Wealth Inequality and Asset Pricing

In an Arrow–Debreu exchange economy with identical agents except for their initial endowment, we examine how wealth inequality affects the equilibrium level of the equity premium and the risk-free rate. We first show that wealth inequality raises the equity premium if and only if the inverse of absolute risk aversion is concave in wealth. We then show that the equilibrium risk-free rate is reduced by wealth inequality if the inverse of the coefficient of absolute prudence is concave. We also prove that the combination of a small uninsurable background risk with wealth inequality biases asset pricing towards a larger equity premium and a smaller risk-free rate.     

Risk, ambiguity, and state-preference theory

The state-preference framework for modeling choice under uncertainty, in which objects of choice are allocations of wealth or commodities across states of the world, is a natural one for modeling ??smooth?? ambiguity-averse preferences. It does not require reference to objective probabilities, personalistic consequences, or counterfactual acts, and it allows for state dependence of utility and unobservable background risk. The decision maker??s local revealed beliefs are encoded in her risk-neutral probabilities (her relative marginal rates of substitution between states) and her local risk preferences are encoded in the matrix of derivatives of the risk-neutral probabilities. This matrix plays a central but generally unappreciated role in the modeling of risk attitudes in the state-preference framework. It can be computed by inverting a bordered Slutsky matrix and vice versa, it generalizes the Arrow?CPratt measure for approximating local risk premia, and its structure reveals whether the decision maker??s risk preferences are ambiguity averse as well as risk-averse. Two versions of the smooth ambiguity model are analyzed??the source-dependent risk aversion model and the second-order uncertainty (KMM) model??and it is shown that in both cases, the overall premium for local uncertainty can be decomposed as the sum of a risk premium and an ambiguity premium.     

Risk Aversion and International Markets: Does Asset Trade Smooth Real Income?*

In a two-country model, complete asset markets do not guarantee that individuals will choose to eliminate all (diverifiable) risk in aggregate consumption. the presence of nontraded goods forces individuals to choose between reducing uncertainty in aggregate consumption and in the composition between traded and nontraded goods. This choice depends on a comparison of the standard coefficient of relative risk aversion with a second type of risk aversion that becomes relevant when nontraded goods are present, one that captures aversion to risk in composition. Regardless of the decision made, asset trade always reduces the risk premium.     

Repetitive risk aversion

We propose a reasonable condition, which we call repetitive risk aversion (RRA), to be imposed on any utility function to account for the observed data on the relationship between the degree of absolute risk aversion and wealth. We deduce this condition from the concept of the fear of ruin (Aumann and Kurz 1977) and show it to be equivalent to the behaviorally meaningful condition that the risk premium is increasing at a non-increasing rate with the size of the bet. We drive mixed risk aversion, which is known to be stronger than standard and thus proper risk aversion, from RRA. We present several economic applications of RRA to demonstrate that it delivers better comparative static results.I am thankful to Jacques Drèze and Louis Eeckhoudt for their comments. I greatly appreciate the comments of an anonymous reviewer of this journal which have resulted in substantial improvement to both the content and presentation of the paper. An earlier version of this paper was presented at seminars at Brown, CORE, Hopkins, HKUST, Yale, and IMS     

Comparing risk aversion in a probability triangle

An agent's acceptance set consists of the probability distributions preferred to the status quo. One agent is more risk averse than another if the more risk averse agent's acceptance set is a proper subset of the less risk averse agent's acceptance set. An agent's odds premium expresses the odds in favor of winning the largest cash prize in a lottery over the best and worst alternatives that is indifferent to the the agent's initial wealth. Comparisons of two agents odds premia completely characterizes the risk aversion relations between them when facing lotteries in a probability triangle. The result applies to expected utility and some non-expected utility theories. Received: December 30, 1998; revised version: February 10, 1999     

When is market incompleteness irrelevant for the price of aggregate risk (and when is it not)?

In a standard incomplete markets model with a continuum of households that have constant relative risk aversion (CRRA) preferences, the absence of insurance markets for idiosyncratic labor income risk has no effect on the premium for aggregate risk if the distribution of idiosyncratic risk is independent of aggregate shocks and aggregate consumption growth is independent over time. In equilibrium, households only use the stock market to smooth consumption; the bond market is inoperative. Furthermore, the cross-sectional distributions of wealth and consumption are not affected by aggregate shocks. These results hold regardless of the persistence of idiosyncratic shocks, even when households face tight solvency constraints. A weaker irrelevance result survives when we allow for predictability in aggregate consumption growth.     

Another Look at the Equity Risk Premium Puzzle

The model of Mehra and Prescott (1985, J. Econometrics, 22, 145–161) implies that reasonable coefficients of risk‐aversion of economic agents cannot explain the equity risk premium generated by financial markets. This discrepancy is hitherto regarded as a major financial puzzle. We propose an alternative model to explain the equity premium. For normally distributed returns and for returns far away from normality (but still light tailed), realistic equity risk premia do not imply puzzlingly high risk aversions. Following our approach, the ‘equity premium puzzle’ does not exist. We also consider fat‐tailed return distributions and show that Pareto tails are incompatible with constant relative risk aversion.     

