The cross-section of expected stock returns and components of idiosyncratic volatility

A theoretical model is used to decompose the variance of stock returns into two volatility and two covariance terms by using a conditional Fama-French three-factor model. This study adopts portfolio analysis and Fama-MacBeth cross-sectional regression to examine the relationship between components of idiosyncratic risk and expected stock returns.The portfolio analysis results show that volatility terms are negatively related to expected stock returns, and alpha risk has the most significant relationship with stock returns. On the contrary, covariance terms have positive relationships with expected stock returns at the portfolio level. Furthermore, the results of the Fama-MacBeth cross-sectional regression show that only alpha risk can explain variations in stock returns at the firm level. Another finding is that when volatility and covariance terms are excluded from idiosyncratic volatility, the relation between idiosyncratic volatility and stock returns becomes weak at the portfolio level and disappears at the firm level. This is the first study that examines the relations between all the components of idiosyncratic risk and expected stock returns. It also suggests a new explanation for the negative relation between idiosyncratic risk and stock returns.

This study examines the effect of the COVID-19 pandemic on the relationship between idiosyncratic volatility and expected stock returns. Using daily stock return data in the US market from the Center for Research in Security Prices (CRSP), we estimate monthly idiosyncratic volatility and investigate the effect of the COVID-19 pandemic at the portfolio and firm level. The results of portfolio analysis and cross-sectional regression show that the relationship between idiosyncratic volatility and subsequent stock returns switches from negative to positive during the pandemic period. Furthermore, we find that the relationship is robust to skewness for the “before the pandemic” and “after pandemic” periods. On the contrary, when we control for the one-month return reversal, the effect of idiosyncratic volatility on the subsequent stock returns becomes insignificant in both periods. Therefore, the short-term return reversal effect is the underlying reason for the relationship switching from negative to positive in the pandemic period. Our results are beneficial for investors and researchers.

Purpose – The purpose of this paper is to understand the controversial issue of whether stock returns and idiosyncratic risks are related positively or negatively in case of Singaporean ethically poor screened stocks. Design/methodology/approach – To achieve the major objectives of this paper, it uses a multiple regression to explore the relationship between expected stock returns and idiosyncratic risk. The paper replicates the Lee and Faff’s (2009) three-factor capital asset-pricing model (CAPM) model in creating the six size/book-to-market portfolios from which it constructs the small minus big (SMB) and high minus low (HML) portfolios that capture the size and book-to-market equity factors, respectively. Findings – The basic finding of the paper is that there is a strong relation between idiosyncratic risk and the expected stock returns. In more details, we observe that the portfolio of stocks with the highest idiosyncratic volatility generates higher average returns (4.36 per cent) than the portfolio of stocks with the lowest idiosyncratic volatility (0.79 per cent) over the sample period. The paper observes that the stock’s idiosyncratic volatility is inversely correlated with the size of the underlying firm. Moreover, there is a pattern of relationships nearer the periods of financial crises: Asian and global financial crises. Research limitations/implications – This paper uses only a three-factor model on a single country. So it cannot be generalized to a multi-country level in the Association of Southeast Asian Nations (ASEAN) region, as the structure of each member country is different. Practical implications – This paper provides guidelines for policymakers and foreign investors in Singapore about the relationship. This research can also be extended to other ASEAN countries to understand this puzzle. Social implications – Ethically sensitive and faithful investors with small investment can benefit from the findings of this paper. Originality/value – The work reported in this paper is original, unpublished and is also not under consideration for publication elsewhere.

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.

This article utilizes panel data regression to explore the random effects between expected stock returns and idiosyncratic risk. We find a strong relation between idiosyncratic risk and the expected stock returns. The results are consistent with Fu's study (2009) and a documented relation exists between the expected stock return autocorrelation, the return reverse effects. This study reveals that idiosyncratic risk has a significantly positive impact on stock returns. It is shown that positive returns have more idiosyncratic volatility, indicating that past higher returns induce lower or negative returns. The results support Huang et al. (2010) stock return reversal effect, as well as Goyal and Santa-Clara's (2003), Bali et al. (2005) and Fu's (2009) hypothesis in which idiosyncratic risk has a positive impact on expected returns. We also find evidence that the FVIX (Mimicking Volatility Index) considering the robustness with high sensitivity to innovation. The aggregate volatility shows low past returns ...

