Habit formation and the equity–premium puzzle: a skeptical view

We argue that, ceteris paribus, introducing a habit that resolves the equity–premium puzzle is equivalent to increasing the Arrow-Pratt coefficient of relative risk aversion, AP-RRA. If we constrain the AP-RRA to a constant ‘acceptable’ level, the effect on the equity premium is quantitatively insignificant. In a dynamic setting, the fluctuations of the habit increase the equity premium, slightly, though generates unrealistic fluctuations in the risk-free interest rate. We conclude a habit is observationally equivalent, up to a first-order approximation, to a higher AP-RRA and to a preference shock. These effects cannot resolve the equity–premium puzzle.      

Myopic loss aversion and the equity premium puzzle reconsidered

Benartzi and Thaler [The Quarterly Journal of Economics 110 (1995) 73–92] offer a quasi-rational explanation for the equity premium puzzle. We reconsider their methodology and, making a simple modification to it, find that their analysis is not robust.     

Isolating the disaster risk premium with equity options

The US equity risk premium is approximated with a mean unhedged equity return. I utilize out-of-the-money put options to obtain a hedged equity return, which allows me to quantify the disaster risk premium as the difference between the means of unhedged and hedged equity returns. I demonstrate that a substantial fraction of the U.S. equity risk premium over the period from 1996 to 2016 is attributed to disasters defined as stock price depreciations below a pre-specified strike price. Employing alternative hedging schemes increases the contribution of disasters to the equity risk premium.     

Monetary policy and the cyclicality of risk

A dynamic general equilibrium model to study the relationship between monetary policy and movements in risk is developed. Variation in risk arises because households face fixed costs of transferring cash across financial accounts, implying that some households rebalance their portfolios infrequently. Accordingly, prices for risky assets respond sharply to aggregate shocks because only a relatively small subset of consumers are available to absorb these shocks. The model can account for both the mean and the volatility of returns on equity and the risk-free rate and generates a decline in the equity premium following an unanticipated easing of monetary policy.     

Entrepreneurial risk aversion,net worth effects and real fluctuations

This paper examines the combined effect of asymmetric information and private entrepreneurial risk aversion on investment decisions. The standard optimal debt contract becomes modified by the introduction of insurance and a risk premium that entrepreneurs demand due to the uncertainty of their investment returns: the private equity premium. In general equilibrium, the private equity premium may become a mechanism that magnifies the effects of shocks. A structural estimation of the model's parameters using Chilean and U.S. data shows that the entrepreneurial risk aversion assumption has more empirical relevance in an economy where smaller privately-held businesses are relatively more prevalent than where the corporate sector predominates, like the U.S.     

Age‐Dependent Increasing Risk Aversion and the Equity Premium Puzzle

We introduce a new preference structure—age‐dependent increasing risk aversion (IRA)—in a three‐period overlapping generations model with borrowing constraints, and examine the behavior of equity premium in this framework. We find that IRA preferences generate results that are more consistent with U.S. data for the equity premium, level of savings and portfolio shares, without assuming unreasonable levels of risk aversion. We find that the relative difference between the two risk aversions (how much more risk‐averse old agents are relative to the middle‐aged) matters more than the average risk aversion in the economy (how much more risk‐averse both cohorts are). Our findings are robust with respect to a number of model generalizations.     

A note on myopic loss aversion and the equity premium puzzle

In 1995, Benartzi and Thaler introduced the concept myopic loss aversion to explain the equity premium puzzle. They provided empirical evidence to support their arguments. Recently, Durand et al. criticized this empirical analysis. They propose an approach which not only rejects the significance of the earlier findings but also suggests a reversal of the original findings. In contrast to their approach, we implement a bootstrap approach and find results in line with the results of Benartzi and Thaler. We further show that the significance of the effect strongly depends on somewhat arbitrary assumptions about the length of data history.     

Displacement risk and asset returns

We study asset-pricing implications of innovation in a general-equilibrium overlapping-generations economy. Innovation increases the competitive pressure on existing firms and workers, reducing the profits of existing firms and eroding the human capital of older workers. Due to the lack of inter-generational risk sharing, innovation creates a systematic risk factor, which we call “displacement risk.” This risk helps explain several empirical patterns, including the existence of the growth-value factor in returns, the value premium, and the high equity premium. We assess the magnitude of displacement risk using estimates of inter-cohort consumption differences across households and find support for the model.     

