Coskewness Risk Research Articles

What we know about the low-risk anomaly: a literature review

It is well documented that less risky assets tend to outperform their riskier counterparts across asset classes. This paper provides a structured summary of the current state of literature regarding this so-called low-risk anomaly. It provides an overview of empirical findings across implementation methodologies and asset classes. Furthermore, it presents the most prevailing causes, which are namely exposure to other factors, coskewness risk, investor constraints, behavioral biases, and agency problems. The paper concludes that despite some critiques there are good reasons to believe that the low-risk anomaly can be evaluated as an investment factor. It also identifies that more research is required to disentangle the proposed causes to fully understand the big picture of the anomaly with certainty.

On the time‐varying relationship between coskewness and returns of banks

AbstractFor a sample of US commercial banks, we find that during the Global Financial Crisis of 2007–2009 and the COVID‐19 pandemic of February–December 2020, bank returns were positively related to their coskewness with the market return, while the relationship was negative during stable periods. The literature on non‐financial firms and global equity indices has shown that the relationship between coskewness and stock returns is time‐variant. The findings of this study extend that evidence to banks. The interpretation is that in normal times, investors show a preference for “lotteryness,” and therefore they are willing to pay a premium for bank stocks with a high coskewness (i.e., low expected return). In contrast, during crises, stocks with a high coskewness are more likely to suffer deep losses, and investors are reluctant to demand these risky high returns. These findings deliver important insights into how to interpret bank capital costs throughout the business cycle, as we suggest that during crises the issuance of equity capital becomes more costly for banks because investors demand higher coskewness risk premiums.

Risk-Return Relationship in the Nigerian Stock Market: Comparative between Fama-French Five-Factor Model and Higher Moment Fama-French Five-Factor Model

The study looked at the relationship between risk and return in the Nigerian stock market using Fama-French five-factor model and Higher Moment Fama-French five-factor model. The employed 90 companies’ stocks that are frequently traded out of the sample size of 113 companies’ stocks. The monthly stock prices, market index, risk-free rate (which was substituted with the rate on Treasury bills), ownership shareholdings, market capitalization, book value of equity, earnings before interest and taxes, and total assets were the data used in this study. The entire sample period covered from 2005-2020. The data was extracted from the Nigerian Group of Exchange (NGX) website, the Central Bank of Nigeria (CBN) website, and the Standard and Poor (S&P) database. The Fama-MacBeth two-step regression method was employed. It was found that systematic risk has significant negative effect on return while unsystematic risk has significant positive effect on return. The study concluded that the long standing view of hypothesised positive relationship between risk and return does not hold in the Nigerian stock market and the assumption that market risk is the only determinant of return is invalidated. Also, systematic coskewness risk is an important risk factor in the Nigerian stock market and higher moment FF5F model and CoFF5F model is superior to FF5F model. The study recommended that the investors should focused on how their investment return co-move with other dimension of risk such as unsystematic risk, systematic cokewness risk, systematic cokurtosis risk and non-market risk apart from the systematic risk.

The beta anomaly in the Australian stock market and the lottery demand

Frazzini and Pedersen (2014) [Betting against beta. Journal of Financial Economics, 111(1), 1–25] report an insignificant performance for the betting against beta (BAB) strategy in the Australian equity market, suggesting that the beta anomaly does not exist in this market. We extend their sample period and find strong evidence for a low-beta effect. The arbitrage portfolio that takes long positions in low-beta stocks and short positions in high-beta stocks generates a significant abnormal return of 5.9% per year. The beta anomaly over 1995–2019 is strong and robust after controlling for risk factors and stock characteristics. Decomposition of the beta anomaly into stock and industry level components shows that the low-beta effect is driven by the firm, and not the industry level beta. We further find that lottery demand explains the low-beta effect. In a series of portfolio and cross-sectional analyses, we show that the abnormal returns related to the beta anomaly become insignificant after controlling for lottery demand. The findings are robust to different proxies for lottery demand, alternative beta estimation and regression analyses. There is no evidence that the beta anomaly can be explained by leverage constraints, coskewness risk or investment and profitability risk factors. We further show that beta anomaly is more pronounced during the upmarket than the downmarket periods and that lottery demand plays a role in its time-variation. The findings have important implications for retail and institutional investors who trade on beta.