The empirical evidence on the cross-sectional relation between idiosyncratic risk and expected stock returns is mixed. We demonstrate that the omission of the previous month's stock returns can lead to a negatively biased estimate of the relation. The magnitude of the omitted variable bias depends on the approach to estimating the conditional idiosyncratic volatility. Although a negative relation exists when the estimate is based on daily returns, it disappears after return reversals are controlled for. Return reversals can explain both the negative relation between value-weighted portfolio returns and idiosyncratic volatility and the insignificant relation between equal-weighted portfolio returns and idiosyncratic volatility. In contrast, there is a significantly positive relation between the conditional idiosyncratic volatility estimated from monthly data and expected returns. This relation remains robust after controlling for return reversals. The Author 2009. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org., Oxford University Press.

In classical asset pricing model, expected stock return is only determined by systematic risk, and idiosyncratic risk can be completely dispersed without asset pricing effect. However, the real world and the assumptions of classical asset pricing model are different, as idiosyncratic risk cannot be completely dispersed and has pricing effect. Recent studies found that the stock idiosyncratic volatility can actually predict stock return negatively, indicating the existence of the " Idiosyncratic volatility puzzle" in the Chinese stock market. There are constraints on margin trading in the Chinese stock market, which can affect investors' investment behavior and expectation of stock return. This article adopts difference-in-differences model and multivariable linear regression mode to test the impact of margin trading on idiosyncratic volatility, and further investigate the impact of margin trading on the " Idiosyncratic volatility puzzle ". The research results found that: In the process from the establishment of the margin trading system to the gradual expansion of underlying stocks, the impact of margin trading on idiosyncratic volatility has shifted from a positive impact to a negative impact. That is to say, margin trading has transitioned from initially increasing idiosyncratic volatility to later reducing idiosyncratic volatility, gradually playing a role in price discovery and reducing idiosyncratic risk in the stock market. The gradual improvement of the margin trading system is driving the development and maturity of the Chinese stock market.

To capture the dynamics of idiosyncratic volatility of stock returns over different horizons and investigate the relationship between idiosyncratic volatility and expected stock returns, this paper develops and estimates a parsimonious model of idiosyncratic volatility consisting of a short-run and a long-run component. The conditional short-run and long-run components are found to be positively and negatively related to expected stock returns, respectively. The positive relation between the short-run component and stock returns may be caused by investors requiring compensation for bearing idiosyncratic volatility risk when facing trading frictions and hold underdiversified portfolios. The negative relationship between the long-run component and stock returns may reflect the fact that stocks with high long-run idiosyncratic volatility are less exposed to systematic risk factors and, hence, earn lower returns. Moreover, the low-risk exposure of stocks characterized by high idiosyncratic volatility lends support to real-option-based mechanisms to explain this negative relation. In particular, the systematic risk of a firm with abundant growth options crucially depends upon the risk exposure of these options. The value of growth options could rise significantly because of convexity when the increase in idiosyncratic volatility occurs over long horizons. And growth options’ systematic risk could fall because the relative magnitude of their value in relation to systematic risk factors decreases.This paper was accepted by David Simchi-Levi, finance.

With the daily data and monthly data of stock market for January 1, 2000 to March 31, 2011 as research sample, use Fama-French three factor regression and EGARCH(1,1) model to estimate idiosyncratic risk, the relationship between idiosyncratic risk and the return of stocks is analyzed based on the cross-sectional regression analysis method. Using Fama-French three factor regression to estimate idiosyncratic risk, a strongly statistically significant positive relation between idiosyncratic risk and the return of stocks is found. Using EGARCH(1,1)model to estimate idiosyncratic risk, there is a strongly statistically significant negative relation between idiosyncratic risk and the weighted return of stocks. Moreover, size, turnover, illiquidity, book-to-market ratio and is positively related to return of stocks, momentum and is negatively related to return of stocks. Two different models (Fama-French Three-factor Model and EGARCH Model) indicate that no robustly significant relationship exists between idiosyncratic volatility and expected return.

