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.     

State-dependent preferences can explain the equity premium puzzle

We introduce state-dependent recursive preferences into the Mehra–Prescott economy. We show that such preferences can match the historical first two moments of the returns on equity and the risk-free rate. Other authors have reported similar results using state-dependent expected utility preferences. These authors have tended to emphasize the importance of countercyclical risk aversion in explaining the equity premium puzzle. We find that countercyclical risk aversion plays an important role but only when combined with modest cyclical variation in intertemporal substitution.     

Euler equation errors

The standard, representative agent, consumption-based asset pricing theory based on CRRA utility fails to explain the average returns of risky assets. When evaluated on cross-sections of stock returns, the model generates economically large unconditional Euler equation errors. Unlike the equity premium puzzle, these large Euler equation errors cannot be resolved with high values of risk aversion. To explain why the standard model fails, we need to develop alternative models that can rationalize its large pricing errors. We evaluate whether four newer theories at the vanguard of consumption-based asset pricing can explain the large Euler equation errors of the standard consumption-based model. In each case, we find that the alternative theory counterfactually implies that the standard model has negligible Euler equation errors. We show that the models miss on this dimension because they mischaracterize the joint behavior of consumption and asset returns in recessions, when aggregate consumption is falling. By contrast, a simple model in which aggregate consumption growth and stockholder consumption growth are highly correlated most of the time, but have low or negative correlation in severe recessions, produces violations of the standard model's Euler equations and departures from joint lognormality that are remarkably similar to those found in the data.     

股权溢价之谜

作为金融市场上的异象之一,股权溢价之谜自被提出之时就引起了金融经济学术界的广泛关注,大量的研究人员试 图以不同的方式对传统模型进行修正来解释股权溢价之谜。本文将试图从古典经济学和行为金融学两个方面对理论学界对 股权溢价之谜的解释进行综述。     

Evaluation periods and asset prices: Myopic loss aversion at the financial marketplace

Examining myopic loss aversion (MLA [Benartzi, S., Thaler, R., 1995. Myopic loss aversion and the equity premium puzzle. Quarterly Journal of Economics 110, 73–92]) in real financial markets has several merits: in repeated situations investors may learn from each other, aggregate market prices may eliminate individual violations of expected utility, and individuals may decide differently in real situations than in laboratories. We utilize a special feature at the Tel Aviv stock exchange (TASE): occasional shifts of securities from daily to weekly trading. If investors’ decisions are influenced by trading frequency manipulation, then returns should be predictably affected. MLA results in a negative relation between risk aversion and the length of the evaluation period. Thus, the longer the evaluation period is, the lower the expected return is. This intuition also suggests reduced sensitivity to economic events in longer evaluation periods. We find strong support for MLA in the marketplace when testing expected return, as well as return sensitivity.     

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.     

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。     

CAN FINANCING CONSTRAINTS EXPLAIN THE ASSET PRICING PUZZLES IN PRODUCTION ECONOMIES?*

General Equilibrium asset pricing models have a difficult time simultaneously delivering a sizable equity premium, a low and counter cyclical real risk free rate, and cyclical variation in return volatility. To explain these stylized facts, this article introduces occasionally binding financing constraints that impede producers’ ability to invest. The financial frictions drive a wedge between the marginal rate of substitution and firms’ internal stochastic discount factors so that the shadow value of capital is not tied to the average price of capital. The model delivers higher and more volatile asset returns during recessions as well as a counter cyclical equity premium.     

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.     

中国居民消费与资产收益:基于收入群体的分析

The equity premium puzzle is found during the test of the Consumption-based Capital Asset Pricing Model (CCAPM) with aggregate consumption data. Because of income disparity, many consumers lack financial assets to intertemporally allocate their consumptions under income constraints. Thus, it is likely to lead to a specification error by employing aggregate consumption data to test the CCAPM. This paper examines the impacts of the economically constrained (low-income) consumers and unconstrained (high-income) consumers on the CCAPM using urban consumption expenditures in China delineated by consumer income, and tests the income constraint hypothesis. The empirical results show that the CCAPM is not more consistent with the consumption pattern of the higher-income consumers. Including the income constraint into the analyses of the consumption and asset returns does not unravel the equity premium puzzle.      

THE RISK PREMIUM FOR EQUITY: IMPLICATIONS FOR RESOURCE ALLOCATION,WELFARE AND POLICY*

Analysis of the equity premium puzzle has focused on private sector capital markets. The object of this paper is to consider the welfare and policy implications of each of the broad classes of explanations of the equity premium puzzle. As would be expected, the greater the deviation from the first‐best outcome implied by a given explanation of the equity premium puzzle, the more interventionist are the implied policy conclusions. Nevertheless, even explanations of the equity premium puzzle consistent with a general consumption‐based asset pricing model have important welfare and policy implications.     