The Ex Ante Physical Distributions of Individual Stock Returns

I present a method for deriving the entire physical return distributions of individual stocks directly from option prices. The method is theoretically nested in an equilibrium model, obeys the law-of one-price, and can be implemented in real-time in a forward-looking manner. The method performs well out-of-sample in predicting ex-post distributions of individual stock returns. The physical stock distributions and the co-moments with the market are important for risk-management decisions, portfolio allocation, and can help understand the cross-section of returns. A tradeable long-short portfolio that buys (sells) low (high) co-skewness stocks yields a monthly five-factor alpha of 0.61% (t-stat 3.25). The equity risk factors: value, profitability, investments, momentum, and betting-against-beta can all be used to hedge co-skewness risk.

Option-Based Estimation of the Price of Coskewness and Cokurtosis Risk

AbstractWe show that the prices of risk for factors that are nonlinear in the market return can be obtained using index option prices. The price of coskewness risk corresponds to the market variance risk premium, and the price of cokurtosis risk corresponds to the market skewness risk premium. Option-based estimates of the prices of risk lead to reasonable values of the associated risk premia. An analysis of factor models with coskewness risk indicates that the new estimates of the price of risk improve the models’ performance compared with regression-based estimates.

Low‐Risk Anomalies?

ABSTRACTThis paper shows that low‐risk anomalies in the capital asset pricing model and in traditional factor models arise when investors require compensation for coskewness risk. Empirically, we find that option‐implied ex ante skewness is strongly related to ex post residual coskewness, which allows us to construct coskewness factor‐mimicking portfolios. Controlling for skewness renders the alphas of betting‐against‐beta and betting‐against‐volatility insignificant. We also show that the returns of beta‐ and volatility‐sorted portfolios are driven largely by a single principal component, which in turn is explained largely by skewness.

Are Higher Co-Moments Priced? A Tale of Two Countries

This study investigates the role of higher co-moments in explaining stock returns in the China and U.K. stock markets. In China, investors price only coskewness risk, while U.K. investors price both coskewness and cokurtosis risks. China investors use a two-year window to evaluate coskewness risk, while U.K. investors utilize a five-year estimation window. In addition, the significant coskewness risk premium in China is driven mainly by the sub-period after the split share structure reform. We argue that differences in market infrastructure and stage of development contribute to explaining the different higher co-moments pricing behavior in the two markets. Key words: Higher co-moments, coskewness, cokurtosis, China stock market, U.K. stock market

China vs. U.S.: is co-skewness risk priced differently?

ABSTRACT We investigate the role of co-skewness in pricing stock returns in the Chinese and U.S. markets. In both markets, co-skewness is priced with a negative premium. The annualized factor-adjusted co-skewness effect is −7.98% in China and −3.53% in the U.S. The negative co-skewness effect coexists with other higher-moment-related pricing effects. Through two natural experiments in the Chinese and U.S. markets, we find that an improvement in the information environment greatly enhances the co-skewness pricing effect in both markets. Furthermore, we find that the governance structure and the efficiency level are the main determinants of the co-skewness premium in the Chinese market.

Coskewness Risk Decomposition, Covariation Risk, and Intertemporal Asset Pricing

We develop an intertemporal asset pricing model where cash-flow news, discount-rate news, and their second moments are priced by the market. This model generalizes the market-return decomposition framework, showing that intertemporal considerations imply a decomposition of squared market returns (coskewness risk). Our model accounts for 68% of the return variation across portfolios sorted by size, book-to-market ratio, momentum, investment, and profitability for a modern U.S. sample period. Further, our findings highlight the importance of covariation risk, that is, the risk of simultaneous unfavorable shocks to cash flows and discount rates, in understanding equity risk premia.

