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Risk-Return Trade-off in International Stock Returns: Skewness and Business Cycles
Abstract
The fundamental risk-return relation is examined with a flexible regime switching model combining the impact of skewness and business cycle regimes in stock returns. Key methodological and empirical findings point out the need for a highly nonlinear and non-Gaussian model to get a reliable picture on the risk-return relationship. With an international dataset of major countries to global financial markets, the empirical results show that accounting especially for skewness patterns leads to the expected positive risk-return relation, which is importantly also maintained over different business cycle conditions.
... The presence of asymmetric signals can induce enough skewness to reject the null hypothesis of time-reversibility. Business cycle asymmetry can be tested with respect to whether macroeconomic fluctuations are time irreversible and can also be exploited for identification purposes as in Virolainen (2020) (see, Nyberg and Savva (2023)). ...
We investigate the risk–return trade-off on the US and European stock markets. We investigate the non-linear risk–return trade-off with a special eye to the tails of the stock returns using quantile regressions. We first consider the US stock market portfolio. We find that the risk–return trade-off is significantly positive at the upper tail (0.9 quantile), where the upper tail is large positive excess returns. The positive trade-off is as expected from asset pricing models. For the lower tail (0.1 quantile), that is for large negative stock returns, the trade-off is significantly negative. Additionally, for the median (0.5 quantile), the risk–return trade-off is insignificant. These results are recovered for the US industry portfolios and for Eurozone stock market portfolios.
We study an equilibrium risk and return model to explore the effects of the coronavirus crisis and associated skewness on the market price of risk. We derive the moment and equilibrium equations, specifying skewness price of risk as an additive component of the effect of variance on mean ex-pected return. We estimate our model using the flexible skewed generalized error distribution, for which we derive the distribution of returns and the likelihood function. Using S&P 500 Index re-turns from January 1980 to mid-October 2020, our results show that the coronavirus crisis generat-ed a deeply negative reaction in the skewness and total market price of risk, more negative even than the subprime and the October 1987 crises.
Shipping freight rates are notoriously volatile and shipping investors are perceived to be risk loving. The paper explores the stochastic properties of freight rates in the shipping industry and derives the analytical equations for their moments in downside and upside markets by using a two‐piece extension of the generalized error distribution. Pricing equations developed across shipping segments show how conditional risk and conditional skewness are priced along with their risk spillover effects. Results reveal the existence of a positive skewness premium, suggesting that shipping investors are willing to accept lower expected returns for the opportunity to earn high pay‐offs in the future.
The relationship between risk and expected returns has been investigated extensively in the financial economics literature. Theoretical models generally predict a positive relation between the two. Nevertheless, the empirical findings so far have been inconclusive. Using a generalization of the analytical framework developed by Theodossiou and Savva (2016) along with time-varying asymmetry, linked to the upside and downside uncertainty, the risk-return puzzle is investigated across international stock markets. The investigation reveals that the contradictory findings are the result of ignoring the impact of skewness on the total price of risk. That is, in the absence of skewness the relationship between risk and return is positive as depicted by finance theory. However, negative skewness results in lowering the total price of risk and in some cases reverting its sign from positive to negative.
The relationship between risk and return has been one of the most important and extensively investigated issues in the financial economics literature. The theoretical results predict a positive relation between the two. Nevertheless, the empirical findings so far have been contradictory. Evidence presented in this paper shows that these contradictions are the result of negative skewness in the distribution of portfolio excess return and the fact that the estimation of intertemporal asset pricing models are based on symmetric log-likelihood specifications.
Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2015.2201 .
This paper was accepted by Jerome Detemple, finance.
This paper considers M-estimators of regression parameters that make use of a generalized functional form for the disturbance distribution. The family of distributions considered is the generalized t (GT), which includes the power exponential or Box-Tiao, normal, Laplace, and t distributions as special cases. The corresponding influence function is bounded and redescending for finite “degrees of freedom.” The regression estimators considered are those that maximize the GT quasi-likelihood, as well as one-step versions. Estimators of the parameters of the GT distribution and the effect of such estimates on the asymptotic efficiency of the regression estimates are discussed. We give a minimum-distance interpretation of the choice of GT parameter estimate that minimizes the asymptotic variance of the regression parameters.
