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.     

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.     

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.      

Disappointment aversion and the equity premium puzzle: new international evidence

Drawing upon the seminal study of Ang, Bekaert, and Liu [2005. “Why Stock May Disappoint?” Journal of Financial Economics 76 (3): 471–508], we incorporate disappointment aversion (DA, that is, aversion to outcomes that are worse than prior expectations) within a simple theoretical portfolio-choice model. Based on the results of this model, we then empirically address the portfolio allocation problem of an investor who chooses between a risky and a risk-free asset using international data from 19 countries. Our findings strongly support the view that DA leads investors to reduce their exposure to the stock market (i.e. DA significantly depresses the portfolio weights on equities in all cases considered). Overall, our study shows that in addition to risk aversion, DA plays an important role in explaining the equity premium puzzle around the world.     

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.     

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.     

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.     

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.     

Estimating the equity premium

Accurate estimation of the equity premium (the expected difference between the returns to a well-diversified stock market portfolio and a riskfree asset) is of central importance in many applications of finance theory including project appraisal and portfolio selection. The standard approach is to take the average observed excess returns to the market over some recent time period (sometimes referred to as the ex post equity premium) and apply this as an unbiased estimate of the ex ante equity premium. The paper reviews the problems associated with such an approach and contrasts it with alternative theoretical techniques.     

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.     

Predicting equity premium out-of-sample by conditioning on newspaper-based uncertainty measures: A comparative study

In finance, the use of newspaper-based uncertainty measures has grown exponentially in recent years. For instance, a growing number of researchers have used the newspaper-based U.S. economic policy uncertainty (EPU) index suggested in Baker et al. (2016) as a predictor in their model to forecast the variable of interest out-of-sample. Likewise, inspired by the approach suggested in Baker et al. (2016), several other newspaper-based uncertainty measures have been introduced, such as indices measuring geopolitical risk (GPR) and monetary policy uncertainty (MPU). This study evaluates the relative out-of-sample predictive power afforded by more than fifty different newspaper-based uncertainty measures with regards to predicting excess returns on the S&P 500 index one-month ahead using data from 1985$m$1 through 2020$m$12. Our predictive model accounts for salient data features, namely, predictor endogeneity and persistence. Furthermore, we evaluate the evidence of conditional as well unconditional predictive ability as outlined in Giacomini and White (2006), and also explore whether any identified level of gains from a statistical viewpoint lead to gains from an economic viewpoint. We find that newspaper-based uncertainty measures linked with certain components of the equity market volatility (EMV) tracker suggested in Baker et al. (2019) help improve the accuracy of one month ahead point predictions relative to the benchmark the most. In contrast, EPU, GPR and MPU indices, which are more frequently used by researchers are much less successful.     

The long-run equity risk premium

Based on a survey of US Chief Financial Officers (CFOs), we present expectations of the equity risk premium measured over a 10-year horizon relative to a 10-year US Treasury bond. This multi-year survey has been conducted each quarter from June 2000 to June 2005. Each quarter the survey also provides measures of cross-sectional disagreement about the risk premium, skewness, and a measure of individual uncertainty. The individual uncertainty is deduced from the 80% confidence interval that each respondent provides for his or her risk premium assessment. We also present evidence on the determinants of the long-run risk premium. Our analysis suggests there is a positive correlation between the ex ante risk premium and real interest rates as reflected in Treasury Inflation Indexed Notes.     

Myopic loss aversion,reference point,and money illusion

We use the portfolio selection model presented in He and Zhou [Manage. Sci., 2011, 57, 315–331] and the NYSE equity and US treasury bond returns for the period 1926–1990 to revisit Benartzi and Thaler’s myopic loss aversion theory. Through an extensive empirical study, we find that in addition to the agent’s loss aversion and evaluation period, his reference point also has a significant effect on optimal asset allocation. We demonstrate that the agent’s optimal allocation to equities is consistent with market observation when he has reasonable values of degree of loss aversion, evaluation period and reference point. We also find that the optimal allocation to equities is sensitive to these parameters. We then examine the implications of money illusion for asset allocation. Finally, we extend the model to a dynamic setting.     

Downside risk aversion,fixed-income exposure,and the value premium puzzle

The value premium is relatively small for investors with a material fixed-income exposure, such as insurance companies and pension funds, especially when they are downside-risk-averse. Value stocks are less attractive to these investors because they offer a relatively poor hedge against poor bond returns. This result arises for plausible, medium-term evaluation horizons of around one year. Our findings cast doubt on the practical relevance of the value premium for these investors and reiterate the importance of the choice of the relevant test portfolio, risk measure and investment horizon in empirical tests of market portfolio efficiency.     

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.     

Investor heterogeneity,market segmentation,leverage and the equity premium puzzle

Financial economists for the past two decades have attempted to explain why the equity premium is so high, now known as the equity premium puzzle (EPP). We model investor heterogeneity, market segmentation and optimal leverage, using the time separable standard power utility, market completeness and ignoring transaction costs to explain the EPP. We explain both the EPP and the related risk-free rate puzzle without resorting to preference modification. Furthermore, we show a unique interior equilibrium for the debt ratio, contrary to the work by F. Modigliani, M.H. Miller (The cost of capital, corporation finance and the theory of investment, American Economic Review 48 (1958) 261–297; Corporate income taxes and the cost of capital, American Economic Review 53 (1963), 433–443) and S.C. Myers (Presidential address: The capital structure puzzle, Journal of Finance 39 (1984), 575–592). Our simulations show the relevance of our models.     

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.     

Equity premium prediction and the state of the economy

We detect cyclical variation in the predictive information of economic fundamentals, which can be used to substantially improve and simplify out-of-sample equity premium prediction. Economic fundamentals based on stock-specific information (notably the dividend yield) deliver better predictions in expansions. Economic fundamentals based on aggregate information (notably the short rate) deliver better predictions in recessions. Accordingly, a simple forecast combination of one predictor that generates cyclical forecasts and one predictor that generates countercyclical forecasts can deliver statistically significant and economically valuable equity premium predictions in both expansions and recessions. A prominent two-predictor forecast combination that performs well is the dividend yield and the short rate. Strategies designed for ex-ante timing of the business cycle can provide additional economic gains in equity premium prediction.     

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.