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.     

Idiosyncratic volatility and equity returns: UK evidence

The proposition that idiosyncratic volatility may matter in asset pricing is currently a topic of research and controversy. Using data from the UK market we examine the predictive ability of various measures of idiosyncratic risk and provide evidence which suggests that: (a) it is the idiosyncratic volatility of small capitalization stocks that matters for asset pricing and (b) that small stocks idiosyncratic volatility predicts the small capitalization premium component of market returns and is unrelated to either the market or the value premium. The predictive power of the aggregate idiosyncratic volatility of small stocks remains intact even after we control for the possible proxying effects of business cycle fluctuations and liquidity and is robust across time and different econometric specifications.     

Explaining the idiosyncratic volatility puzzle using Stochastic Discount Factors

I use Stochastic Discount Factors to examine the sources of the idiosyncratic volatility premium. I find that non-zero risk aversion and firms’ non-systematic coskewness determine the premium on idiosyncratic volatility risk. The firm’s non-systematic coskewness measures the comovement of the asset’s volatility with the market return. When I control for the non-systematic coskewness factor, I find no significant relation between idiosyncratic volatility and stock expected returns. My results are robust across different sample periods and firm characteristics.     

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.     

Idiosyncratic risk and the cross-section of expected stock returns

Theories such as Merton [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510] predict a positive relation between idiosyncratic risk and expected return when investors do not diversify their portfolio. Ang, Hodrick, Xing, and Zhang [2006. The cross-section of volatility and expected returns. Journal of Finance 61, 259–299], however, find that monthly stock returns are negatively related to the one-month lagged idiosyncratic volatilities. I show that idiosyncratic volatilities are time-varying and thus, their findings should not be used to imply the relation between idiosyncratic risk and expected return. Using the exponential GARCH models to estimate expected idiosyncratic volatilities, I find a significantly positive relation between the estimated conditional idiosyncratic volatilities and expected returns. Further evidence suggests that Ang et al.'s findings are largely explained by the return reversal of a subset of small stocks with high idiosyncratic volatilities.     

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.     

EXPECTED VOLATILITY,UNEXPECTED VOLATILITY,AND THE CROSS‐SECTION OF STOCK RETURNS

The existing literature finds conflicting results on the cross‐sectional relation between expected returns and idiosyncratic volatility. We contend that at the firm level, the sample correlation between unexpected returns and expected idiosyncratic volatility can cloud the true relation between the expected return and expected idiosyncratic volatility. We show strong evidence that unexpected idiosyncratic volatility is positively related to unexpected returns. Using unexpected idiosyncratic volatility to control for unexpected returns, we find expected idiosyncratic volatility to be significantly and positively related to expected returns. This result holds after controlling for various firm characteristics, and it is robust across different sample periods.     

Additional evidence on transparency and bank financial performance

This paper examines the relationship between volatility and the probability of occurrence of expected extreme returns in the Canadian market. Four measures of volatility are examined: implied volatility from firm option prices, conditional volatility calculated using an EGARCH model, idiosyncratic volatility, and expected shortfall. A significantly positive relationship is observed between a firm's idiosyncratic volatility and the probability of occurrence of an extreme return in the subsequent month for firms. A 10% increase in idiosyncratic volatility in a given month is associated with the probability of an extreme shock in the subsequent month (top or bottom 1.5% of the returns distribution) of 26.4%. Other firm characteristics, including firm age, price, volume and book‐to‐market ratio, are also shown to be significantly related to subsequent firm extreme returns. The effects of conditional and implied volatility are mixed. The E‐GARCH and expected shortfall measures of conditional volatility are consistent with mean reversion: high short term realizations of conditional volatility foreshadow a lower probability of extreme returns.     

Idiosyncratic Volatility and the Expected Stock Returns for Exploring the Relationship with Panel Threshold Regression

This paper utilizes panel threshold regression to study the impact of idiosyncratic risk of stock returns on the Taiwan Security Market over the period from 2000 to 2011, during which there has been a noticeable increase idiosyncratic volatility. An innovative panel threshold regression model is applied to test the panel threshold effect of idiosyncratic risk on expected stock returns. The results support Merton’s (J Financ 42:579–590, 1987) investor recognition hypothesis and confirm that a threshold effect does exist. This study shows that it is possible to identify the definitive level beyond which a further increase in idiosyncratic volatility does not improve proportional expected stock returns. Some important policy implications arise from these findings. The conditional distribution of expected stock returns is allowed to vary across low volatility states. The evidence suggests that in Taiwan, idiosyncratic risk is a predictor of future market returns based upon threshold value during the lower variance state. In contrast, when the threshold value is exceeded, the relation between idiosyncratic risk and expected stock returns is not statistically significant.     

Corporate Bond Returns and Volatility

Recent literature emphasizes the relation of stock volatility to corporate bond yields. We demonstrate that during 1996–2005 corporate bond excess return volatility is directly related to contemporaneous corporate bond excess returns. In fact, the decompositions of aggregate bond volatility have a higher contemporaneous correlation with bond yields in comparison to idiosyncratic stock risk. Additionally, bond volatility and idiosyncratic risk are significant predictors of corporate three‐month and six‐month ahead bond excess returns. We also find that corporate bond volatility contains both slow moving and time‐varying components.     

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.     

