Changes in Risk and the Demand for Saving

How does risk affect saving? Empirical work typically examines the effects of detectible differences in risk within the data. How these differences affect saving in theoretical models depends on the metric one uses for risk. For labor-income risk, second-degree increases in risk require prudence to induce increased saving demand. However, prudence is not necessary for first-degree risk increases and not sufficient for higher-degree risk increases. For increases in interest rate risk, a precautionary effect and a substitution effect need to be compared. This paper provides necessary and sufficient conditions on preferences for an Nth-degree change in risk to increase saving.precautionary saving, prudence, stochastic dominance, temperance

Optimal Catastrophe Insurance with Multiple Catastrophes

This paper adopts a normative approach to catastrophe insurance. It addresses the question of how innovations in the design of insurance contracts could help resolve the capacity gap in the provision of insurance against natural catastrophes. It extends previous research with the same approach first by considering the case of "uncorrelated catastrophes", and second by combining the influence of catastrophes on claims amounts (severity risk) and on the probability of loss (frequency risk). We show that the menu of contracts proposed in previous research, where only one type of catastrophe is considered, is dominated by the menu of contracts proposed in this paper, taking into account the absence of correlation between catastrophes of different kinds.

Putting Risk in its Proper Place

This paper examines preferences towards particular classes of lottery pairs. We show how concepts such as prudence and temperance can be fully characterized by a preference relation over these lotteries. If preferences are defined in an expected-utility framework with differentiable utility, the direction of preference for a particular class of lottery pairs is equivalent to signing the nth derivative of the utility function. What makes our characterization appealing is its simplicity, which seems particularly amenable to experimentation.properness, prudence, risk apportionment, risk aversion, stochastic dominance, temperance, utility premium

Exploring Higher-Order Risk Effects

Higher-order risk effects play an important role in examining economic behavior under uncertainty. A precautionary demand for saving has been linked to the property of prudence and the property of temperance has been used to show how the presence of an unavoidable risk affects one’s behavior towards a second risk. These two properties also play key roles in aversion to negative skewness and to kurtosis, respectively. Both properties recently have been characterized by preferences over lottery pairs in simple 50-50 gambles. The simplicity of this characterization is ideal for experimental investigation. This paper reports the results of such experiments and concludes that there is behavioral evidence for prudence, but not for temperance. Implications of these results for both expected-utility and non-expected-utility models are examined.risk, prudence, temperance, laboratory experiments

Changes in Risk and Asset Prices

We examine asset prices in a representative-agent model of general equilibrium. Assuming only that individuals are risk averse, we determine conditions on the changes in asset risk that are both necessary and sufficient for the asset price to fall. We show that these conditions neither imply, nor are implied by the conditions for second-degree stochastic dominance. For example, if the payoff on an asset becomes riskier in the sense of second-degree stochastic dominance, the equilibrium price of the asset need not necessarily fall. We further demonstrate how our results can be imbedded into a market that is incomplete in the sense of containing an uninsurable background risk, such as a risk on labor income. We extend our model to show how a miscalibration of the asset risk can lead to a partial explanation of high equity premia (i.e., the "equity premium puzzle").Asset pricing; stochastic dominance; equity premium puzzle

Coping with Credit Risk

We consider a pool of bank loans subject to a credit risk and develop a method for decomposing the credit risk into idiosyncratic and systemic components. The systemic component accounts for the aggregate statistical difference between credit defaults in a given period and the long-run average of these defaults. We show how financial contracts might be redesigned to allow for banks to manage the idiosyncratic component for their own accounts, while allowing the systemic component to be handled separately. The systemic component can be retained, passed off to the capital markets, or shared with the borrower. In the latter case, we introduce a type of floating rate interest, in which the rate is set in arrears, based on a composite index for the systemic risk. This is shown to increase the efficiency of risk sharing between borrowers, lenders and the capital market.

Insurance Contracts and Securitization

High correlations between risks can increase required insurer capital and/orreduce the availability of insurance. For such insurance lines, securitizationis rapidly emerging as an alternative form of risk transfer. The ultimatesuccess of securitization in replacing or complementing traditional insuranceand reinsurance products depends on the ability of securitization to facilitateand/or be facilitated by insurance contracts. We consider how insuredlosses might be decomposed into separate components, one of which is atype of “systemic risk” that is highly correlated amongst insureds. Such acorrelated component might conceivably be hedged directly by individuals,but is more likely to be hedged by the insurer. We examine how insurancecontracts may be designed to allow the insured a mechanism to retain all orpart of the systemic component. Examples are provided, which illustrate ourmethodology in several types of insurance markets subject to systemic risk.

Adverse Selection in an Insurance Market with Government-Guaranteed Subsistence Levels

We consider a competitive insurance market with adverse selection. Unlike the standard models, we assume that individuals receive the benefit of some type of potential government assistance that guarantees them a minimum level of wealth. For example, this assistance might be some type of government-sponsored relief program, or it might simply be some type of limited liability afforded via bankruptcy laws. Government assistance is calculated ex post of any insurance benefits. This alters the individuals’ demand for insurance coverage. In turn, this affects equilibria in various insurance models of markets with adverse selection.adverse selection, insurance, government relief

Non-Market Wealth, Background Risk and Portfolio Choice

We examine the effects of non-portfolio risks on optimal portfolio choice. Examples of non-portfolio risks include, among others, uncertain labor income, uncertainty about the terminal value of fixed assets such as housing and uncertainty about future tax liabilities . In particular, while some of these risks are added to portfolio value and have been amply studied, others are multiplicative in nature and have received far less attention. Moreover, the combined effects of multiple risks lead to some seemingly paradoxical choice behavior. We rationalize such behavior and we show how non-portfolio risks might lead to seemingly U-shaped relative risk aversion for a representative investor, as found empirically by Ait-Sahilia and Lo (2000) and Jackwerth (2000).Portfolio choice, Derived relative risk aversion, Additive background risk, Multiplicative background risk

Apportioning of Risks via Stochastic Dominance

Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable Xi dominates Yi via ith-order stochastic dominance for i = M,N. We show that the 50-50 lottery [XN + YM, YN + XM] dominates the lottery [XN + XM, YN + YM] via (N + M)th-order stochastic dominance. The basic idea is that a decision maker exhibiting (N + M)th-order stochastic dominance preference will allocate the state-contingent lotteries in such a way as not to group the two "bad" lotteries in the same state, where "bad" is defined via ith-order stochastic dominance. In this way, we can extend and generalize existing results about risk attitudes. This lottery preference includes behavior exhibiting higher order risk effects, such as precautionary effects and tempering effects.downside risk, precautionary effects, prudence, risk apportionment, risk aversion, stochastic dominance, temperance