Turnover is usually used as a proxy for stock liquidity. The negative relation between turnover and expected stock returns is regarded as evidence of the existence of liquidity premium. Turnover is also often used to measure the firm-specific uncertainty. The positive relation between turnover and expected stock returns is considered as the compensation for uncertain risks. Obviously, there is a conflict in the interpretation of the turnover risk information. Taking A shares in the Chinese stock market as the research object, we find that stocks with low turnover generally have higher risk premium than those with high turnover through portfolio analyses and cross-sectional regression analyses. Moreover, after controlling variables such as size, trading volume, beta, liquidity and uncertainty, the result is still robust. However, after building more subdivided portfolios according to turnover, we find that turnover can positively predict stock returns for stocks with low turnover, but it can negatively predict stock returns for stocks with high turnover. That is, the cross-sectional expected return is the first increasing and next descending function of turnover. We take the directional reversal point of the return forecast ability as the dividing point of the turnover level, and find that the uncertainty proxied by the total volatility and the idiosyncratic volatility can significantly explain the positive relationship between turnover and expected returns for stocks with turnover below the cross-sectional dividing point, but the liquidity can significantly explain the negative relationship between turnover and expected returns for stocks with turnover above the cross-sectional dividing point. Thus, the lower degree of turnover contains more firm-specific uncertainty information, and the higher degree of turnover reflects more stock liquidity information. During our sample period, the trading mechanism in the Chinese stock market has undergone major changes. After the sample period is divided into four stages according to several major trading mechanism reforms in the Chinese stock market, the empirical results are still significant and therefore the reforms of the transaction mechanism have not fundamentally changed the turnover risk information. By defining the turnover risk information, this paper not only provides theoretical support for other related research by dint of turnover, but also has direct guiding significance for investment practice according to turnover.

