Equity risk premium and time horizon: What do the U.S. secular data say?

We consider a representative investor whose wealth is made up of the equity market portfolio and the riskless asset, and who maximizes the expected utility of his/her future wealth for a given horizon. The solution of this program shows that the equilibrium value of the equity risk premium – the latter being measured by the difference between the expected equity portfolio return and the risk-free interest rate – is given by the product of the price of risk by the expected variance of stock returns. When returns are predictable, these two magnitudes are both time-varying and horizon-dependent. In accordance with this theoretical framework, our paper presents an econometric model of the equity risk premia for two traditional horizons: the one-period-ahead horizon (i.e. the ‘short-term’ premium) and the infinite-time horizon (i.e. the ‘long-term’ premium). Using annual US secular data from 1871 to 2008, and representing the expected returns by mixing the three traditional adaptive, extrapolative and regressive processes, large disparities in the dynamics of the two premia are evidenced. Concerning the determination of the equilibrium values of the two premia, the expected variances depend on the past values of the centered squared returns while the prices of risk (unobservable variables) are estimated according to the Kalman filter methodology, which enables us to capture the influence of hidden variables and of non-directly measurable psychological effects. A spread of interest rates adds to this determination. Possibly due to risky arbitrage and transaction costs, the results show that observed premia gradually converge towards their equilibrium values, this process being described by an error correction model. Overall, our model provides a rather satisfactory representation of ‘short-term’ and ‘long-term’ premia.     

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.     

Wealth inequality, preference heterogeneity and macroeconomic volatility in two-sector economies

We explore the link between wealth inequality, preference heterogeneity and macroeconomic volatility in a two-sector neoclassical growth model. First we prove that, if agents have homogeneous preferences, when the absolute risk tolerance is a strictly convex (concave) function, sufficiently high (low) levels of wealth inequality may lead to endogenous fluctuations in the neighborhood of the steady state. Second, we consider the effects of preference heterogeneity when agents are homogeneous with respect to their wealth. We show that when the utility function belongs to the HARA class, sufficiently high levels of preference heterogeneity may lead to endogenous fluctuations in the neighborhood of the steady state if the elasticity of intertemporal substitution in consumption is greater than one.     

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.     

A Model of economic mobility and the distribution of wealth

This paper introduces new techniques to obtain a closed-form rank-by-rank characterization of the equilibrium distribution of wealth in a model in which finitely lived households face uninsurable idiosyncratic investment risk. A central result is that the extent of inequality is determined entirely by two factors. The first factor, household exposure to idiosyncratic investment risk, increases inequality. The second factor, cross-sectional mean reversion of household wealth, decreases inequality. We show that economic mobility is decreasing in inequality and increasing in mean reversion, a result that is consistent with recent empirical observations about the geographic variation in mobility that exists both domestically and internationally. Our approach allows us to examine the implications of increased market completeness in the form of a risk-sharing subgroup of households. We show that a risk-sharing subgroup rises or falls in the equilibrium wealth distribution depending on the level of inequality, and that its presence raises welfare and the rate of wealth accumulation for all households in the economy.     

High equity premia and crash fears - Rational foundations

Summary. We show that in a Lucas endowment economy in which the process for dividends is described by a lattice tree subject to infrequent but observable structural breaks, in equilibrium recursive rational learning may inflate the equity risk premium and reduce the risk-free interest rate for low levels of risk aversion. The key condition for these results to obtain is the presence of sufficient initial pessimism. The relevance of these findings is magnified by the fact that under full information our artificial economy cannot generate asset returns matching the empirical evidence for any positive relative risk aversion.Received: 20 September 2003, Revised: 27 April 2005, JEL Classification Numbers: D83, E44, G12.I am indebted to Mordecai Kurz (the co-Editor), one anonymous Referee, Gabriele Camera, Sadayuki Ono, Olesia Verchenko, and Allan Timmermann for many useful comments. I also think seminar paticipants at the European Economic Association meetings in Stockholm (August 2003) and the Midwest Economics Association in St. Louis (March 2003).     