We propose an asset pricing model where preferences display generalized disappointment aversion (Routledge and Zin, 2009) and the endowment process involves long-run volatility risk. These preferences, which are embedded in the Epstein and Zin (1989) recursive utility framework, overweight disappointing results as compared to expected utility, and display relatively larger risk aversion for small gambles. With a Markov switching model for the endowment process, we derive closed-form solutions for all returns moments and predictability regressions. The model produces first and second moments of price-dividend ratios and asset returns and return predictability patterns in line with the data. Compared to Bansal and Yaron (2004), we generate: i) more predictability of excess returns by price-dividend ratios; ii) less predictability of consumption growth rates by price-dividend ratios. Differently from the Bansal and Yaron model, our results do not depend on a value of the elasticity of intertemporal substitution greater than one.
In this paper, we propose a new GARCH-in-Mean (GARCH-M) model allowing for conditional skewness. The model is based on the so-called z distribution capable of modeling skewness and kurtosis of the size typically encountered in stock return series. The need to allow for skewness can also be readily tested. The model is consistent with the volatility feedback effect in that conditional skewness is dependent on conditional variance. Compared to previously presented GARCH models allowing for conditional skewness, the model is analytically tractable, parsimonious and facilitates straightforward interpretation.Our empirical results indicate the presence of conditional skewness in the monthly postwar US stock returns. Small positive news is also found to have a smaller impact on conditional variance than no news at all. Moreover, the symmetric GARCH-M model not allowing for conditional skewness is found to systematically overpredict conditional variance and average excess returns.
The expectati on of the excess holding yield on a long bond is postulated to depend upon its conditional variance. Engle's ARCH model is extended to allow the conditional variance to be a determinant of the mean and is called ARCH-M. Estimation and infer ence procedures are proposed, and the model is applied to three interest rate data sets. In most cases the ARCH process and the time varying risk premium are highly significant. A collection of LM diagnostic tests reveals the robustness of the model to various specification changes such as alternative volatility or ARCH measures, regime changes, and interest rate formulations. The model explains and interprets the recent econometric failures of the expectations hypothesis of the term structure. Copyright 1987 by The Econometric Society.
An intertemporal model for the capital market is deduced from the portfolio selection behavior by an arbitrary number of investors who act so as to maximize the expected utility of lifetime consumption and who can trade continuously in time. Explicit demand functions for assets are derived, and it is shown that, unlike the one-period model, current demands are affected by the possibility of uncertain changes in future investment opportunities. After aggregating demands and requiring market clearing, the equilibrium relationships among expected returns are derived, and contrary to the classical capital asset pricing model, expected returns on risky assets may differ from the riskless rate even when they have no systematic or market risk.
Quasi-Maximum Likelihood (QML) procedures are theoretically appealing and widely used for statistical inference. While there are extensive references on QML estimation in batch settings, it has attracted little attention in streaming settings until recently. An investigation of the convergence properties of the QML procedure in a general conditionally heteroscedastic time series model is conducted, and the classical batch optimization routines extended to the framework of streaming and large-scale problems. An adaptive recursive estimation routine for GARCH models named AdaVol is presented. The AdaVol procedure relies on stochastic approximations combined with the technique of Variance Targeting Estimation (VTE). This recursive method has computationally efficient properties, while VTE alleviates some convergence difficulties encountered by the usual QML estimation due to a lack of convexity. Empirical results demonstrate a favorable trade-off between AdaVol’s stability and the ability to adapt to time-varying estimates for real-life data.
The econometric framework of the contemporaneous asset pricing model used by Theodossiou and Savva and Savva and Theodossiou to investigate the relationship between risk and expected returns in financial markets is generalized to a class of two-sided, asymmetry separable distributions. The latter class of distributions includes as special cases the skewed forms for the normal, Student’s t, Laplace, generalized error, generalized t, logistic and generalized type III logistic. All distributions document a positive and statistically significant relationship between risk and expected returns. A comparison of their data fitting ability shows that the generalized t distribution provides the best overall results.