This thesis focuses on the Malaysian stock market, investigating return predictability and the time series and cross-sectional behaviour of idiosyncratic volatility. Emerging markets are classified as Global Growth Generators (3G countries) by Citigroup. 3G countries are considered to be a group with potential growth and profitable investment opportunities. Even though Malaysia is not on the list of 3G countries, it is classified as a high growth country in the Citigroup study of February, 2011. The Malaysian stock market is similar to other emerging markets in terms of its political and economic force. This study is intended to provide useful inspirations for investors who are searching for investment opportunities in emerging countries. Chapter 1 outlines the empirical investigations carried out in each chapter and emphasizes the relevant research questions and contributions of the study to the existing literature. Chapter 2 to Chapter 5 investigate the return predictability and idiosyncratic volatility, and form the main body of the thesis. Chapter 2 studies return predictability in the Malaysian stock market by synthesizing the conventional return predictability methods, such as constant variance over time and the absence of autocorrelation. A comprehensive study is undertaken of returns at the market, industry and firm levels. Both macroeconomic and firm attributes which may explain the stock return predictability are also investigated in this chapter. Although return predictability is observed at the market level, it is not common at the security level. While market returns are unpredictable during crisis periods, the number of individual securities with predictable returns increased. Money growth and changes in interest rates explain the return predictability at the macro level. Size is one factor that affects the return predictability at the micro level. In the third chapter, the time series behaviour of idiosyncratic volatility is examined. This chapter provides an in-depth analysis of the characteristics of idiosyncratic volatility. Both economic conditions and firm variables are investigated as potential explanatory variables of the dynamics of idiosyncratic volatility. In addition, versatile models for estimating the idiosyncratic volatility are also discussed. Using a robust trend test, trending behaviours of the idiosyncratic volatility are examined. The aim here is to provide additional insights, from an emerging market, into either the increasing trend in idiosyncratic volatility found by Campbell et al. (2001) or the no-trend behaviour found by Brandt et al. (2010) in the U.S. market. The evidence shows a declining trend in idiosyncratic volatility after the Asian financial crisis. An upward trend in small, low-priced firms and a downward trend in large firms contributed somewhat to the declining trend. We further show, both analytically and empirically, that the dynamics of the idiosyncratic volatility are caused by stock return synchronicity, market volatility and systematic risk. The empirical literature provides various contentious results on the pricing ability of idiosyncratic volatility. The most common arguments for these controversial results are sample specificity, data frequency, and the weighting schemes used in the construction of idiosyncratic volatility. In the fourth chapter, the contradictory results of Fu (2009) and Ang et al. (AHXZ, 2006, 2009) on the relationship between idiosyncratic volatility and stock returns in the case of Malaysia are examined. In this chapter, we forecast the idiosyncratic volatility by taking into account the regime-switching behaviour of returns and the volatility clustering in the variance. Several control variables (such as an omitted variables bias, return reversal, and liquidity bias) are used to rule out the possibility of a spurious relationship between idiosyncratic volatility and stock returns. An analysis at the portfolio level explores the arbitrage or investment opportunities. We find a significant contemporaneous negative relationship between idiosyncratic volatility and stock returns. The results are robust to liquidity, return reversal, idiosyncratic skewness and momentum. The fifth chapter investigates the relationship between the idiosyncratic volatility and stock returns, conditional on trading patterns, by adopting the signal decomposition methodology of wavelet analysis. Return series are decomposed using wavelet analysis, and three mutually exclusive and exhaustive components of the idiosyncratic volatility are constructed, after which the relationship between idiosyncratic volatility and returns is examined at different timescales. Different trading patterns are found at different timescales. Previous studies have identified an inverse relationship, using time series data without decomposition, and may therefore have failed to uncover the true effects of idiosyncratic volatility on stock returns. We uncover the fact that the negative relationship is generated from the short run dynamics, while there is no association between this relationship and the long run idiosyncratic volatility. Chapter 6 summarises the key findings of this thesis, and also highlights potential areas for future research.

My 2009 JFE paper [Idiosyncratic Risk and the Cross-Section of Expected Stock Returns', Journal of Financial Economics, Vol. 91, pp. 24-37] documents a positive and statistically significant cross-sectional relation between expected idiosyncratic volatility (E(IVOL)) and expected stock return. A recent working paper titled On the Relation between EGARCH Idiosyncratic Volatility and Expected Stock Returns by Guo, Ferguson, and Kassa of University of Cincinnati suggests that the positive relation is driven by an in-sample approach to estimate E(IVOL). They fail to find a significant relation between return and their E(IVOL) estimated out of sample. I find that two estimation settings in their SAS code, one of which limits the maximum number of iterations and the other accepts estimates with a questionable convergence status, lead to potentially unreliable estimates and ultimately, the failure to find the positive relation between return and E(IVOL). Using more reliable settings, I re-estimate E(IVOL) strictly out of sample, and confirm a robust and significantly positive relation between return and E(IVOL), just as reported in my JFE paper.

Idiosyncratic risk and the cross-section of expected stock returns

Idiosyncratic risk, costly arbitrage, and the cross-section of stock returns

We test a new cross-sectional relation between expected stock return and idiosyncratic risk implied by the theory of costly arbitrage. If arbitrageurs find it more difficult to correct the mispricing of stocks with high idiosyncratic risk, there should be a positive (negative) relation between expected return and idiosyncratic risk for undervalued (overvalued) stocks. We combine several well-known anomalies to measure stock mispricing and proxy stock idiosyncratic risk using an exponential GARCH model for stock returns. We confirm that average stock returns monotonically increase (decrease) with idiosyncratic risk for undervalued (overvalued) stocks. Overall, our results support the importance of idiosyncratic risk as an arbitrage cost.