol 4 (1) ◽

Cited By ~ 5

Author(s):

Christian Gollier

Keyword(s):

Relative Risk ◽

Risk Aversion ◽

Interest Rates ◽

Stock Returns ◽

Bayesian Learning ◽

Absolute Risk ◽

Second Order ◽

Relative Risk Aversion ◽

Portfolio Risk ◽

First Order

We consider a two-period portfolio problem with predictable assets returns. First-order (second-order) predictability means that an increase in the first period returns yields a first-order (second-order) stochastically dominated shift in the distribution of the second period state prices. Mean reversion in stock returns, Bayesian learning, stochastic volatility and stochastic interest rates (bond portfolios) belong to one of these two types of predictability. We first show that a first-order stochastically dominated shift in the state price density reduces the marginal value of wealth if and only if relative risk aversion is uniformly larger than unity. This implies that first-order predictability generates a positive hedging demand for portfolio risk if this condition is met. A similar result is obtained with second-order predictability under the condition that absolute prudence be uniformly smaller than twice the absolute risk aversion. When relative risk aversion is constant, these two conditions are equivalent. We also examine the effect of exogenous predictability, i.e., when the information about the future opportunity set is conveyed by signals not contained in past asset prices.

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