Markov switching (MS-)GARCH(1,1) models allow for structural changes in volatility dynamics between a finite number of regimes. Since the regimes are not observed, computation of the likelihood requires integrating over an exponentially increasing number of regime paths, which is intractable. An existing smooth likelihood estimation procedure for sequential Monte Carlo (SMC), that is currently limited to hidden Markov models with a one-dimensional state variable, is modified to enable likelihood estimation and maximisation for MS-GARCH(1,1) models, a model which requires two dimensions, volatility and regime, to evolve its hidden state process. Furthermore, the modified SMC procedure is shown to be easily adapted to fitting MS-GARCH(1,1) models even when there are missing observations. The proposed methodology is validated with simulated data and is also illustrated with analysis of two financial time series, the daily returns on the S&P 500 index and on the Henry Hub natural gas spot price, with the latter series containing a gap caused by shutdown in response to hurricane Rita in 2005.
We propose a new decomposition of the variance risk premium (VRP) in terms of upside and downside VRPs. These components reflect market compensation for changes in good and bad uncertainties. Empirically, we establish that the downside VRP is the main component of the VRP. We find a positive and significant link between the downside VRP and the equity premium, and a negative but statistically insignificant link between the upside VRP and the equity premium. The opposite relationships between these two components and the equity premium explains the stronger link found between the downside VRP and the equity premium compared with the well-established relationship between VRP and the equity premium. A simple equilibrium consumption-based asset pricing model, fitted to the U.S. data, supports our decomposition. © The Author, 2017. Published by Oxford University Press. All rights reserved.
We investigate the role of uncertainty in business cycles. First, we demonstrate that microeconomic uncertainty rises sharply during recessions, including during the Great Recession of 2007–2009. Second, we show that uncertainty shocks can generate drops in gross domestic product of around 2.5% in a dynamic stochastic general equilibrium model with heterogeneous firms. However, we also find that uncertainty shocks need to be supplemented by first‐moment shocks to fit consumption over the cycle. So our data and simulations suggest recessions are best modelled as being driven by shocks with a negative first moment and a positive second moment. Finally, we show that increased uncertainty can make first‐moment policies, like wage subsidies, temporarily less effective because firms become more cautious in responding to price changes.
A typical MIDAS regression involves estimating parameters via nonlinear least squares, unless U-MIDAS is applied – which involves OLS – the latter being appealing when the sampling frequency differences are small. It is proposed to use OLS estimation of the MIDAS regression slope and intercept parameters combined with profiling the polynomial weighting scheme parameter(s). The use of Beta polynomials is particularly attractive for such an approach. The new procedure shares many of the desirable features of U-MIDAS, while it is not restricted to small sampling frequency differences.
This paper assesses the econometric and economic value consequences of neglecting structural breaks in dynamic correlation models and in the context of asset allocation framework. It is shown that changes in the parameters of the conditional correlation process can lead to biased estimates of persistence. Monte Carlo simulations reveal that short-run persistence is downward biased while long-run persistence is severely upward biased, leading to spurious high persistence of shocks to conditional correlation. An application to stock returns supports these results and concludes that neglecting such structural shifts could lead to misleading decisions on portfolio diversification, hedging and risk management.
This paper examines the usefulness of asset prices in predicting the beginnings of recessions in the G-7 countries. It finds that equity/house price drops have a substantial marginal effect on the likelihood of a new recession. Increased market uncertainty, which is a second-moment variable associated with equity price changes, is also a useful predictor of new recessions in these countries. These findings are robust to the inclusion of the term spread and oil prices. The new recession forecasting performance of our baseline model is superior to that of a similar model estimated over all recession and expansion periods, highlighting a difference between the probabilities of a new recession versus a continuing recession.
A general partial risk-return relation is derived based on return decomposition to allowing for the effect of time-varying skewness and kurtosis on the risk-return trade-off. Empirically estimated for 12 international financial markets, the proposed risk-return trade-off is significantly positive even after controlling for time-varying higher moments. Moreover, the stochastic dominance test reveals that modeling time-varying skewness significantly lowers the level of the risk-return trade-off. More importantly, the empirical evidence shows that the risk-return trade-off is countercyclical in the U.S. markets, consistent with the theoretical habit-formation model of Campbell and Cochrane (1999), whereas the risk-return trade-offs in European and emerging markets appear to be procyclical over a 12-month horizon, but countercyclical for a shorter horizon of 3 months. Finally, common macroeconomic variables can significantly explain risk-return trade-off dynamics.
