Preferences, consumption smoothing, and risk premia (original) (raw)

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Consumption growth, preference for smoothing, changes in expectations and risk premium

The Quarterly Review of Economics and Finance, 2015

This paper derives a relationship between consumption growth, the consumption-wealth ratio and its first-difference, and asset returns. Using quarterly data for sixteen OECD countries, we find that the three-factor asset pricing model explains a large fraction of the variation in real stock returns. The model captures: (i) the concerns of agents with states of the world in which consumption growth is low; (ii) the preference of investors for a smooth consumption path as implied by the intertemporal budget constraint; and (ii) the role played by shifts in expectations about future returns due to positive or negative news about their wealth.

Consumption Smoothing and the Equity Premium

SSRN Electronic Journal, 2000

I assume an overlapping generations economy with agents that live for two periods and maximize a Kihlstrom-Mirman expected utility function. The representative agent is subject to shocks that include rare disasters. I find various combinations of intertemporal elasticity of substitution ( IES ) and risk aversion coefficients that can account for a risk free rate in the range of 0-2 percent and an equity premium in the range of 5-9 percent. Among these are: IES = 2 and a risk aversion coefficient of 8 and IES = 0.5 and a risk aversion coefficient of 5. Welfare calculations also depend on the combinations of IES and risk aversion chosen. When IES = 2 and the risk aversion coefficient is 8, the society would willingly reduce consumption by 0.6% each year to eliminate the uncertainty about the rate of consumption growth.

THE SHARPE RATIO AND PREFERENCES: A PARAMETRIC APPROACH

Macroeconomic Dynamics, 2002

We use a log-normal framework to examine the effect of preferences on the market price for risk, that is, the Sharpe ratio. In our framework, the Sharpe ratio can be calculated directly from the elasticity of the stochastic discount factor with respect to consumption innovations as well as the volatility of consumption innovations. This can be understood as an analytical shortcut to the calculation of the Hansen-Jagannathan volatility bounds, and therefore provides a convenient tool for theorists searching for models capable of explaining asset-pricing facts. To illustrate the usefulness of our approach, we examine several popular preference specifications, such as CRRA, various types of habit formation, and the recursive preferences of Epstein-Zin-Weil. Furthermore, we show how the models with idiosyncratic consumption shocks can be studied.

The wealth-consumption ratio: A litmus test for consumption-based asset pricing models

2007

We propose a new method to measure the wealth-consumption ratio. We estimate an exponentially affine model of the stochastic discount factor on bond yields and stock returns and use that discount factor to compute the no-arbitrage price of a claim to aggregate US consumption. We find that total wealth is much safer than stock market wealth. The consumption risk premium is only 2.2%, substantially below the equity risk premium of 6.9%. As a result, our estimate of the wealth-consumption ratio is much higher than the price-dividend ratio on stocks throughout the postwar period. The high wealth-consumption ratio implies that the average US household has a lot of wealth, most of it human wealth. The wealthconsumption ratio also has lower volatility than the price-dividend ratio on equity. A variance decomposition of the wealth-consumption ratio shows that future returns account for most of its variation. The predictability is mostly for future interest rates, not future excess returns. We conclude that the properties of total wealth are more similar to those of a long-maturity bond portfolio than those of a stock portfolio. Many dynamic asset pricing models require total wealth returns as inputs, but equity returns are commonly used as a proxy. The differences we find between the risk-return characteristics of equity and total wealth suggest that equity is special.

Consumption and Asset Prices with Recursive Preferences

SSRN Electronic Journal, 2000

We analyze consumption and asset pricing with recursive preferences given by Kreps-Porteus stochastic differential utility (K-P SDU). We show that utility depends on two state variables: current consumption and a second variable (related to the wealth-consumption ratio) that captures all information about future opportunities. This representation of utility reduces the internal consistency condition for K-P SDU to a restriction on the second variable in terms of the dynamics of a forcing process (consumption, the state-price deflator, or the return on the market portfolio). Solving the model for (i) optimal consumption, (ii) the optimal portfolio, and (iii) asset prices in general equilibrium amounts to finding the process for the second variable that satisfies this restriction. We show that the wealth-consumption ratio is the value of an annuity when the numeraire is changed from units of the consumption good to units of the consumption process, and we characterize certain features of the solution in a non-Markovian setting. In a Markovian setting, we provide a solution method that it quite general and can be used to produce fast, accurate numerical solutions that converge to the Taylor expansion.