社会地位、非期望效用函数、资产定价和经济增长

本文利用非期望偏好结构 ,讨论消费和资产收益的时间序列行为。在这种递归偏好结构中 ,投资者积累财富不仅仅为了消费 ,也为了财富所带来的社会地位 ,我们研究这一假设对消费、投资组合策略、证券市场价格以及经济增长的影响 ,并利用所得到的定价方程讨论风险溢金问题。     

The monetary utility premium and interpersonal comparisons

The utility premium is generally defined as the pain or reduction in expected utility caused by an n$n$th-degree risk increase, where n≥2$n\ge 2$. While it is a very useful concept in understanding a decision maker’s choice in uncertain situations, the utility premium is not interpersonally comparable. This note shows that the monetary utility premium–the utility premium divided by the expected marginal utility at the random starting wealth–is interpersonally comparable, and the comparison is characterized by Ross more risk aversion of the corresponding degree.     

“Fair go” for all? Wealth and Risk Aversion of Australian Households*

A mean‐variance framework is applied to Australian household financial portfolios in order to provide estimates of relative risk aversion in the economy. Controlling for various socio‐economic characteristics, we explore whether risk aversion heterogeneity is a function of wealth heterogeneity. In contrast to most studies, we find evidence of very high risk aversion amongst the majority of households of poor households but vastly lower risk aversion amongst the high percentiles in the wealth distribution. Applying a first differences model across three survey waves spanning 2002 to 2010, we find that risk tolerance increases significantly with wealth. Risk tolerance is positively associated with mortgage payments, but rental payments have no relationship. In addition, we found no evidence that holding a university education has any discernible impact on risk aversion. Lastly, we present some preliminary findings as to the impact of financial advice on observed risk aversion. Financial advice is found to accentuating risk aversion, particularly amongst the wealthiest households. The findings have potential implications for the distribution of wealth in Australia that has received renewed interest recently.     

Precautionary savings of agents with heterogeneous risk aversion

This article focuses on the estimation of the importance of the precautionary motive in the wealth accumulation decision. We use the micro data set of the De Nederlandsche Bank (DNB) Household Survey (DHS) (CentERdata, Tilburg University), a Dutch household survey containing information on wealth, a subjective measure of income uncertainty and subjective qualitative measures of risk aversion. We find that only a small share of wealth is accumulated for the precautionary motive by the Dutch households. This share of wealth is constant across assets with different degrees of liquidity. The economic downturn of the period 2008 to 2010 seems to affect risk attitudes and precautionary saving. Our findings also suggest that the more risk-averse individuals are those who hold less savings.     

Risk aversion,impatience, and optimal timing decisions

In this paper, a theory measuring a decision maker's aversion to temporal risks is developed in the context of a simple choice framework that admits the interpretation “time varying utility of wealth.” A relation “more temporally risk averse” is defined and characterized in terms of instantaneous risk aversion (the usual single variable case) and impatience. A further characterization of this relation is obtained in the context of a class of action timing problems known as optimal stopping problems and is applied to preference based investigations of information production, incentives to innovate, and job search.     

Junior is rich: bequests as consumption

We explore the consequences for asset pricing of admitting a bequest motive into an otherwise standard overlapping generations economy where agents trade equity, a risk free asset and consol bonds. With low risk aversion, the calibrated model produces realistic values for the mean equity premium and the risk free rate, the variance of the equity premium, and the ratio of bequests to wealth. However, the variance of the risk free rate is unrealistically high. Security prices tend to be substantially higher in an economy with bequests as compared to an otherwise identical one where bequests are absent. We are able to keep the prices sufficiently low to generate reasonable returns and premia by stipulating that a portion of the bequests skips a generation and is received by the young.

“You never actually own a Patek Philippe. You merely take care of it for the next generation.” Patek Philippe & Co.

We thank John Cox, Jean Pierre Danthine, Felix Kubler, Edward Prescott and seminar participants at The Bank of Italy, Columbia, Lausanne, Mannheim, MIT, Lugano, SIFR, the University of New South Wales, USC, Yale and the University of Zurich for insightful xcomments. The usual caveat applies.     

Market Instability and Revision Error in Risk Premium

This paper provides a theory and evidence that the risk premium puzzle is viewed as a phenomenon pertaining to the unstable foreign exchange market. In an unstable market, revision error uncompensated by an initial risk premium accrues due to consumer expectation revision about the ex ante uncertainty of the exchange rate. The risk premium widely deviates from its initial level, depending on the frequency of the consumer expectation revision and the degree of risk aversion. Subsequent evidence shows the existence of the revision errors for the risk premium during the Asian currency crisis and the recent financial crisis periods.     