This paper introduces a regime switching vector autoregressive model with time-varying regime probabilities, where the regime switching dynamics is described by an observable binary response variable predicted simultaneously with the variables subject to regime changes. Dependence on the observed binary variable distinguishes the model from various previously proposed multivariate regime switching models, facilitating a handy simulation-based multistep forecasting method. An empirical application shows a strong bidirectional predictive linkage between US interest rates and NBER business cycle recession and expansion periods. Due to the predictability of the business cycle regimes, the proposed model yields superior out-of-sample forecasts of the US short-term interest rate and the term spread compared with the linear and nonlinear vector autoregressive (VAR) models, including the Markov switching VAR model.
The problem of ergodicity, stationarity and maximum likelihood estimation is studied for binary time series models that include a latent process. General models are considered, covered by different specifications of a link function. Maximum likelihood estimation is discussed and it is shown that the MLE satisfies standard asymptotic theory. The logistic and probit models, routinely employed for the analysis of binary time series data, are of special importance in this study. The results are applied to simulated and real data.
Recent research has identified skewness and downside risk as one of the most important features of risk. We present a new distribution which makes modeling skewed risks no more difficult than normally distributed (symmetric) risks. Our distribution is a combination of the “downside” and “upside” half of two normal distributions, and its parameters can be calculated in closed form to match a given mean, variance, and skewness. Value at risk, expected shortfall, portfolio weights, and risk premia have simple expressions for our distribution and show economically meaningful deviations from the normal case already for very modest levels of skewness. An empirical application suggests that our distribution fits the data well.
Investigations of the basic risk-return trade-off for the market return typically use maximum likelihood estimation (MLE) with a monthly or quarterly horizon and data sampled to match the horizon even though daily data are available. We develop an overlapping data inference methodology for such models that uses all of the data while maintaining the monthly or quarterly forecasting period. Our approach recognizes that the first order conditions of MLE can be used as orthogonality conditions of the generalized method of moments (GMM). While parameter estimates from the different non-overlapping monthly samples that start on different days vary substantively, a formal test does not reject parameter equality and constrained estimation of the risk-return trade-off produces a statistically significant value of 3.35 in post-1955 data.
We present a consumption-based model that explains a wide variety of dynamic asset pricing phenomena, including the procyclical variation of stock prices, the long-horizon predictability of excess stock returns, and the countercyclical variation of stock market volatility. The model captures much of the history of stock prices from consumption data. It explains the short- and long-run equity premium puzzles despite a low and constant risk-free rate. The results are essentially the same whether we model stocks as a claim to the consumption stream or as a claim to volatile dividends poorly correlated with consumption. The model is driven by an independently and identically distributed consumption growth process and adds a slow-moving external habit to the standard power utility function. These features generate slow countercyclical variation in risk premia. The model posits a fundamentally novel description of risk premia: Investors fear stocks primarily because they do poorly in recessions unrelated to the risks of long-run average consumption growth.
We propose a new method for constructing the hedge component in Merton's ICAPM that uses a daily summary measure of economic
activity to track time-varying investment opportunities. We then use nonparametric projections to compute a robust estimate
of the conditional covariance between stock market returns and our daily economic activity index. We find that the new conditional
covariance risk measure plays an important role in explaining time variation in the equity risk premium. Specification tests
as well as out-of-sample forecasts of aggregate stock returns suggest that the new covariance risk measure performs well compared
to alternative covariance measures previously proposed in the literature.
We uncover a strong comovement of the stock market risk–return trade‐off with the consumption–wealth ratio (CAY). The finding reflects time‐varying investment opportunities rather than countercyclical aggregate relative risk aversion. Specifically, the partial risk–return trade‐off is positive and constant when we control for CAY as a proxy for investment opportunities. Moreover, conditional market variance scaled by CAY is negatively priced in the cross‐section of stock returns. Our results are consistent with a limited stock market participation model, in which shareholders require an illiquidity premium that increases with CAY, in addition to the risk premium that is proportional to conditional market variance.
