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.     

Firm age and realized idiosyncratic return volatility in China: The role of short-sales constraints

This paper investigates how realized idiosyncratic return volatility changes with firm age in the Chinese stock market. By employing a sample of 26,676 firm-year observations of 2798 A-share listed Chinese firms from 2001 to 2019, we find that realized idiosyncratic return volatility is negatively associated with firm age. Further, we find that loosening short-sales constraints strengthens this negative association, and that heterogeneity of investor beliefs is the most likely mechanism driving the negative relation, rather than the alternative explanations of cash flow volatility and growth options. Our results are fairly consistent under two different measures of firm age, and are robust to a choice of two multiple-factor models (the Fama-French three-factor and five-factor models) as well as two data frequencies (daily and monthly) used to estimate realized idiosyncratic return volatility.     

Cross section of option returns and idiosyncratic stock volatility

This paper presents a robust new finding that delta-hedged equity option return decreases monotonically with an increase in the idiosyncratic volatility of the underlying stock. This result cannot be explained by standard risk factors. It is distinct from existing anomalies in the stock market or volatility-related option mispricing. It is consistent with market imperfections and constrained financial intermediaries. Dealers charge a higher premium for options on high idiosyncratic volatility stocks due to their higher arbitrage costs. Controlling for limits to arbitrage proxies reduces the strength of the negative relation between delta-hedged option return and idiosyncratic volatility by about 40%.     

Transparency,idiosyncratic risk,and convertible bonds

We first investigate the relationship among a company's information transparency, idiosyncratic risk, and return of its convertible bonds. The effects of a company's idiosyncratic risk on its equity's value volatility and its credit risk are also examined. The findings indicate that when a company discloses a significant amount of information, it is likely to have a higher idiosyncratic risk and a lower credit risk, with no impact on returns on convertible bonds. The volatility of stock returns is positively related to returns on convertible bonds, and it is found that diversified strategies and returns on a company's equity help to improve its credit rating and that a better credit rating triggers an increase in returns on convertible bonds and idiosyncratic risk, indicating that evaluations of the value of convertible bonds must take pure bonds and equity (option) values into account. After excluding conversion values and estimating the idiosyncratic risk on daily, weekly, and monthly bases, this study suggests that there is a positive relation between returns on convertible bonds and information transparency when estimating idiosyncratic risk on a monthly basis and that a positive association also exists between credit rating, idiosyncratic risk, and returns on bonds.     

Expected stock returns,common idiosyncratic volatility and average idiosyncratic correlation

Motivated by Herskovic et al. (2016), we examine the role of the average idiosyncratic correlation (ICOR) in two types of markets: an emerging market and a developed market. Examining daily stock data from the Chinese stock market for the period 1995 to 2020 and from the US for the period 1926 to 2019, we adopt high-dimensional principal component analysis (PCA) and thresholding methods to re-estimate ICOR. We find that ICOR plays an important role in explaining the expected stock returns, as the common idiosyncratic volatility (CIV) does in Herskovic et al. (2016). ICOR has been neglected in the literature due to large estimation error in the idiosyncratic covariance matrix and our analysis provides evidence that ICOR is nonnegligible in both markets when we control for several common market factors. We show that the average idiosyncratic covariance, which is the numerator of ICOR, exhibits the same pattern as CIV. Furthermore, our regression analyses of expected stock returns in response to ICOR change in both markets show that, in contrast to the negative result for CIV, the stocks’ high risk exposure to ICOR change comes with a higher risk premium, perhaps because of the synchronized but disproportionate changes in the monthly idiosyncratic covariance and idiosyncratic volatility.     