Unconventional monetary policy announcements and risk aversion: evidence from the U.S. and European equity markets

ABSTRACT

This paper examines the role of unconventional monetary policy announcements on risk aversion – as proxied by the variance premium – by using panel data analysis. The objective of this empirical analysis is to investigate the risk-taking channel of monetary policy for the major European and U.S. equity markets by studying the impact that the announcements of an unconventional monetary policy has on market uncertainty and risk perception. By measuring the difference between risk-neutral and realised and conditional variance, we estimate the variance premium, which captures the impact that pricing concerns have on the prices of options. The empirical analysis indicates that easing monetary policies can significantly reduce the variance premium. In addition, we examine the risk premium structure across markets to determine the potential differences in investors’ risk aversion.     

The equity premium implied by production

This paper studies the determinants of the equity premium as implied by producers’ first-order conditions. A simple closed form expression is presented for the Sharpe ratio as a function of investment volatility and technology parameters. Calibrated to the US postwar economy, the model can match the historical first and second moments of the market return and the risk-free interest rate. The model also generates a very volatile Sharpe ratio and market price of risk.     

Loss aversion,asymmetric market comovements,and the home bias

Loss aversion has been used to explain why a high equity premium might be consistent with plausible levels of risk aversion. The intuition is that the first-order-different utility impact of wealth gains and losses leads loss-averse investors to behave similarly to investors with high risk aversion. But if so, should those agents not perceive larger gains from international diversification than standard expected-utility investors with plausible levels of risk aversion? They might not, because comovements in international stock markets are asymmetric: correlations are higher in market downturns than in upturns. This asymmetry dampens the gains from diversification relatively more for loss-averse investors. We analyze the portfolio problem of such an investor who has to choose between home and foreign equities in the presence of asymmetric comovement in returns. Perhaps surprisingly, in the context of the home bias puzzle we find that loss-averse investors behave similarly to those with standard expected-utility preferences and plausible levels of risk aversion. We argue that preference specifications that appear to perform well with respect to the equity premium puzzle should be subjected to this “test”.     

Rare disaster risk and the expected equity risk premium

Consistent with the predictions of rare disaster models, we find that a proxy for the time‐varying probability of rare disasters helps to explain fluctuations in expectations of the equity risk premium. Our proxy for disaster risk is a recently developed measure of global political instability, and the expected market risk premium is from Value Line analysts' expected stock returns. Consistent with long‐run risk models, uncertainty about expected GDP growth and expected consumption growth is also significantly positively related to the expected market risk premium. We obtain similar results when we use the earnings–price ratio and the dividend–price ratio as proxies for the expected market risk premium.     

Growth uncertainty,generalized disappointment aversion and production-based asset pricing

We study a production economy with regime switching in the conditional mean and volatility of productivity growth. The representative agent has generalized disappointment aversion (GDA) preferences. We show that volatility risk in productivity growth carries a positive and sizable risk premium in levered equity. Our model can endogenously generate long-run risks in the volatility of consumption growth observed in the data. We show that introducing leverage with a procyclical dividend process consistent with the data is critical for the GDA preferences to have a large impact on equity returns.     

Time varying consumption covariance and dynamics of the equity premium: Evidence from the G7 countries

We examine implications of time-varying correlation and covariance between excess equity returns and consumption growth for the equity premium of the G7 countries. We find that the correlation and covariance are higher when there is a negative shock to labor income and a positive shock to returns. The combined effect is that the correlation and covariance are countercyclical and so is the equity premium. We test asset pricing models with time-varying consumption risk and find that the conditional price of risk is generally positive. These results survive several robustness checks. Our results highlight the importance of labor income for understanding dynamics of the equity premium.     