In the empirical finance literature, findings on the risk-return tradeoff in excess stock market returns are ambiguous. In this study, I develop a new qualitative response (QR)-generalized autoregressive conditional heteroskedasticity-in-mean (GARCH-M) model combining a probit model for a binary business cycle indicator and a regime-switching GARCH-M model for excess stock market return with the business cycle indicator defining the regime. Estimation results show that there is statistically significant variation in the U.S. excess stock returns over the business cycle. However, consistent with the conditional intertemporal capital asset pricing model (ICAPM), there is a positive risk-return relationship between volatility and expected return independent of the state of the economy.
The authors are respectively in the School of Business, Rutgers University, Camden, New Jersey; and School of Business and Public Administration, University of the Pacific, Stockton, California.
We investigate the intertemporal hedging demands for stocks and bonds for investors in the U.S., Australia, Canada, France, Germany, Italy, and U.K. Using the methodology of Campbell et al. [Campbell, J.Y., Chan, Y.L., Viceira, L.M., 2003a. A multivariate model of strategic asset allocation. Journal of Financial Economics 67(1), 41–81], we solve a multi-period portfolio choice problem for an investor in each country with an infinite horizon and Epstein–Zin–Weil utility, where the dynamics governing asset returns are described by a vector autoregressive process. We find sizable mean intertemporal hedging demands for domestic stocks in the U.S. and U.K. and considerably smaller mean hedging demands for domestic stocks in the other countries. An investor in the U.S. who has access to foreign stocks and bonds displays small mean intertemporal hedging demands for foreign stocks and bonds, while investors in Australia, Canada, France, Germany, Italy, and the U.K. who have access to U.S. stocks and bonds all exhibit sizable mean hedging demands for U.S. stocks.
The type of return generating process we test here on three European markets are GARCH and AR-GARCH in mean models with innovations that have either normal or student-t densities with time dependent variances. These models are appealing in that they estimate time varying volatility in disturbances of stock returns series and ex-ante relationship between stock returns and volatility. Our results indicate that there is no statistically significant coefficient estimates for the volatility in the mean equation and that variance might not be appropriate as a measure of risk. Other proxies for risk should then be searched for.
Index option prices differ systematically from Black–Scholes prices. Out-of-the-money put prices (and in-the-money call prices) are relatively high compared to the Black–Scholes price. Motivated by these empirical facts, we develop a new discrete-time dynamic model of stock returns with inverse Gaussian innovations. The model allows for conditional skewness as well as conditional heteroskedasticity and a leverage effect. We present an analytic option pricing formula consistent with this stock return dynamic. An extensive empirical test of the model using S&P500 index options shows that the new inverse Gaussian GARCH model's performance is superior to a standard existing nested model for out-of-the money puts.
Previous studies typically find a statistically insignificant relation between the market risk premium and its expected volatility. Further, several of these studies estimate a negative risk return tradeoff, contrary to the predictions of mainstream theory. Using simulations, I demonstrate that even 100 years of data constitute a small sample that may easily lead to this finding even though the true risk return tradeoff is positive. Small-sample inference is plagued by the fact that conditional volatility has almost no explanatory power for realized returns. Using the nearly two century history of U.S. equity market returns from Schwert [1990. Indexes of United States stock prices from 1802 to 1987. Journal of Business 63, 399–426], I estimate a positive and statistically significant risk return tradeoff. Finally, exploratory analysis suggests a role for a time-varying relation linked to the changing nature of the U.S. economy.
The low power of the standard Wald test in a GARCH-in-Mean model with an unnecessary intercept is shown to explain the apparent absence of a risk–return tradeoff in stocks. The importance of this finding is illustrated with monthly U.S. data.
In this paper, various financial variables are examined as predictors of the probability of a recession in the USA and Germany. We propose a new dynamic probit model that outperforms the standard static model, giving accurate out-of-sample forecasts in both countries for the recession period that began in 2001, as well as the beginning of the recession in 2008. In accordance with previous findings, the domestic term spread proves to be an important predictive variable, but stock market returns and the foreign term spread also have predictive power in both countries. In the case of Germany, the interest rate differential between the USA and Germany is also a useful additional predictor. Copyright © 2009 John Wiley & Sons, Ltd.
