Stock return volatility,operating performance and stock returns: International evidence on drivers of the ‘low volatility’ anomaly

This study highlights the link between stock return volatility, operating performance, and stock returns. Prior studies suggest that there is a ‘low volatility’ anomaly, where firms with a low stock return volatility out-perform firms with a high stock return volatility. This paper confirms that low volatility stocks earn higher returns than high volatility stocks in emerging markets and developed markets outside of North America. We also show that low volatility stocks have higher operating returns and this might explain why low volatility stocks earn higher stock returns. These results provide a partial explanation for the ‘low volatility effect’ that is independent from the existence of market anomalies or per se inefficiencies that might otherwise drive a low volatility effect. We emphasize the importance of controlling for stock return volatility when analyzing operating performance and stock performance.     

Risk Interpretation of the CAPM's Beta: Evidence from a New Research Method

This study tests the validity of using the CAPM beta as a risk control in cross‐sectional accounting and finance research. We recognize that high‐risk stocks should experience either very good or very bad returns more frequently compared to low‐risk stocks, that is, high‐risk stocks should cluster in the tails of the cross‐sectional return distribution. Building on this intuition, we test the risk interpretation of the CAPM's beta by examining if high‐beta stocks are more likely than low‐beta stocks to experience either very high or very low returns. Our empirical results indicate that beta is a strong predictor of large positive and large negative returns, which confirms that beta is a valid empirical risk measure and that researchers should use beta as a risk control in empirical tests. Further, we show that because the relation between beta and returns is U‐shaped, that is, high betas predict both very high and very low returns, linear cross‐sectional regression models, for example, Fama–MacBeth regressions, will fail on average to reject the null hypothesis that beta does not capture risk. This result explains why previous studies find no significant cross‐sectional relation between beta and returns.     

Have European Stocks become More Volatile? An Empirical Investigation of Idiosyncratic and Market Risk in the Euro Area

We examine the dynamics of idiosyncratic risk, market risk and return correlations in European equity markets using weekly observations from 3515 stocks listed in the 12 euro area stock markets over the period 1974–2004. Similarly to Campbell et al. (2001) , we find a rise in idiosyncratic volatility, implying that it now takes more stocks to diversify away idiosyncratic risk. Contrary to the US, however, market risk is trended upwards in Europe and correlations are not trended downwards. Both the volatility and correlation measures are pro‐cyclical, and they rise during times of low market returns. Market and average idiosyncratic volatility jointly predict market wide returns, and the latter impact upon both market and idiosyncratic volatility. This has asset pricing and risk management implications.     

The return impact of realized and expected idiosyncratic volatility

We show that the negative relation between realized idiosyncratic volatility, measured over the prior month, and returns is robust in non-January months. Controlling for realized idiosyncratic volatility, we show that the relation between returns and expected idiosyncratic volatility is positive and robust. Realized and expected idiosyncratic volatility are separate and important effects describing the cross-section of returns. We find the negative return on a zero-investment portfolio that is long high realized idiosyncratic volatility stocks and short low realized idiosyncratic volatility stocks is dependent on aggregate investor sentiment. In cross-sectional tests, we find the negative relation is weaker for stocks with a large analyst following and stronger for stocks with high dispersion of analyst forecasts. The positive relation between expected idiosyncratic volatility and returns is not due to mispricing.     

High Idiosyncratic Volatility and Low Returns: A Prospect Theory Explanation

The well‐documented negative relationship between idiosyncratic volatility and stock returns is puzzling if investors are risk‐averse. However, under prospect theory, while investors are risk‐averse in the domain of gains, they exhibit risk‐seeking behavior in the domain of losses. Consistent with risk‐seeking investors’ preference for high‐volatility stocks in the loss domain, we find that the negative relationship between idiosyncratic volatility and stock returns is concentrated in stocks with unrealized capital losses, but is nonexistent in stocks with unrealized capital gains. This finding is robust to control for short‐term return reversals and maximum daily return, among other variables.     

The Cross-Section of Volatility and Expected Returns

We examine the pricing of aggregate volatility risk in the cross‐section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. Stocks with high idiosyncratic volatility relative to the Fama and French (1993, Journal of Financial Economics 25, 2349) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book‐to‐market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility.     

Risk‐Adjusted Long‐Term Contrarian Profits: Evidence from Non‐S&P 500 High‐Volume Stocks

Can trading volume help unravel the long‐term overreaction puzzle? With portfolios of non‐S&P 500 NYSE stocks, we show that (1) both the high‐ and low‐volume (abnormal volume) contrarian portfolios earn a much higher market‐adjusted excess return than the normal‐volume contrarian portfolio, (2) however, when leverage‐induced risk is factored in, excess returns from contrarian portfolios with normal‐ and low‐volume stocks are insignificant, (3) only excess returns from high‐volume contrarian stocks are significant and cannot be explained by the time‐varying risk and return framework, and (4) such high‐volume, risk‐adjusted excess returns arise mainly from winner (glamour) stocks.     