On model ambiguity and money neutrality

We solve for the equilibrium of a stochastic neo-classical continuous time model without and with money under model ambiguity. We show that: (i) the correction for ambiguity stemming from the money supply is nil at equilibrium; (ii) money is neutral with respect to the stock market equilibrium (the equity risk premium); (iii) money is not neutral with respect to consumption and capital accumulation, and its effect may be quantitatively substantial; (iv) the preference for model robustness affects all the real economic variables as well as the expected inflation rate and the nominal interest rate.     

Redistributive effects of minimal equal sacrifice taxation

We examine the circumstances under which minimal equal sacrifice taxation reduces income inequality. Focusing on absolute sacrifice and relative inequality, we show that after tax incomes are more equally distributed than before tax incomes and that after tax inequality decreases with the revenue to be raised if and only if the elasticity of the marginal utility of income is decreasing. However, other things equal, after tax inequality is shown to decline as the utility function becomes more concave. We investigate next how these conclusions extend when one takes the absolute inequality view and considers that it is the relative loss in utility that has to be equalized across individuals.     

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.     

Currency Hedging and Siegel's Paradox: On Black's Universal Hedging Rule*

In an international multicurrency context, with nonstochastic inflation, equilibrium asset pricing models dictate that all investors should hold a combination of their national risk-free bill and the world market portfolio partly hedged against currency risk. We show that the equilibrium hedge ratios are not universal and depend on investors' preferences and relative wealth. So-called universal hedging rules are devoid of solid theoretical underpinning and practical applicability.     

Rational inattention,long-run consumption risk,and portfolio choice

This paper explores how the introduction of rational inattention (RI) – that agents process information subject to finite channel capacity – affects optimal consumption and investment decisions in an otherwise standard intertemporal model of portfolio choice. We first explicitly derive optimal consumption and portfolio rules under RI and then show that introducing RI reduces the optimal share of savings invested in the risky asset because inattentive investors face greater long-run consumption risk. We also show that the investment horizon matters for portfolio allocation in the presence of RI, even if investment opportunities are constant and the utility function of investors is constant relative risk aversion. Second, after aggregating across investors, we show that introducing RI can better explain the observed joint dynamics of aggregate consumption and the equity return. Finally, we show that RI increases the implied equity premium because investors under RI face greater long-run consumption risk and thus require higher compensation in equilibrium.     

The equity premium in a small open economy and an application to Israel

We show that the preferences suggested by Greenwood, Hercowitz and Huffman (GHH), which are quite common in real business cycle (RBC) models of small open economies, are not suited for reproducing both the business cycle and the equity premium facts of a small open economy. We show that by assuming a moderate degree of a wealth effect on labor supply, together with some limitations on labor supply (in the form of real wage rigidity), we can increase the volatility of the stochastic discount factor (SDF), thereby increasing the equity premium and improving the fit of the business cycle moments. We also find that under the aforementioned assumptions, a shock to the realized return on foreign bonds can help in reproducing the equity premium.     

Heterogeneity of First-order Risk Aversion and the Equity Premium

I show that stockholders and non-stockholders can coexist in equilibrium even if securities markets are perfect and complete. This is due to a heterogeneous safety inclination, which is defined as heterogeneity in first-order risk aversion (Segal and Spivak, 1990). A static two-security market model is analysed by the mean–standard deviation approach, where safety inclination is described by the degree of the marginal rate of substitution between the mean and the standard deviation at a certain point. In equilibrium, aggregate shocks may be concentrated on stockholders, which may lead to a high equity premium.
JEL Classification Numbers: D81, E44.     

Stochastic optimization applied to self-financing portfolio: does bequest matter?