The macroeconomic determinants of technology stock price volatility

Stock prices reflect the value of anticipated future profits of companies. Since business cycle conditions impact the future profitability of firms, expectations about the business cycle will affect the current value of firms. This paper uses daily and monthly data from July 1986 to December 2000 to investigate the macroeconomic determinants of US technology stock price conditional volatility. Technology share prices are measured using the Pacific Stock Exchange Technology 100 Index. One of the novel features of this paper is to incorporate a link between technology stock price movements and oil price movements. The empirical results indicate that the conditional volatilities of oil prices, the term premium, and the consumer price index each have a significant impact on the conditional volatility of technology stock prices. Conditional volatilities calculated using daily stock return data display more persistence than conditional volatilities calculated using monthly data. These results further our understanding of the interaction between oil prices and technology share prices and should be of use to investors, hedgers, managers, and policymakers.     

Estimating the expected marginal rate of substitution: A systematic exploitation of idiosyncratic risk

We develop a methodology to estimate the shadow risk free rate or expected intertemporal marginal rate of substitution, “EMRS”. Our technique relies upon exploiting idiosyncratic risk, since theory dictates that idiosyncratic shocks earn the EMRS. We apply our methodology to recent monthly and daily data sets for the New York and Toronto Stock Exchanges. We estimate EMRS with precision and considerable time-series volatility, subject to an identification assumption. Both markets seem to be internally integrated; different assets traded on a given market share the same EMRS. We reject integration between the stock markets, and between stock and money markets.     

The MAX effect: European evidence

The maximum daily return over the previous month (MAX) of Bali et al. (2011) is a strong and significant predictor of future stock returns in non-U.S. equity markets. Once it is controlled for MAX in the cross-section of average returns, the puzzling negative idiosyncratic volatility-return relation disappears. Consistent with the assumption that MAX is the true effect, for which idiosyncratic volatility is just a proxy, we find that MAX can be traced back to firm fundamentals in the manner of idiosyncratic volatility. The negative MAX-return relation is stronger among firms with high cash flow volatility and weaker among firms with high profitability.     

How is illiquidity priced in the Chinese stock market?

This study investigates the liquidity premium in the Chinese stock market. We found that the expected stock returns increase monotonically with the quintile sort on characteristic liquidity with descending patterns. The characteristic liquidity premium ranges from 0.82% to 1.28% per month, which is much higher than that of their US counterparts. Moreover, our multivariate decomposition approach highlights that characteristic illiquidity premiums can be explained mainly by size, idiosyncratic volatility and momentum. The net systematic liquidity premium reaches 0.84% per month, driven mainly by commonality beta. The finding shows that a liquidity-based strategy forecasts cross-section and time-series 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.     

ON ESTIMATING STOCK MARKET VOLATILITY: AN EXPLORATORY APPROACH

Traditional methods of estimating market volatility use daily return observations from a stock index to calculate monthly variance. We break with tradition and estimate stock market volatility using the daily, cross-sectional standard deviation of returns for all firms trading on the New York Stock Exchange and the American Stock Exchange. We find a significantly positive relation between risk and return. Market volatility is estimated to be about half the volatility level previously reported. The intraday, cross-sectional market volatility measure provides findings consistent with risk-return theory.     

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.     

Do idiosyncratic jumps matter?

We show that idiosyncratic jumps are a key determinant of mean stock returns from both an ex post and ex ante perspective. Ex post, the entire annual average return of a typical stock accrues on the four days on which its price jumps. Ex ante, idiosyncratic jump risk earns a premium: a value-weighted weekly long-short portfolio that buys (sells) stocks with high (low) predicted jump probabilities earns annualized mean returns of 9.4% and four-factor alphas of 8.1%. This strategy’s returns are larger when there are greater limits to arbitrage. These results are consistent with investor aversion to idiosyncratic jump risk.     

Idiosyncratic return volatility and the role of firm fundamentals: A cross-country analysis

We investigate the relation between fundamental idiosyncratic volatility and stock returns idiosyncratic volatility using data from 56 countries. We find a strong positive relation between fundamental idiosyncratic volatility and idiosyncratic volatility of returns. This association, however, seems to be entirely concentrated in the developed economies, and we find no effect in the emerging markets. Specifically, fundamental idiosyncratic volatility does not lead to more idiosyncratic return volatility in countries with poor legal institutions and weak shareholder protection laws.     