Idiosyncratic Risk in Emerging Markets

In this study, I examine the properties and portfolio management implications of value‐weighted idiosyncratic volatility in 24 emerging markets. This paper provides evidence against the view that the rise of idiosyncratic risk is a global phenomenon. Furthermore, specific and market risks jointly predict market returns as there is a negative (positive) relation between idiosyncratic (market) risk and subsequent stock returns. Idiosyncratic volatility is the most important component of tracking error volatility, and it does not exhibit either an upward or a downward trend. Thus, investors do not have to increase, on average, the number of stocks they hold to keep the active risk constant.     

ESTIMATING EXPECTED EXCESS RETURNS USING HISTORICAL AND OPTION‐IMPLIED VOLATILITY

We test the relation between expected and realized excess returns for the S&P 500 index from January 1994 through December 2003 using the proportional reward‐to‐risk measure to estimate expected returns. When risk is measured by historical volatility, we find no relation between expected and realized excess returns. In contrast, when risk is measured by option‐implied volatility, we find a positive and significant relation between expected and realized excess returns in the 1994–1998 subperiod. In the 1999–2003 subperiod, the option‐implied volatility risk measure yields a positive, but statistically insignificant, risk‐return relation. We attribute this performance difference to the fact that, in the 1994–1998 subperiod, return volatility was lower and the average return was much higher than in the 1999–2003 subperiod, thereby increasing the signal‐to‐noise ratio in the latter subperiod.     

A behavioural explanation to the asymmetric volatility phenomenon: Evidence from market volatility index

This study examines how the behavioural explanations, in particular loss aversion, can be used to explain the asymmetric volatility phenomenon by investigating the relationship between stock market returns and changes in investor perceptions of risk measured by the volatility index. We study the behaviour of India volatility index vis‐à‐vis Hong Kong, Australia and UK volatility index, and provide a comprehensive comparative analysis. Using Bai‐Perron test, we identify structural breaks and volatility regimes in the time series of volatility index, and investigate the volatility index‐return relation during high, medium and low volatility periods. Regardless of volatility regimes, we find that volatility index moves in opposite direction in response to stock index returns, and contemporaneous return is the most dominating across the four markets. The negative relation is strongest for UK followed by Australia, Hong Kong and India. Second, volatility index reacts significantly different to positive and negative returns; negative return has higher impact on changes in volatility index than positive return across the markets over full‐sample and sub‐sample periods. The asymmetric effect is stronger in low volatility regime than in high and medium volatility periods for all the markets except UK. The strength of asymmetric effect is strongest for Hong Kong and weakest for India. Finally, negative returns have exponentially increasing effect and positive returns have exponentially decreasing effect on the changes in volatility index.     

Can tail risk explain size,book‐to‐market,momentum, and idiosyncratic volatility anomalies?

We examine the impact of tail risk on the return dynamics of size, book‐to‐market ratio, momentum and idiosyncratic volatility sorted portfolios. Our time‐series analyses document significant portfolio return exposures to aggregate tail risk. In particular, portfolios that contain small, value, high idiosyncratic volatility and low momentum stocks exhibit negative and statistically significant tail risk betas. Our cross‐sectional analyses at the individual stock level suggest that tail risk helps in explaining the four pricing anomalies, particularly size and idiosyncratic volatility anomalies.     

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.     

Relation between time-series and cross-sectional effects of idiosyncratic variance on stock returns

Consistent with the post-1962 US evidence by Ang et al. [Ang, A., Hodrick, R., Xing Y., Zhang, X., 2006. The cross-section of volatility and expected returns. Journal of Finance 51, 259–299], we find that stocks with high idiosyncratic variance (IV) have low CAPM-adjusted expected returns in both pre-1962 US and modern G7 data. We also test in three ways the conjecture that IV is a proxy of systematic risk. First, the return difference between low and high IV stocks – that we dub as IVF – is a priced factor in the cross-section of stock returns. Second, loadings on lagged market variance and lagged average IV account for a significant portion of variation in average returns on portfolios sorted by IV. Third, the variance of IVF correlates closely with average IV, and the two variables have similar explanatory power for the time-series and cross-sectional stock returns.     

Asymmetric risk premium in value and growth stocks

There are two competing explanations for the existence of a value premium, a rational market risk explanation, whereby value stocks are inherently more risky than growth stocks, and a market over-reaction hypothesis, where agents overstate future returns on growth stock. Using asymmetric GARCH-M models this paper tests the predictions of the two hypotheses. Specifically, examining whether returns exhibit a positive (negative) risk premium resulting from a negative (positive) shock and the relative size of any premium. The results of the paper suggest that following a shock, volatility and expected future volatility are heightened, leading to a rise in required rates of return which depresses current prices. Further, these effects are heightened for value stock over growth stock and for negative shocks over positive shocks. Thus, in support of the rational risk interpretation, with a volatility feedback explanation for predictive volatility asymmetry.     