Multifactor asset pricing model incorporating coskewness and cokurtosis: the evidence from Asian mutual funds

This research adds cokurtosis risk factor as a new factor into Moreno and Rodriguez (2009) five-factor model to be six-factor model to evaluate the equity mutual fund performance of three selected countries in Asia - China, Singapore and Thailand as representatives of fast growing Asian countries. To my knowledge, this is the first research to incorporate both coskewness and cokurtosis risk factors into Carhart (1997) four-factor model, to become a six-factor model, to explain the equity mutual fund returns. The result shows that coskewness risk factor show significance in Singapore for mutual fund evaluation. There are some little sign of mild support for the pricing of cokurtosis in Singapore and Thailand too. In China, even coskewness is not statistically but shows economically significantly difference at 2.7% per month. Adding coskewness and cokurtosis risk factors in CAPM or Carhart (1997), four-factor model show little increment in the explanatory power of the models.

Are Higher Co-Moments Priced? A Tale of Two Countries

This study investigates the role of higher co-moments in explaining stock returns in the China and UK stock markets. In China, investors price only coskewness risk, while UK investors price both coskewness and cokurtosis risks. China investors use a two-year window period to evaluate coskewness risk, while UK investors utilize a five-year window period to evaluate. In addition, the significant coskewness risk premium in China is driven mainly by the sub-period after the split share structure reform. We argue that differences in market infrastructure and stage of development contribute to explaining the different higher co-moments pricing behavior in the two markets.

Higher-moment liquidity risks and the cross-section of stock returns

In this paper, we derive higher-moment liquidity risks theoretically and examine whether they are empirically priced. We discover that when investors add trading cost to the utility function, the expected return of a stock should contain premia related to three higher-moment liquidity risks. We show that one of our higher-moment liquidity risks, or liquidity coskewness risk, measures an individual stock's marginal contribution to the skewness of portfolio liquidity and is consistently priced. In addition, our analysis of the Hansen-Jagannathan distance and the maximum Sharpe ratio show that the liquidity coskewness risk plays a substantial role in asset pricing and portfolio management.

Is Systematic Downside Beta Risk Really Priced? Evidence in Emerging Market Data

Several studies advocating safety first as a major concern to investors propose downside beta risk as an alternative to the traditional systematic risk-beta. Downside measures are concerned with a subset of the data and therefore the results in the studies that consider the downside beta only may be biased. This study addresses this issue by including downside co-skewness risk in addition to the downside beta risk in the pricing model. In a sample of 27 emerging markets two-stage rolling regression analysis fails to support pricing models with downside risk measures. In a cross-sectional analysis inclusion of downside co-skewness improves model fit. When considered together, downside beta is potential and downside co-skewness is a risk to the rational investor. Even though our results are inconclusive the evidence strongly suggests a need for further investigation of co-skewness risk in pricing models that adopt a downside risk framework.

Is systematic downside beta risk really priced? evidence in emerging market data

Several studies advocating safety first as a major concern to investors propose downside beta risk as an alternative to the traditional systematic risk- beta. Downside measures are concerned with a subset of the data and therefore the results in the studies that consider the downside beta only may be biased. This study addresses this issue by including downside co-skewness risk in addition to the downside beta risk in the pricing model. In a sample of 27 emerging markets two-stage rolling regression analysis fail to support pricing models with downside risk measures. In a cross-sectional analysis inclusion of downside co-skewness improves model fit. When considered together, downside beta is potential and downside co-skewness is a risk to the rational investor. Even though our results are inconclusive the evidence strongly suggests a need for further investigation of co-skewness risk in pricing models that adopt a downside risk framework.

