Asset Pricing in a General Equilibrium Production Economy with Chew-Dekel Risk Preferences

In this paper we provide a thorough characterization of the asset returns implied by a simple general equilibrium production economy with convex investment adjustment costs. When households have Epstein-Zin preferences, there exist plausible parametervalues such that the model generates unconditional mean risk--free rate and equity return, and volatility of consumption growth, which are in line with historical averages for the US economy. Consistently with the data, the model's implied price--dividendratio is pro-cyclical and stock returns are predictable (and increasingly so as the time horizon increases), while dividend growth is not. The model also implies realistic values for (i) the correlation of the risk--free rate with output growth and consumption growth and (ii) the correlation pattern between risk--free rate, equity return, and equity premium. The risk implied by the model is rather low. At the modal state of nature, an individual that expects to consume for 100,000 dollars a year faces a lottery over future consumption with a standard deviation of 55 dollars (per quarter). Her risk aversion is such that she's willing to pay 1 dollar (per quarter) in order to avoid that lottery. Very similar results can be obtained assuming that agents are disappointment averse in the sense of Gul (1991). With such risk preferences, the universality requirement is not a problem to the extent that it is in the case of expected utility. In fact, faced with a lottery that has a coefficient of variation 100 times as large as that implied by our model, a disappointment averse agent displays the same relative risk aversion as an expected utility agent with logarithmic utility!Equity Premium, Business Cycle, Predictability, Disappointment Aversion.

Heterogeneous Impatience in a Continuous-Time Model

In a continuous-time economy with complete markets, we show how the heterogeneity in the individual consumers' risk attitudes and impatience would affect the representative consumer's counterparts. Specifically, our formulas tell us how his risk tolerance and impatience will change over time, and how his impatience will be affected by the changes in aggregate consumption levels. Under the assumption of equal and constant relative risk aversion across individual consumers, we characterize his discount factor by means of a completely monotone function of time. These results are used to analyze short-rate processes.Representative consumer, expected utility, time additivity, multiplicative separability, impatience, risk tolerance, state-price deflator, short-rate process, complete monotonicity

Wealth Shocks and Risk Aversion

Modern literature departs from time-separable constant relative risk aversion preferences to explain asset pricing facts. This deviation typically implies that wealth shocks generate transitory variations in agents’ relative risk aversion and, possibly, portfolio re-allocations over time. I empirically analyze this relationship using U.S. macroeconomic data and and evidence for time-variation in portfolio shares that is consistent with counter-cyclical risk aversion. These results suggest, therefore, that wealth-dependent, habit-formation or loss and disappointment aversion utility functions are a good description of preferences. Controlling for observed versus expected asset returns, I also show that: (i) wealth effects are significant (although temporary) and there is no evidence of inertia contrary to Brunnermeier and Nagel (2006); and (ii) the consumption-wealth ratio (Lettau and Ludvigson, 2001), the labor income risk (Julliard, 2004) and the labor income-consumption ratio (Santos and Veronesi, 2006) partially explain changes in the risky asset share.wealth, risk aversion.

Evaluating Risky Consumption Paths: The Role of Intertemporal Substitutability

In dynamic stochastic welfare comparisons, a failure clearly to distinguish between risk aversion and intertemporal substitutability can result in misleading assessments of the impact of risk aversion on the welfare costs of consumption-risk changes. The problem arises in any setting in which uncertainty is propagated over time, notably, but not exclusively, in economies with stochastic consumption trends. Regardless of the preference setup adopted, an increase in risk aversion amplifies the per-period costs of risks. The weights consumers use to cumulate the per-period costs of risks with persistent effects should, however, depend on intertemporal substitutability as well as on risk aversion. Under time-separable expected-utility preferences, an increase in the period utility function's curvature therefore alters the welfare effect of risk for reasons that in part are unrelated to risk aversion.