市场摩擦对特质风险溢价的影响效应——基于A股主板市场的实证分析

与国外发达市场相比,我国A股主板市场的市场摩擦因素对市场微观结构和资产定价的影响更大。在防范和化解系统性风险的过程中,进一步分析市场摩擦如何作用于特质风险定价效应的问题具有重要的理论和现实意义。本文通过采用多维市场摩擦指标来代理信息不对称、交易成本、买卖限制、卖空限制、风险对冲和外部冲击,检验中国股市特质风险和预期收益率的关系,并判断出市场摩擦因素间的差异性影响机制。回归发现,市场摩擦和特质风险因子(特质波动率和特质偏度)都具有定价效应。各维度市场摩擦因素降低了股票流动性,进而增强了特质波动率的负向定价效应,部分解释了“特质波动率之谜”,但市场摩擦对特质偏度因子溢价的影响较为微弱。同时,基于特质波动率和特质偏度因子的投资策略能够产生超越CAPM、三因子和五因子模型的绝对收益,并印证了市场摩擦对特质风险因子绝对收益的影响作用。     

Idiosyncratic Volatility Covariance and Expected Stock Returns

Given that the idiosyncratic volatility (IDVOL) of individual stocks co‐varies, we develop a model to determine how aggregate idiosyncratic volatility (AIV) may affect the volatility of a portfolio with a finite number of stocks. In portfolio and cross‐sectional tests, we find that stocks whose returns are more correlated with AIV innovations have lower returns than those that are less correlated with AIV innovations. These results are robust to controlling for the stock's own IDVOL and market volatility. We conclude that risk‐averse investors pay a premium for stocks that pay well when AIV is high, consistent with our model.     

High idiosyncratic volatility and low returns: International and further U.S. evidence

Stocks with recent past high idiosyncratic volatility have low future average returns around the world. Across 23 developed markets, the difference in average returns between the extreme quintile portfolios sorted on idiosyncratic volatility is -1.31%$-1.31\%$ per month, after controlling for world market, size, and value factors. The effect is individually significant in each G7 country. In the United States, we rule out explanations based on trading frictions, information dissemination, and higher moments. There is strong covariation in the low returns to high-idiosyncratic-volatility stocks across countries, suggesting that broad, not easily diversifiable factors lie behind this phenomenon.     

Idiosyncratic Cash Flows and Systematic Risk

We show that unpriced cash flow shocks contain information about future priced risk. A positive idiosyncratic shock decreases the sensitivity of firm value to priced risk factors and simultaneously increases firm size and idiosyncratic risk. A simple model can therefore explain book‐to‐market and size anomalies, as well as the negative relation between idiosyncratic volatility and stock returns. Empirically, we find that anomalies are more pronounced for firms with high idiosyncratic cash flow volatility. More generally, our results imply that any economic variable correlated with the history of idiosyncratic shocks can help to explain expected stock returns.     

Are idiosyncratic volatility and MAX priced in the Canadian market?

The negative relationship between realized idiosyncratic volatility (RIvol) and future returns uncovered by Ang et al. (2006) for the U.S. market has been attributed to return reversals. For the Canadian market where return reversals are considerably less important, we find that RIvol is positively related to future returns, even after controlling for risk loadings, illiquidity and reversals. Unlike the findings of Bali et al. (2001) for the U.S. market, we find that the relationship between extreme positive returns (MAX) and future returns for the Canadian market is positive and that idiosyncratic volatility continues to be consistently positively related to future returns after controlling for MAX. We find evidence that suggests that reversals for stocks with extreme daily returns are confined to (typically small) stocks with low institutional holdings.     

Idiosyncratic volatility and cross‐sectional stock returns in Southeast Asian stock markets

We examine the role of idiosyncratic risk in five ASEAN markets of Malaysia, Singapore, Thailand, Indonesia, and the Philippines. Our research was motivated by the findings of Ang et al. (2006, 2009) of a ‘puzzling’ negative relation between idiosyncratic volatility and 1‐month ahead stock returns in developed markets and the suggestion of the ubiquity of these results in other markets. In contrast, we find no evidence of an idiosyncratic volatility puzzle in these Asian stock markets; instead, we document a positive relationship between idiosyncratic volatility and returns in Malaysia, Singapore, Thailand, and Indonesia and no relationship in the Philippines. The idiosyncratic volatility trading strategy could result in significant trading profits in Malaysia, Singapore, Thailand, and to some extent in Indonesia. Our study underscores the fact that generalizing empirical results obtained in developed stock markets to new and emerging markets could potentially be misleading.     

Effects of Passive Intensity on Aggregate Price Dynamics

We find that passive intensity (PI), measured by the passive‐linked share of total stock market trading volume, is strongly related to the overall pattern of stock price movements. A one‐standard‐deviation increase in PI is associated with an 8% higher price synchronicity. We further investigate the channels through which this relation is established by separately analyzing its impact on aggregate systematic and idiosyncratic volatility of stock returns. PI has a positive effect on systematic volatility and a negative impact on firm‐specific volatility. Consistent with the effect of passive trading on price dynamics, we find evidence that PI is negatively associated with mutual funds alpha dissimilarity. After controlling for market and idiosyncratic volatility, a one‐standard‐deviation increase in PI corresponds to a 0.20% decrease in fund dissimilarity. Our findings are robust after controlling for various macro and corporate factors known to affect systematic or firm‐specific volatility.     

The second moment matters! Cross-sectional dispersion of firm valuations and expected returns

Behavioral theories predict that firm valuation dispersion in the cross-section (“dispersion”) measures aggregate overpricing caused by investor overconfidence and should be negatively related to expected aggregate returns. This paper develops and tests these hypotheses. Consistent with the model predictions, I find that measures of dispersion are positively related to aggregate valuations, trading volume, idiosyncratic volatility, past market returns, and current and future investor sentiment indexes. Dispersion is a strong negative predictor of subsequent short- and long-term market excess returns. Market beta is positively related to stock returns when the beginning-of-period dispersion is low and this relationship reverses when initial dispersion is high. A simple forecast model based on dispersion significantly outperforms a naive model based on historical equity premium in out-of-sample tests and the predictability is stronger in economic downturns.