Endogenous uncertainty and market volatility

We advance the theory that the distribution of beliefs in the market is the most important propagation mechanism of economic volatility. Our model is based on the theory of Rational Beliefs (RB) and Rational Belief Equilibrium (RBE) developed by Kurz (1994, 1997). We argue that the diverse market puzzles which are examined, such as the equity premium puzzle, are all driven by the structure of market expectations. In support of our view, we present an RBE model with which we study financial markets. The model is able to simulate the correct order of magnitude of: (i) the long term mean and standard deviation of the price\dividend ratio; (ii) the long term mean and standard deviation of the risky rate of return on equities; (iii) the long term mean and standard deviation of the riskless rate; (iv) the long term mean equity premium. In addition, the model predicts (v) the GARCH property of risky asset returns; (vi) the observed pattern of the predictability of long returns on assets, and (vii) the Forward Discount Bias in foreign exchange markets. The common economic explanation for these phenomena is the existence of heterogenous agents with diverse but correlated beliefs such that some agents are optimistic and some pessimistic about future capital gains. The model has a unique parameterization under which the model makes all the above predictions simultaneously. The parameterization requires the optimists to be in the majority but the rationality of belief conditions of the RBE require the pessimists to have a higher intensity level. In simple terms, the large equity premium and the low equilibrium riskless rate are the result of the fact that at any moment of time there are agents who hold extreme pessimistic beliefs and they have a relatively stronger impact on the market. The paper also studies the effect of correlation of beliefs among investors. It shows that the main effect of such correlation is on the dynamic patterns of asset prices and returns and is hence important for studying such phenomena as stochastic volatility. Received: May 16, 2000; revised version: November 15, 2000     

The Home Bias in Equities and Distribution Costs

We show that incorporating distribution costs into a general equilibrium model of international portfolio choice helps to explain the home bias in international equity investment. Our model is able to replicate observed investment positions for a wide range of parameter values, even if agents have an incentive to hedge labor income risk by purchasing foreign equity. This is because the existence of a retail sector affects both the correlation of domestic returns with the domestic price level and the correlation between financial and non‐financial income.     

Some recent developments in capital market theory: A survey

This paper surveys some recent developments in the theory of capital markets. Particular emphasis is given to two strands of the literature. The first covers some recent and fundamental extensions to the theory of risk aversion and the demand for risky assets. These papers are concerned with the effect of non-hedgeable background risk on risk attitudes. The important implications for finance are for the size of the risk premium (the equity premium puzzle) and for the demand for and pricing of contingent claims. For example, background risk may help to explain the apparent over-pricing of options on equity indices. The second topic is interest rate term structure models. Stochastic term structure models try to capture the possible future shapes of the term structure of interest rates. This is relevant for the pricing of contingent claims, in particular for the pricing of interest rate derivatives such as American-style swaptions. The paper will survey the most important recent models in the literature, each of which satisfies the fundamental no-arbitrage property. It will discuss the implications of the models for the pricing of both European-style and American-style options.     

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.     

Labour Relations and Asset Returns

This paper proposes a dynamic GE model with standard business cycle properties that also achieves a satisfactory replication of the major financial stylized facts. We ride on two major ideas. First, we show that operating leverage, originating in the priority status of wage claims given the observed business cycle characteristics of the latter, magnifies the risk properties of the residual payments to firm owners and justifies a substantial risk premium. Further we build on the observation that the low frequency variations in income shares constitute a significant source of risk, one that is unlikely to be insurable. When we price this risk in an incomplete market framework, we obtain a GE model with return volatilities close to observations and a sizable equity premium. This is accomplished in a world of low risk aversion and standard utility function but with agent heterogeneity. Workers with restricted access to financial markets are insured by firms and the consumption and preferences of firm owners solely determine the pricing kernel.     

How does a pay-as-you-go system affect asset returns and the equity premium?

When applying a differences-in-differences approach, equity returns and the equity premium are both estimated to be more than four percentage points higher after the introduction of a pay-as-you-go (PAYGO) system. In a realistically calibrated model, the PAYGO system is also found to increase the returns and the premium, although the effects are smaller than in the data. Intuitively, the system lowers asset prices, which in turn increases the importance of dividend risk. Since only equity is subject to dividend risk, equity returns become more volatile relative to bond returns.     

Migration decisions under ambiguity: Migration distance effects revisited

There is ample evidence that distance has a strong negative effect on migration. Despite its significance in migration decisions, scholars rarely explore the migration distance effect deeper than the first level of interpretation derived from the simple neoclassical theory of migration. This study revisits the migration distance effect in the spirit of Knightian distinction between risk and uncertainty. To this end, this study attempts to construct estimates of the risk premium migrants are willing to pay to avoid the risk associated with migration distance. The results show that the magnitude of the distance effect is not rationalized by risk aversion in the Arrow–Pratt sense (Arrow, 1965, The theory of risk aversion, Yrjo Jahnssonin Saatio, Helsinki, Finland, 90; Pratt, 1964, Econometrica, 32, 122). In particular, the risk premium demanded by distant rural residents is unjustifiably higher compared with that of those living closer to urban areas in their migration decisions. The results suggest that the migration distance effect is analogous to the equity home bias puzzle and the Ellsberg paradox in that the assumption of subjective expected utility can lead to seemingly irrational human behaviors. Some of the findings in this study shed light on the role of subjective aspects such as perception, confidence, and pessimism in migration decisions, which have been neglected in the literature.     

Behavioral Factors in Equity Allocation Decisions: A Large-Scale Experimental Study With Context

Traditional models of rational behavior struggle to explain how individuals allocate their money over a variety of financial instruments, including annuities, the stock market, and risk-free bonds. This study uses a large and diverse data set from an investment experiment that is rich in context and captures some important features of actual financial decision making. The focus of the article is to build on the literature documenting behavioral explanations for investment choices by studying the equity allocation decision across different financial tools. The authors find evidence that risk aversion, inertia, and excessive extrapolation are associated with investment behavior even when it is clear that return rates are independent across decision-making periods. Further, subjects have an asymmetric response to positive versus negative returns. In addition to having a novel experimental design, the authors also examine behavior before and after the recent financial crisis. The authors find that the financial crisis indirectly affects the first-stage annuity take-up rate in the experiments vis-à-vis a higher average level of risk aversion after the start of the crisis.     

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.