The pricing of idiosyncratic risk: evidence from the implied volatility distribution

A recent strand in the literature has investigated the relationship between idiosyncratic risk and future stock returns. Although several authors have found significant predictive power of idiosyncratic volatility, the magnitude and direction of the dependence is still being debated. Using a sample of all S&P 100 constituents, we identify positive risk premia for option-implied idiosyncratic risk. Depending on the model used to identify unsystematic risk, we observe a statistically and economically significant average annual premium of 1.72 percent. To investigate whether this impact is driven by the definition of idiosyncratic risk, we extend the pricing kernel by implied skewness. Using a double-sorting procedure, we show that the compensation of unsystematic risk is mainly driven by firms with high positive implied skewness.     

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,fundamentals, and institutional herding: Evidence from the Japanese stock market

Using Japanese data from 1975 to 2003, we show that both institutional herding and firm earnings are positively related to idiosyncratic volatility. We reject the hypothesis that institutional investors herd toward stocks with high idiosyncratic volatility and systematic risk. Our results suggest that a behavior story may explain the negative premium earned by high idiosyncratic volatility stocks found by Ang et al. [Ang, Andrew, Hodrick, Robert J., Yuhang Xing, Xiaoyan Zhang, 2004. The cross-section of volatility and expected returns, Forthcoming Journal of Finance]. We also find that the dispersions of change in institutional ownership and return-on-asset move together with the market aggregate idiosyncratic volatility over time. Our results suggest that investor behavior and stock fundamentals may both help explain the time-series pattern of market aggregate idiosyncratic volatility.     

Idiosyncratic volatility and the pricing of poorly-diversified portfolios

This article examines the role of idiosyncratic volatility in explaining the cross-sectional variation of size- and value-sorted portfolio returns. We show that the premium for bearing idiosyncratic volatility varies inversely with the number of stocks included in the portfolios. This conclusion is robust within various multifactor models based on size, value, past performance, liquidity and total volatility and also holds within an ICAPM specification of the risk–return relationship. Our findings thus indicate that investors demand an additional return for bearing the idiosyncratic volatility of poorly-diversified portfolios.     

Does more information in stock price lead to greater or smaller idiosyncratic return volatility?

We investigate the relation between price informativeness and idiosyncratic return volatility in a multi-asset, multi-period noisy rational expectations equilibrium. We show that the relation between price informativeness and idiosyncratic return volatility is either U-shaped or negative. Using several price informativeness measures, we empirically document a U-shaped relation between price informativeness and idiosyncratic return volatility. Our study therefore reconciles the opposing views in the following two strands of literature: (1) the growing body of research showing that firms with more informative stock prices have greater idiosyncratic return volatility, and (2) the studies arguing that more information in price reduces idiosyncratic return volatility.     

The impacts of climate policy uncertainty on stock markets: Comparison between China and the US

The interplay between climate policy uncertainty and stock market performance has emerged as a pressing research question in light of the challenges posed by climate change to financial markets. This paper measures China's daily and monthly climate policy uncertainty (CPU) from Jan 2000 to Mar 2022 based on Chinese news data for the first time. Then, the nonlinear and lag impacts of the US CPU and China's CPU on the return, volatility, correlation and tail dependence of China's and US stock markets are investigated and compared by adopting copula function and the distribution lag nonlinear model (DLNM). The data of stock markets includes the Shanghai Composite Index (SSCI) and NASDAQ from Jan 2000 to Mar 2022 from the Choice database, and the Shenzhen Composite Index (SCI) and S&P 500 are used for the robustness test. The empirical results indicate that (1) the growth trend of China’s CPU index is similar to that of the US. However, there are significant differences between the impacts of these two CPUs on stock markets. (2) For China, high CPU decreases current stock market return and increases volatility but decreases it in the future. It could also increase the upper tail dependence between China’s and the US stock markets’ volatilities in current period. (3) For the US, CPU decreases stock market return in the short term but increases it in the long term. High CPU increases volatility in short term, decreases volatility in 5 months and increases it again after 6 months. Both low and high CPU could increase the correlation between China's and US stock markets' volatilities.