Preferred risk habitat of individual investors

The preferred risk habitat hypothesis, introduced here, is that individual investors select stocks whose volatilities are commensurate with their risk aversion. The data, 1995–2000 holdings of over 20,000 clients at a large German broker, are consistent with the predictions of the hypothesis: the returns of stocks within each portfolio have remarkably similar volatilities, when stocks are sold they are replaced by stocks of similar volatilities, and the more risk-averse customers indeed hold less volatile stocks. Greater volatility specialization is associated with lower Sharpe ratios, primarily because more specialized investors hold fewer stocks and thereby expose themselves to more unsystematic risk.     

The effect of growth opportunities on the market reaction to dividend cuts: evidence from the 2008 financial crisis

We consider returns from rebalanced and buy and hold portfolios consisting of the same stocks. Theoretical properties are derived using Jensen’s inequality and the Hölder’s Defect Formula. Simulations are used to confirm theory and to investigate ambiguous cases where theory is silent. Rebalancing decreases total return volatility, while buy and hold produces greater expected return. Results are more opaque with respect to Sharpe Ratios and expected geometric means. Our empirical tests are based on portfolios composed of the risk-free asset, CRSP market value returns and returns from five Fama–French industries. While rebalancing reduces volatility and momentum effect, our tests largely favor the buy and hold strategy due to the high relative returns enjoyed by stocks vis-a-vis the risk-free asset. Transactions cost for rebalancing the portfolio are economically negligible.     

The high returns to low volatility stocks are actually a premium on high quality firms

Recent empirical research shows that low volatility stocks outperform high volatility stocks around the world. This study documents that the volatility effect is associated with the quality of the firm using a large sample of international stocks. First, adding a quality factor to the Fama–French model contributes to the explanation of the volatility effect. Furthermore, the negative volatility–return relation is shown to be stronger and significant only among high quality firms which are profitable and have stable cash flows. Second, a fundamental investment strategy that goes long high quality firms and short low quality firms performs like a volatility strategy and cannot be explained by common asset pricing models. However, a low–high volatility factor adds to the explanation of the return difference between high and low quality stocks as volatility and quality strategies have a common component.     

Cross-section of option returns and volatility

We study the cross-section of stock option returns by sorting stocks on the difference between historical realized volatility and at-the-money implied volatility. We find that a zero-cost trading strategy that is long (short) in the portfolio with a large positive (negative) difference between these two volatility measures produces an economically and statistically significant average monthly return. The results are robust to different market conditions, to stock risks-characteristics, to various industry groupings, to option liquidity characteristics, and are not explained by usual risk factor models.     

Asset pricing and foreign exchange risk

According to the International Capital Asset Pricing Model (ICAPM), the covariance of assets with foreign exchange currency returns should be a risk factor that must be priced when the purchasing power parity is violated. The goal of this study is to re-examine the relationship between stock returns and foreign exchange risk. The novelties of this work are: (a) a data set that makes use of daily observations for the measurement of the foreign exchange exposure and volatility of the sample firms and (b) data from a Eurozone country.The methodology we make use in reference to the estimation of the sensitivity of each stock to exchange rate movements is that it allows regressing stock returns against factors controlling for market risk, size, value, momentum, foreign exchange exposure and foreign exchange volatility. Stocks are then classified according to their foreign exchange sensitivity portfolios and the return of a hedge (zero-investment) portfolio is calculated. Next, the abnormal returns of the hedge portfolio are regressed against the return of the factors. Finally, we construct a foreign exchange risk factor in such manner as to obtain a monotonic relation between foreign exchange risk and expected returns.The empirical findings show that the foreign exchange risk is priced in the cross section of the German stock returns over the period 2000-2008. Furthermore, they show that the relationship between returns and foreign exchange sensitivity is nonlinear, but it takes an inverse U-shape and that foreign exchange sensitivity is larger for small size firms and value stocks.     

Time-varying risk The case of the American computer industry

A bivariate GARCH-in-mean model for individual stock returns and the market portfolio is designed to model volatility and to test the conditional Capital Asset Pricing Model versus the conditional Residual Risk Model. We find that a univariate model of volatility for individual stock returns is misspecified. A joint modelling of the market return and the individual stock return shows that a major force driving the conditional variances of individual stocks is the history contained in the market return variance. We find that a conditional residual risk model, where the variance of the individual stock return is used to explain expected returns, is preferred to a conditional CAPM. We propose a partial ordering of securities according to their market risk using first and second order dominance criteria.