The explanatory power of higher moment capital asset pricing model in the Karachi stock exchange

The study investigates the empirical validity of the higher-moment capital asset pricing model in the Karachi stock exchange. The sample consists of 313 stocks listed on the KSE over the sample period from July 2000 to June 2011. The findings suggest that covariance, co-skewness and co-kurtosis risks are mostly insignificantly priced in conditional and unconditional form over the full and sub-sample periods. However, over the sub-sample period of June 2007 to July 2009, the unconditional co-skewness risk is negatively and statistically significantly priced (white heteroskedasticity-consistent standard errors and covariance matrix). Co-skewness risk is marginally statistically significantly (at 10%) and correctly priced over the full sample period using the three-moment specification using white heteroskedasticity-consistent standard errors and covariance matrix. Furthermore, co-kurtosis risk is positively and statistically significantly priced over the sub-sample periods of July 2003 to February 2006 and July 2003 to June 2005 using Generalized Least Squares as estimation technique for the cross sectional regression.

Option-Based Estimation of the Price of Co-Skewness and Co-Kurtosis Risk

We show that the prices of risk for factors that are nonlinear in the market return are readily obtained using index option prices. The price of co-skewness risk corresponds to the market variance risk premium, and the price of co-kurtosis risk corresponds to the market skewness risk premium. Option-based estimates of the prices of risk lead to reasonable values of the associated risk premia. An out-of-sample analysis of factor models with co-skewness and co-kurtosis risk indicates that the new estimates of the price of risk improve the models' performance.

Multifactor Asset Pricing Model Incorporating Coskewness and Cokurtosis: The Evidence from Asian Mutual Funds

This research adds cokurtosis risk factor as a new factor into Moreno and Rodriguez (2009) five-factor model to be six-factor model to evaluate the equity mutual fund performance of three selected countries in Asia — China, Singapore, and Thailand as representatives of fast growing Asian countries. To my knowledge, this is the first research to incorporate both coskewness and cokurtosis risk factors into Carhart (1997) four-factor model, to become a six-factor model, to explain the equity mutual fund returns. The result shows that coskewness and cokurtosis risk factors show some significance in some countries in Asia. Adding coskewness and cokurtosis risk factors in both CAPM and four-factor model, show some increment in the explanatory power of the models.

An Empirical Analysis of Higher Moment Capital Asset Pricing Model for Bangladesh Stock Market

Capital Asset Pricing Model (CAPM) describes a relationship which is linear between expected return and risk of an asset. Within the contents of this paper, the higher moments of return distributions for companies listed in the Dhaka Stock Exchange (DSE) market have been inspected for the period of January 2005 to December 2009. The mean-variance CAPM model is extended by taking higher moments-Skewness and Kurtosis. Monthly stock returns from 80 non-financial companies, covering ten sectors (Engineering, Food & Allied, Fuel & Power, Textile, Pharmaceuticals, Services & Real Estate, Cement, Tannery, Ceramic and Miscellaneous) are studied in this research. From the empirical analysis, it is observed that the intercept term is significantly different from zero and insignificant relationship between beta and excess returns both in mean-variance CAPM and higher moment CAPM conditions. This means that the market excess returns provide no explanation for the asset rate of return, whether or not third and fourth moments are considered in the regression model. But, when the higher moments are introduced, the adjusted R-square increases 0.037 to 0.257. It is noticed that the risk premium for co-skewness risk is positive for the period 2005-2009, indicating that the co-skewness risk is compensated in the DSE market for the studied period. Also, the co-kurtosis risk is rewarded by the market. Thus, in describing risk-return relationship in emerging markets like Bangladesh stock market, the higher moment CAPM performs comparatively well.

Asset pricing and co-skewness risk: evidence from India

This paper analyses the validity of the three-moment CAPM model in the Indian context. The study is intended to find out whether co-skewness risk is priced in the Indian capital market. To analyse the validity of the three-moment CAPM model in the Indian context, a time period of around 12 years from January 1999 to June 2010 has been chosen. The sample covers 283 companies comprised in BSE-500 index of Bombay Stock Exchange of India. S&P CNX 500 index has been considered as a proxy for the market portfolio. The empirical results of the study confirm the validity of the three-moment CAPM in the Indian capital market and suggest that in addition to systematic standard deviation risk, co-skewness risk is also priced in the Indian capital market when investors price individual securities. The results of the study further show if co-skewness risk is not incorporated in the CAPM model, the traditional CAPM overestimates the expected market premium by 0.30% per month (3.67% per annum compounded annually).