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.     

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.     

Exploring risk premium factors for country equity returns

In this paper, we study a comprehensive set of risk premia of country equity returns for 45 countries over the sample period 2002 - 2018 in both a single and a multiple factor setting. Using a new three-pass estimation method for factor risk premia by Giglio and Xiu (2021), we find that several factors, including default risk, are also priced in country equity excess returns, controlled by the Fama–French 5-factor and Carhart models. Moreover, we apply a novel approach to investigate the multi-factor impact on country equity returns. We find that the multi-factor information, constructed from the first principal component of the statistically significant single factors, provides a consistent and stronger prediction of anomalies in country equity returns.     

w-MPS risk aversion and the shadow CAPM: theory and empirical evidence

This paper presents the shadow capital asset pricing model (CAPM) of Ma [2011a. Advanced Asset Pricing Theory. London: Imperial College Press] as an intertemporal equilibrium asset pricing model, and tests it empirically. In contrast to the classical CAPM – a single-factor model based on a strong behavioral or distributional assumption – the shadow CAPM can be represented as a two-factor model, and only requires a modest behavioral assumption of weak form mean-preserving spread risk aversion. The empirical tests provide support in favor of the shadow CAPM over the classical CAPM, the consumption CAPM, or the Epstein and Zin [1991. “Substitution, Risk Aversion and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis”. Journal of Political Economy 99, 263–286] model. Moreover, the shadow CAPM provides a consistent explanation for the cross-sectional variations of expected returns on the stocks and for the time-varying equity premium.     

Disaggregation and the equity premium puzzle

Standard macroeconomic models cannot explain why stocks so greatly outperform bonds. However, this result depends on the use of aggregate consumption data. If markets are incomplete, then a representative agent might not exist and it is necessary to use consumption data at the household rather than aggregate level. In the household data, I fail to reject the Euler equation when the coefficient of relative risk aversion is as low as 2.7–3.8. This result is robust in a very general framework and I prove that many of the tests used in the literature are biased.     

风险厌恶、失望厌恶和期货套期保值

本文考察失望厌恶对期货套期保值的影响。我们把一个不变的绝对风险厌恶（CARA）效用函数放进Gul（1991）的失望厌恶框架之内。它显示出，一个更厌恶失望的套期保值者会比一个厌恶失望程度较低的套期保值者选择一个更接近于最小方差套期保值的最优期货头寸。当套期保值者厌恶风险的程度较低时，失望厌恶的效应更强。对失望很小程度的厌恶会使一个接近于风险中性的套期保值者持有一个截然不同的头寸。此外，一个更厌恶风险或失望的套期保值者会有一个较低的参考点reference point。数字上的结果显示，厌恶失望的套期保值者的参考点往往会低于传统的厌恶损失的套期保值者的参考点。于是，厌恶失望的套期保值者的行动会更加保守，利用机会牟利的行为会少于传统的厌恶损失的套期保值者。     

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.      

Downside beta and the cross section of equity returns: A decade later

This study reexamines the relation between downside beta and equity returns in the United States. First, we replicate the 2006 work of Ang, Chen, and Xing who find a positive relation between downside beta and future equity returns for equal‐weighted portfolios of NYSE stocks. We show that this relation doesn't hold after using value‐weighted returns or controlling for various return determinants. We also extend the original sample, add AMEX/NASDAQ stocks or utilize alternative downside beta measures and still find no downside risk premium. We focus on factor analysis results, persistence of downside beta, and various subsamples to understand the economic reasons behind the findings.     

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.     

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.     

The Equity Premium: Consistent with GDP Growth and Portfolio Insurance

We find that the long‐term equity premium is consistent with both GDP growth and portfolio insurance. We use a supply‐side growth model and demonstrate that the arithmetic average stock market return and the returns on corporate assets and debt depend on GDP per capita growth. The implied equity premium matches the U.S. historical average over 1926–2001. Separately, we find that the equity premium tracks the value of a put option on the S&P 500. Our theory predicts a smaller equity premium in the future, assuming that the recent regime shifts in dividend policies, interest rates, and tax rates are permanent.     

The cost of equity of internet stocks: a downside risk approach

Beta as a measure of risk has been under fire for many years. Although practitioners still widely use the CAPM to estimate the cost of equity of companies, they are aware of its problems and are looking for alternatives. A possible alternative is to estimate the cost of equity based on the semideviation, a well-known and intuitively plausible measure of downside risk. Complementing evidence reported elsewhere about the ability of the semideviation to explain the cross-section of returns in emerging markets and that of industries in emerging markets, this article reports results showing that the semideviation also explains the cross-section of Internet stock returns.     