Re-examination of the historical equity risk premium in Australia

In light of the ongoing debate over the value of the equity risk premium, its increasing use in the regulatory setting, and the impact of dividend imputation on the premium, this paper presents a timely new look at the historical equity risk premium in Australia, and provides an improved understanding of the historical record. We document concerns about data quality that become increasingly important the further back in time one looks. In particular, there are sufficient question marks over the quality of data prior to 1958 to warrant any estimates based thereon to be treated with caution. Accordingly, we present a new set of estimates of the historical equity risk premium corresponding to periods of increasing data quality but of decreasing sample size. Relative to bonds (bills), the equity premium has averaged 6.3 per cent (6.8 per cent) per annum over 1958–2005, which is a period of relatively good data quality. Together with other results in the paper, the findings reveal a historical estimate that is substantially less than widely cited historical studies would otherwise indicate. We reconcile prior evidence through documenting a dividend adjustment that has typically been overlooked. We also provide estimates that incorporate an adjustment for imputation credits.     

The Effect of Temporal Risk Aversion on Optimal Consumption,the Equity Premium,and the Equilibrium Interest Rate

This paper demonstrates that temporal risk aversion makes smoothing consumption over time less attractive, while the usual risk aversion makes it more attractive. As temporal risk aversion increases, the equilibrium interest rate decreases and the equity premium increases. This paper also shows a striking and novel result that an increase in time impatience can lead to either a decrease or an increase in the interest rate, depending on the nature of the nonseparability.     

Home bias in equity portfolios, inflation hedging, and international capital market equilibrium

We test whether the home bias in equity portfolios is causedby investors trying to hedge inflation risk. The empirical evidenceis consistent with this motive only if investors have very highlevels of risk tolerance and equity returns are negatively correlatedwith domestic inflation. We then develop a model of internationalportfolio choice and equity market equilibrium that integratesinflation risk and deadweight costs. Using this model we estimatethe levels of costs required to generate the observed home biasin portfolios consistent with different levels of risk aversion.For a level of risk aversion consistent with standard estimatesof the domestic equity market risk premium these costs are abouta few percent per annum greater than observable costs such aswithholding taxes. Thus, the home bias cannot be explained byeither inflation hedging or direct observable costs of internationalinvestment unless investors have very low levels of risk aversion.     

Computing the market price of volatility risk in the energy commodity markets

In this paper, we demonstrate the need for a negative market price of volatility risk to recover the difference between Black–Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654]/Black [Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, pp. 177–181] implied volatility and realized-term volatility. Initially, using quasi-Monte Carlo simulation, we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk-neutral and statistical volatility in both equity and commodity-energy markets. This is robust to multiple specifications that also incorporate jumps. Next, using futures and options data from natural gas, heating oil and crude oil contracts over a 10 year period, we estimate the volatility risk premium and demonstrate that the premium is negative and significant for all three commodities. Additionally, there appear distinct seasonality patterns for natural gas and heating oil, where winter/withdrawal months have higher volatility risk premiums. Computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets.     

An Equilibrium Model of Rare-Event Premia and Its Implication for Option Smirks

This article studies the asset pricing implication of impreciseknowledge about rare events. Modeling rare events as jumps inthe aggregate endowment, we explicitly solve the equilibriumasset prices in a pure-exchange economy with a representativeagent who is averse not only to risk but also to model uncertaintywith respect to rare events. The equilibrium equity premiumhas three components: the diffusive- and jump-risk premiums,both driven by risk aversion; and the "rare-event premium,"driven exclusively by uncertainty aversion. To disentangle therare-event premiums from the standard risk-based premiums, weexamine the equilibrium prices of options across moneyness or,equivalently, across varying sensitivities to rare events. Wefind that uncertainty aversion toward rare events plays an importantrole in explaining the pricing differentials among options acrossmoneyness, particularly the prevalent "smirk" patterns documentedin the index options market.     

A new approach to measuring riskiness in the equity market: Implications for the risk premium

We introduce a new approach to measuring riskiness in the equity market. We propose option implied and physical measures of riskiness and investigate their performance in predicting future market returns. The predictive regressions indicate a positive and significant relation between time-varying riskiness and expected market returns. The significantly positive link between aggregate riskiness and market risk premium remains intact after controlling for the S&P 500 index option implied volatility (VIX), aggregate idiosyncratic volatility, and a large set of macroeconomic variables. We also provide alternative explanations for the positive relation by showing that aggregate riskiness is higher during economic downturns characterized by high aggregate risk aversion and high expected returns.