Finite Horizon Portfolio Selection

We study the problem of maximising expected utility of terminal wealth over a nite horizon, with one risky and one riskless asset available, and with trades in the risky asset subject to proportional transaction costs. In a discrete time setting, using a utility function with hyperbolic risk aversion, we prove that the optimal trading strategy is characterised by a function of time (t), which represents the ratio of wealth held in the risky asset to that held in the riskless asset. There is a time varying no transaction region with boundaries b(t) < s(t), such that the portfo- lio is only rebalanced when (t) is outside this region. The results are consistent with similar studies of the in nite horizon problem with in- termediate consumption, where the no transaction region has a similar, but time independent, characterisation. We solve the problem numerically and compute the boundaries of the no transaction region for typical model parameters. We show how the results can be used to implement option pricing models with transaction costs based on utility maximisation over a nite horizo

Wealth shocks and risk aversion

Modern literature departs from time-separable constant relative risk aversion preferences to explain asset pricing facts. This deviation typically implies that wealth shocks generate transitory variations in agents’ relative risk aversion and, possibly, portfolio re-allocations over time. I empirically analyze this relationship using U.S. macroeconomic data and and evidence for time-variation in portfolio shares that is consistent with counter-cyclical risk aversion. These results suggest, therefore, that wealth-dependent, habit-formation or loss and disappointment aversion utility functions are a good description of preferences. Controlling for observed versus expected asset returns, I also show that: (i) wealth effects are significant (although temporary) and there is no evidence of inertia contrary to Brunnermeier and Nagel (2006); and (ii) the consumption-wealth ratio (Lettau and Ludvigson, 2001), the labor income risk (Julliard, 2004) and the labor income-consumption ratio (Santos and Veronesi, 2006) partially explain changes in the risky asset share.Fundação para a Ciência e a Tecnologia (FCT) - SFRH/BD/12985/2003

Discounting for Climate Change. ESRI WP276. January 2009

It is well-known that the discount rate is crucially important for estimating the social cost of carbon, a standard indicator for the seriousness of climate change and desirable level of climate policy. The Ramsey equation for the discount rate has three components: the pure rate of time preference, a measure of relative risk aversion, and the rate of growth of per capita consumption. Much of the attention on the appropriate discount rate for long-term environmental problems has focussed on the role played by the pure rate of time preference in this formulation. We show that the other two elements are numerically just as important in considerations of anthropogenic climate change. The elasticity of the marginal utility with respect to consumption is particularly important because it assumes three roles: consumption smoothing over time, risk aversion, and inequity aversion. Given the large uncertainties about climate change and widely asymmetric impacts, the assumed rates of risk and inequity aversion can be expected to play significant roles. The consumption growth rate plays four roles. It is one of the determinants of the discount rate, and one of the drivers of emissions and hence climate change. We find that the impacts of climate change grow slower than income, so that the effective discount rate is higher than the real discount rate. The differential growth rate between rich and poor countries determines the time evolution of the size of the equity weights. As there are a number of crucial but uncertain parameters, it is no surprise that one can obtain almost any estimate of the social cost of carbon. We even show that, for a low pure rate of time preference, the estimate of the social cost of carbon is indeed arbitrary – as one can exclude neither large positive nor large negative impacts in the very long run. However, if we probabilistically constrain the parameters to values that are implied by observed behaviour, we find that the social cost of carbon, corrected for uncertainty and inequity, is 61 US dollar per metric tonne of carbon

A Dynamic Model of Differential Human Capital and Criminal Activity

This paper presents a new, dynamic economic model of criminal activity. Individuals are endowed with legal and criminal human capital. Potential incomes in legal and criminal sectors depend on the level of the relevant human capital, the rate of return, and random shocks. Both types of human capital can be enhanced by participating in the relevant sector. Legal human capital can also be enhanced through savings. Each type of human capital is subject to depreciation. Individuals maximize expected discounted lifetime utility, which depends on consumption. In this two-stage dynamic stochastic model, in each period the individual decides in which sector to participate (legal or illegal), and after the realization of income in that period, he decides on the optimal amount of consumption. A particular decision (e.g. participation in the criminal sector) has implications both for future decisions as well as the choices available to the individual in later periods. The model allows analyses of the effects of recessions, neighborhood effects, various imprisonment/rehabilitation scenarios, risk aversion, and time preferences on criminal behavior. It provides new insights, which are different from existing models, and it is able to explain the declining propensity of individuals to commit crimes over time.