Small caps in international equity portfolios: the effects of variance risk

We show that predictable covariances between means and variances of stock returns may have a first order effect on portfolio composition. In an international asset menu that includes both European and North American small capitalization equity indices, we find that a three-state, heteroskedastic regime switching VAR model is required to provide a good fit to weekly return data and to accurately predict the dynamics in the joint density of returns. As a result of the non-linear dynamic features revealed by the data, small cap portfolios become riskier in bear markets, i.e., display negative co-skewness with other stock indices. Because of this property, a power utility investor ought to hold a well-diversified portfolio, despite the high risk premium and Sharpe ratios offered by small capitalization stocks. On the contrary, small caps command large optimal weights when the investor ignores variance risk, by incorrectly assuming joint normality of returns.      

Predicting the equity market with option-implied variables

We comprehensively analyze the predictive power of several option-implied variables for monthly S&P 500 excess returns and realized variance. The correlation risk premium (CRP) and the variance risk premium (VRP) emerge as strong predictors of both excess returns and realized variance. This is true both in- and out-of-sample. Our results also reveal that statistical evidence of predictability does not necessarily lead to economic gains. However, a timing strategy based on the CRP leads to utility gains of more than 5.03% per annum. Forecast combinations provide stable forecasts for both excess returns and realized variance, and add economic value.     

Recovering the market risk premium from higher-order moment risks

We propose a consistent approach for the estimation of the market risk premium. As a first step, we define the broadest possible set of ex ante estimators from the viewpoint of a power utility optimiser holding the market portfolio. We then employ an evaluation framework to optimise the parametrisation of the methodology. We show that this theoretical framework can still produce reasonable market risk premium estimates, even when the representative agent is not a power utility optimiser. Our results show that the inclusion of higher-order moment risk premia improves the accuracy of the method.     

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.     

Economic uncertainty: Mispricing and ambiguity premium

We uncover two channels of effect in the financial market when investors face macroeconomic uncertainty. Conditional on a common mispricing index, we find that economic uncertainty exposure (EUE) induces disagreement, which amplifies mispricing. The highest EUE quintile produces an annualised mispricing alpha of 9.96%, more than double the unconditional mispricing effect. An ambiguity premium of 3.84% alpha is documented in the “non-mispricing” quintile. The EUE-induced mispricing effect is different from the existing limits of arbitrage explanations. The ambiguity premium is predictably observed during the unfolding of shocks of COVID-19 to the market.     

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.     

Relative risk aversion once more: An analysis of Japanese households' financial asset holding pattern

It is widely accepted that as the total assets increse, households tend to diversify their portfolios. In other words, absolute risk aversion is decreasing. On the other hand, the proportion of risky assets may increase or decrease depending on whether relative risk aversion (RRA) is decreasing or increasing, and its direction is still left open as an empirical question. This study examines the constancy of RRA from Japanese individual households' financial asset holding data collected in 1984. Constant RRA implies that the proportion of risky assets in one's portfolio is constant regardless of the amount of total assets. A casual observation of household portfolio holding pattern suggests that this implication is clearly violated by the data, because there are substantial proportion of households which do not hold any risky assets. Zero-holding, however, may be interpreted as a result of fixed transaction cost incurred by individual investors when they hold risky assets. Then, we pose a question, ‘Do investors hold constant proportion of risky assets, when they decide to hold them?’ In order to explain a substantial number of zero risky asset holders in the sample, we propose a portfolio selection model with a transaction cost, and estimate the model using a variant of Heckman's two-step method. In estimation we control for individual investors' socioeconomic characteristics, as well as income and total assets. The construction of the model imposes nonlinear restrictions on the two estimators, from which we can test the specification of the model. The estimation results suggest that there is a statistically significant decreasing tendency linked to total assets but that its rate of change tapers off as total assets increase. Our results are consistent with the previous studies which tended to support constant RRA for the higher asset holders, and complement previous studies in explaining lower asset holders' investment behavior.     

Market incompleteness and the equity premium puzzle: Evidence from state-level data

This paper investigates the importance of market incompleteness by comparing the rates of risk aversion estimated from complete and incomplete markets environments. For the incomplete-markets case, we use consumption data for the 50 US states. We find that the rate of risk aversion under the incomplete-markets setup is much lower. Furthermore, including the second and third moments of the cross-sectional distribution of consumption growth in the pricing kernel lowers the estimate of risk aversion. These findings suggest that market incompleteness ought to be seen as an important component of solutions to the equity premium puzzle.