Substitution, Risk Aversion and Asset Prices: An Expected Utility Approach

The standard power utility function is widely used to explain asset prices. It assumes that the coefficient of relative risk aversion is the inverse of the elasticity of substitution. Here I use the Kihlstrom and Mirman (1974) expected utility approach to relax this assumption. I use time consistent preferences that lead to time consistent plans. In our examples, the past does not matter much for current portfolio decisions. The risk aversion parameter can be inferred from experiments and introspections about bets in terms of permanent consumption (wealth). Evidence about the change in the attitude towards bets over the life cycle may also restrict the value of the risk aversion parameter. Monotonic transformations of the standard power utility function do not change the predictions about asset prices by much. Both the elasticity of substitution and risk aversion play a role in determining the equity premium.

Risk Aversion and Intertemporal Substitution in the Capital Asset Pricing Model

1989

When tastes are represented by a class of generalized preferences which-unlike traditional Von-Neumann preferencesdo not confuse behavior towards risk with attitudes towards intertemporal substitution, the true beta of an asset is, in general, an average of its consumption and market betas. We show that the two parameters measuring risk aversion and intertemporal substitution affect consumption and portfolio allocation decisions in symmetrical ways. A unit elasticity of intertemporal substitution gives rise to myopia in consumption-savings decisions (the future does not affect the optimal consumption plan), while a unit coefficient of relative risk aversion gives rise to myopia in portfolio allocation (the future does not affect optimal portfolio allocation). The empirical evidence is consistent with the behavior of intertemporal maximizers who have a unit coefficient of relative risk aversion and an elasticity of intertemporal substitution different from 1.

Consumption asset pricing models: Evidence from the UK

We analyse the ability of the consumption-based capital asset pricing model (C-CAPM) using traditional power utility, the recursive preferences model proposed by Epstein and Zin and two habit formation specifications proposed by Abel and Campbell and Cochrane to explain asset returns at both the economy level and, novelly, four individual sector groupings. We also investigate whether the models are capable of explaining the variation in the Fama–French factors. We find evidence supportive of both the habit formation specifications and the traditional power utility C-CAPM. The Epstein–Zin specification is clearly rejected. The preferred specification is that of Campbell and Cochrane. Importantly, parameter estimates for the sector groupings are consistent with theory, suggesting risk aversion is the same in all sectors. However, the ability of the models to describe the behaviour of the Fama–French factors is mixed.

Asset Pricing with Delayed Consumption Decisions

2004

The attempt to match asset price characteristics such as the risk-free interest rate, equity premium and the Sharpe ratio with data for models with instantaneous consumption decisions and time separable preferences has not been very successful. Many recent versions of asset pricing models have, in order to match those financial characteristics better with the data, employed habit formation where past consumption acts as a constraint on current consumption. In those models, surplus consumption, consumption over and above past consumption, improves welfare, yet habit formation gives rise to an additional state variable. By studying such a model we also allow for adjustment costs of investment. The asset price characteristics that one obtains from those models may depend on the solution techniques employed. In this paper a stochastic version of a dynamic programming method with adaptive grid scheme is applied to compute the above mentioned asset price characteristics where past consumption decisions are treated as an additional state variable. Since, as shown in , our method produces only negligible errors it is suitable to be used as solution technique for such models with more complicated decision structure. Using our solution methods shows that there are still remaining puzzles for the consumption based asset pricing model. JEL Classification: C60, C61, C63, D90, G12

Asset Pricing - Constrained by Past Consumption Decisions

2004

The attempt to match asset price characteristics such as the risk-free interest rate, equity premium and the Sharpe ratio with data for models with instantaneous consumption decisions and time separable preferences has not been very successful. Many recent versions of asset pricing models have, in order to match those financial characteristics better with the data, employed habit formation where past consumption acts as a constraint on current consumption. In those models, surplus consumption, consumption over and above past consumption, improves welfare, yet habit formation gives rise to an additional state variable. By studying such a model we also allow for adjustment costs of investment. The asset price characteristics that one obtains from those models may depend on the solution techniques employed. In this paper a stochastic version of a dynamic programming method with adaptive grid scheme is applied to compute the above mentioned asset price characteristics where past consumption decisions are treated as an additional state variable. Since, as shown in , our method produces only negligible errors it is suitable to be used as solution technique for such models with more complicated decision structure. Using our solution methods shows that there are still remaining puzzles for the consumption based asset pricing model. JEL Classification: C60, C61, C63, D90, G12