This paper examines the out-of-sample performance of various financial variables as predictors of U.S. recessions. Series such as interest rates and spreads, stock prices, and monetary aggregates are evaluated individually and in comparison with other financial and nonfinancial indicators. The analysis focuses on out-of-sample performance from one to eight quarters ahead. Results show that stock prices are useful with one- to three-quarter horizons, as are some well-known macroeconomic indicators. Beyond one quarter, however, the slope of the yield curve emerges as the clear individual choice and typically performs better by itself out of sample than in conjunction with other variables. © 2000 by the President and Fellows of Harvard College and the Massachusetts Institute of Technolog
This paper examines the intertemporal relation between risk and return for the aggregate stock market using high-frequency data. We use daily realized, GARCH, implied, and range-based volatility estimators to determine the existence and significance of a risk-return trade-off for several stock market indices. We find a positive and statistically significant relation between the conditional mean and conditional volatility of market returns at the daily level. This result is robust to alternative specifications of the volatility process, across different measures of market return and sample periods, and after controlling for macro-economic variables associated with business cycle fluctuations. We also analyze the risk-return relationship over time using rolling regressions, and find that the strong positive relation persists throughout our sample period. The market risk measures adopted in the paper add power to the analysis by incorporating valuable information, either by taking advantage of high-frequency intraday data (in the case of realized, GARCH, and range volatility) or by utilizing the market's expectation of future volatility (in the case of implied volatility index). Copyright © 2006 John Wiley & Sons, Ltd.
This paper investigates the joint time series behavior of monthly stock returns and growth in industrial production. We find that stock returns are well characterized by year-long episodes of high volatility, separated by longer quiet periods. Real output growth, on the other hand, is subject to abrupt changes in the mean associated with economic recessions. We study a bivariate model in which these two changes are driven by related unobserved variables, and conclude that economic recessions are the primary factor that drives fluctuations in the volatility of stock returns. This framework proves useful both for forecasting stock volatility and for identifying and forecasting economic turning points. Copyright 1996 by John Wiley & Sons, Ltd.
R. F. Engle's autoregressive conditional heteroskedastic model is extended to permit parametric specifications for conditional dependence beyond the mean and variance. The suggestion is to model the conditional density with a small number of parameters, and then model these parameters as functions of the conditioning information. This method is applied to two data sets. The first application is to the monthly excess holding yield on U.S. Treasury securities, where the conditional density used is a Student's t distribution. The second application is to the U.S. Dollar/Swiss Franc exchange rate, using a new skewed Student t conditional distribution. Copyright 1994 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.
The existing empirical literature fails to agree on the nature of the intertemporal relation between risk and return. This paper attempts to resolve the issue by estimating a conditional two-factor model motivated by Merton's intertemporal capital asset pricing model. When long-term government bond returns are included as a second factor, the "partial" relation between the market risk premium and conditional market variance is found to be positive and significant. The paper also helps explain the convoluted empirical relation between the market risk premium, conditional market variance, and the nominal risk-free rate previously reported in the literature. Copyright The American Finance Association 1998.
The authors find support for a negative relation between conditional expected monthly return and conditional variance of monthly return using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, they also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility, whereas negative unanticipated returns result in an upward revision of conditional volatility. Copyright 1993 by American Finance Association.
This paper analyzes the relation of stock volatility with real and nominal macroeconomic volatility, economic activity, financial leverage, and stock trading activity using monthly data from 1857 to 1987. An important fact, previously noted by Robert R. Officer (1973), is that stock return variability was unusually high during the 1929-39 Great Depression. While aggregate leverage is significantly correlated with volatility, it explains a relatively small part of the movements in stock volatility. The amplitude of the fluctuations in aggregate stock volatility is difficult to explain using simple models of stock valuation, especially during the Great Depression. Copyright 1989 by American Finance Association.