Human capital and the private equity premium

When capital market is imperfect, an entrepreneur has to invest substantial personal funds to start a firm and has to bear large firm-specific risk. Furthermore, if a typical entrepreneur is risk averse, private equity should earn a premium for idiosyncratic risk. In this paper I explore the interaction of human capital with the decision to become an entrepreneur. I calibrate a model of entrepreneurial choice to illustrate a significant attenuating effect of human capital on the premium for firm-specific risk. When an entrepreneur can quit the business and work for hire, the firm-specific risk premium is order of magnitude lower than without this option. While an entrepreneur puts at risk a substantial fraction of financial wealth, she does not commit all human capital to the current business. At stake is only the labor income forgone while managing the firm and the rest of human capital is unaffected by the business risk. Empirical evidence suggests that private equity does not earn any significant premium over publicly traded equity. The model with human capital is consistent with this observation, assuming typical entrepreneur forgoes a small expected return (1.5%) in lieu of intangible benefits of entrepreneurship.     

How much does schooling disutility matter?

Studies on structural education choice models are often inconsistent in choosing whether and how to include a disutility of education, especially in an environment with risk and wealth inequality. We show that adding a disutility term to the education decision, a human capital investment option, is equivalent to assuming a relationship between wealth, risk, and education. Utility gain from education is increasing in the riskiness of future consumption. A riskier environment further propels an agent to choose the human capital investment option that maximizes future income. If the degree of risk increases heterogeneously across multiple human capital investment options, risk aversion and the precautionary savings motive can compound or negate each other depending on which option has a greater increase in risk.     

Wealth inequality and dynamic stability

We explore the link between wealth inequality and stability in a two-sector neoclassical growth model with heterogeneous agents. We show that when the inverse of absolute risk aversion (or risk tolerance) is a strictly convex function, wealth inequality is a factor that favors instability. In the opposite case, inequality favors stability. Our characterization also shows that whenever absolute risk tolerance is linear, as when preferences exhibit hyperbolic absolute risk aversion (HARA), wealth heterogeneity is neutral.     

Epstein–Zin Utility in DICE: Is Risk Aversion Irrelevant to Climate Policy?

Climate change involves uncertain probabilities of catastrophic risks, and very longterm consequences of current actions. Climate economics, therefore, is centrally concerned with the treatment of risk and time. Yet conventional assumptions about utility and optimal economic growth create a perverse connection between risk aversion and time preference, such that more aversion to current risks implies less concern for future outcomes, and vice versa. The same conflation of risk aversion and time preference leads to the equity premium puzzle in finance. A promising response to the equity premium puzzle, the recursive utility of Epstein and Zin, allows separation of risk aversion and time preference—at the cost of considerable analytic complexity. We introduce an accessible implementation of Epstein–Zin utility into the DICE model of climate economics, creating a hybrid “EZ-DICE” model. Using Epstein–Zin parameters from the finance literature and climate uncertainty parameters from the science literature, we find that the optimal climate policy in EZ-DICE calls for rapid abatement of carbon emissions; it is similar to standard DICE results with the discount rate set to equal the risk-free rate of return. EZ-DICE solutions are sensitive to the intertemporal elasticity of substitution, but remarkably insensitive to risk aversion. Insensitivity to risk aversion may reflect the difficulty of modeling catastrophic risks within DICE. Implicit in DICE are strong assumptions about the cost of climate stabilization and the certainty and speed of success; under these assumptions, risk aversion would in fact be unimportant. A more realistic analysis will require a subtler treatment of catastrophic climate risk.     

The effect of decision weights in bargaining problems

Bargaining problems are considered where the preferences of the bargainers deviate from expected utility but can be modelled according to rank-dependent utility theory. Under rank-dependent utility both the utility function and the probability weighting function influence the risk attitude of a decision maker. The same definition of risk aversion leads to two forms of risk aversion: utility risk aversion and probabilistic risk aversion. The main finding is that these two forms can have surprisingly opposite consequences for bargaining solutions that exhibit a weak monotonicity property. In particular, in a large class of bargaining problems both increased utility risk aversion and decreased probabilistic risk aversion of the opponent are advantagous for a player. This is demonstrated for the Kalai-Smorodinsky bargaining solution. The Nash bargaining solution does not behave regularly in this respect.     

Life with habit and expectation: A new explanation of equity premium puzzle

Previous writers have attempted to resolve the equity premium puzzle by employing a utility function that depends on current consumption minus (or relative to) past habit consumption. This paper points out that an individual's current utility may also depend upon how well off in the recent past he or she had expected to be today. Hence we add the concept “expectation formation” to the utility modification term in a model with a habit‐formation utility function. We apply the model to the equity premium puzzle and find that it is able to fit the data with a relatively low coefficient of relative risk aversion. Furthermore, we introduce an updated data sample and apply different values of discounting factors, and find that in all circumstances, the model is able to generate coefficients of risk aversion that are consistent with theory. Hence we conclude that the model is able to resolve the equity premium puzzle.