The article studies stochastic optimization of an intertemporal consumption model to allocate financial assets between risky and risk-free assets. We use a stochastic optimization technique, in which utility is maximized subject to a self-financing portfolio constraint. The papers in literature have estimated the errors of Euler equations using data from financial markets. It has been shown that it is sufficient to test the first order Euler equation implied by the model. However, they all assume a constant consumption–wealth ratio that constrains the boundary conditions, hence influencing the coefficient of the risk premium. The main contribution of our article is that we drop the assumption of a constant consumption–wealth ratio. We have an analytical solution using a utility maximization model with a stochastic self-financing portfolio. We introduce a terminal condition of wealth with and without bequests. We also simulate the stochastic optimization with a self-financing portfolio, distinguishing risk neutral investors (γ-low) from high risk averse investors (γ-high). We show that the model with bequest has a higher level of wealth and a smoother decline of consumption over time than the model with no bequest at the end of the period. The model with no bequest has the same level of consumption and a sharp fall at the end of the period. Risk averse agents with high return assets have a higher amount of wealth than risk-neutral agents with lower return assets.     

基于效用成本风险异质性的消费资本资产定价模型

资产定价既是现代金融的核心,也是许多困惑之所在,其中最著名的就是股权溢价之谜和无风险利率之谜。本文对消费资本资产定价模型中的效用成本做了重新思考,引入"效用成本风险异质性"的概念,并将效用成本区分为"消费效用成本"和"风险效用成本"。在此基础上,本文提出了消费资本资产定价模型的新形式,并对股权溢价之谜和无风险利率之谜进行解释。     

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.     

Consensus Consumer and Intertemporal Asset Pricing with Heterogeneous Beliefs

The aim of this paper is to analyse the impact of heterogeneous beliefs in an otherwise standard competitive complete market economy. The construction of a consensus probability belief, as well as a consensus consumer, is shown to be valid modulo an aggregation bias, which takes the form of a discount factor. In classical cases, the consensus probability belief is a risk tolerance weighted average of the individual beliefs, and the discount factor is proportional to beliefs dispersion. This discount factor makes the heterogeneous beliefs setting fundamentally different from the homogeneous beliefs setting, and it is consistent with the interpretation of beliefs heterogeneity as a source of risk.
We then use our construction to rewrite in a simple way the equilibrium characteristics (market price of risk, risk premium, risk-free rate) in a heterogeneous beliefs framework and to analyse the impact of beliefs heterogeneity. Finally, we show that it is possible to construct specific parametrizations of the heterogeneous beliefs model that lead to globally higher risk premia and lower risk-free rates.     

Asset pricing in an Islamic economy

ABSTRACT

We define an Islamic economy as one with borrowing restrictions, no leverage, and no risk-free asset. We derive a consumption-based asset pricing model for this economy under standard preferences. We demonstrate that news to consumption growth is the main driver of Islamic financial markets, but the degree of borrowing constraints also affects the pricing of Islamic assets. Using Saudi Arabian data, simulations show that our model does a good job in matching the observed equity premium as well as the volatility of the market return. Our model implies that the price-dividend ratio predicts dividend growth, and as a result that prices are driven mainly by cash-flow news rather than by discount rate news. Empirical tests show that our model is consistent with the data.     

Why progressive redistribution can hurt the poor

Recent macroeconomic research discusses credit market imperfections as a key channel through which inequality retards growth: With convex technologies, progressive transfers increase aggregate output because marginal returns become more equalized across investment opportunities. We argue that this reasoning may not hold in general equilibrium. Since the investment functions are concave in wealth, reducing inequality increases capital demand and the interest rate. Hence, through the impact on capital costs, shifting wealth from the rich to the middle class depletes the poorest investors' access to credit. But because the poor face the highest marginal returns, the net effect on output may be negative. We find, however, that redistributing towards the bottom-end of the distribution has a clear positive impact. Finally, we discuss the implications of our theoretical findings for future empirical research.     

Uncertainty and the comparative dynamics of stock price

This article derives an envelope theorem for dynamic economic problems under conditions of uncertainty. The theorem is motivated through analysis of a firm with an objective of maximizing shareholders' wealth. Envelope results are used to determine how the value of the optimizing firm is expected to change in response to shifts in several variables including the risk-free interest rate, the market risk premium, the tax rate, and the prices of output and inputs. Uncertainty is introduced into the model using a general measure-theoretic approach which does not require restrictive assumptions regarding the behavior of the problem's stochastic variables.