It seems plausible that an increase in stock market volatility raises required stock returns, and thus lowers stock prices. We develop a formal model of this volatility feedback effect using a simple model of changing variance (a quadratic generalized autoregressive conditionally heteroskedastic, or QGARCH, model). Our model is asymmetric and helps to explain the negative skewness and excess kurtosis of U.S. monthly and daily stock returns over the period 1926–1988. We find that volatility feedback normally has little effect on returns, but it can be important during periods of high volatility.
This paper examines the relation between stock returns and stock market volatility. We find evidence that the expected market risk premium (the expected return on a stock portfolio minus the Treasury bill yield) is positively related to the predictable volatility of stock returns. There is also evidence that unexpected stock market returns are negatively related to the unexpected change in the volatility of stock returns. This negative relation provides indirect evidence of a positive relation between expected risk premiums and volatility.
Are excess stock market returns predictable over time and, if so, at what horizons and with which economic indicators? Can stock return predictability be explained by changes in stock market volatility? How does the mean return per unit risk change over time? This chapter reviews what is known about the time-series evolution of the risk-return tradeoff for stock market investment, and presents some new empirical evidence using a proxy for the log consumption-aggregate wealth ratio as a predictor of both the mean and volatility of excess stock market returns. We characterize the risk-return tradeoff as the conditional expected excess return on a broad stock market index divided by its conditional standard deviation, a quantity commonly known as the Sharpe ratio. Our own investigation suggests that variation in the equity risk-premium is strongly negatively linked to variation in market volatility, at odds with leading asset pricing models. Since the conditional volatility and conditional mean move in opposite directions, the degree of countercyclicality in the Sharpe ratio that we document here is far more dramatic than that produced by existing equilibrium models of financial market behaviour, which completely miss the sheer magnitude of variation in the price of stock market risk.
"We study how three interrelated phenomena-excess stock returns and risk relation, risk aversion, and asymmetric volatility movement-change over business cycles. Using an asymmetric generalized autoregressive conditional heteroskedasticity in mean model and a Markov switching model, we find that excess stock return increases and asymmetric volatility movement is weakened during boom periods. This suggests that investors become more risk-averse during boom periods (i.e., procyclical risk aversion), which we confirm using a calibration of a simple equilibrium model". ("JEL "C32, E32, G12) Copyright (c) 2007 Western Economic Association International.
The econometrics literature contains many alternative measures of goodness of fit, roughly analogous to R-squared, for use with equations with dichotomous dependent variables. There is, however, no consensus as to the measures' relative merits or about which ones should be reported in empirical work. This article proposes a new measure that possesses several useful properties that the other measures lack. The new measure may be interpreted intuitively in a similar way to R-squared in the linear regression context.
If asset returns have systematic skewness, expected returns should include rewards for accepting this risk. We formalize this intuition with an asset pricing model that incorporates conditional skewness. Our results show that conditional skewness helps explain the cross-sectional variation of expected returns across assets and is significant even when factors based on size and book-to-market are included. Systematic skewness is economically important and commands a risk premium, on average, of 3.60 percent per year. Our results suggest that the momentum effect is related to systematic skewness. The low expected return momentum portfolios have higher skewness than high expected return portfolios. THE SINGLE FACTOR CAPITAL ASSET PRICING MODEL ~CAPM! of Sharpe ~1964! and Lintner ~1965! has come under recent scrutiny. Tests indicate that the crossasset variation in expected returns cannot be explained by the market beta alone. For example, a growing number of studies show that "fundamental" variables such as size, book-to-market value, and price to earnings ratios account for a sizeable portion of the cross-sectional variation in expected returns ~see, e.g., Chan, Hamao, and Lakonishok ~1991! and Fama and French ~1992!!. Fama and French ~1995! document the importance of SMB ~the difference between the return on a portfolio of small size stocks and the return on a portfolio of large size stocks! and HML ~the difference between the return on a portfolio of high book-to-market value stocks and the return on a portfolio of low book-to-market value stocks!. There are a number of responses to these empirical findings. First, the single-factor CAPM is rejected when the portfolio used to proxy for the market is inefficient ~see Roll ~1977! and Ross ~1977!!. Roll and Ross ~1994! an...
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