Comoment risk and stock returns

We estimate investable comoment equity risk premiums for the US markets. The stock's contribution to the asymmetry and the fat tails of the market portfolio's payoff are priced into a coskewness premium and a cokurtosis premium. We construct zero-investment strategies that are long and short in coskewness and cokurtosis equity risks; we infer from the spread the returns attached to a unit exposure to US equity coskewness and cokurtosis. The coskewness and cokurtosis premiums present positive monthly average returns of 0.27% and 0.14% from January 1959 to December 2011. Comoment risks appear to be significantly priced within the US stock market and display significant explanatory power regarding the US size and book-to-market effects. The premiums do not subsume, but rather complement the empirical capital asset pricing model. Our analysis relies on data collected from CRSP (Chicago Research Center for Security Prices) over December 1955 to December 2011. To our knowledge, the paper is the first to propose investable higher-moment risk factors over such an extensive time period.     

The value of coskewness in mutual fund performance evaluation

Recent asset pricing studies demonstrate the relevance of incorporating coskewness in asset pricing models, and illustrate how this component helps to explain the time variation of ex-ante market risk premiums. This paper analyzes the role of coskewness in mutual fund performance evaluation and finds evidence that adding a coskewness factor is economically and statistically significant. It documents that coskewness is sometimes managed and shows persistence of the coskewness policy over time. One of the most striking results is that many negative (positive) alpha funds, measured relative to the CAPM risk adjustments, would be reclassified as positive (negative) alpha funds using a model with coskewness. Therefore, performance ranking based on risk-adjusted returns without considering coskewness could generate an erroneous classification. Moreover, some fund characteristics, such as turnover ratio or category, are related to the likelihood of managing coskewness.     

Asymmetric Volatility,Skewness, and Downside Risk in Different Asset Classes: Evidence from Futures Markets

This study examines the cross‐sectional variation of futures returns from different asset classes. The monthly returns are positively correlated with downside risk and negatively correlated with coskewness. The asymmetric volatility effect generates negatively skewed returns. Assets with high coskewness and low downside betas provide hedges against market downside risk and offer low returns. The high returns offered by assets with low coskewness and high downside betas are a risk premium for bearing downside risk. The asset pricing model that incorporates downside risk partially explains the futures returns. The results indicate a unified risk perspective to jointly price different asset classes.     

Conditional extreme risk,black swan hedging,and asset prices

Motivated by the asset pricing theory with safety-first preference, we introduce and operationalize a conditional extreme risk (CER) measure to describe expected stock performance conditional on a small-probability market downturn (black swan). We document a significant CER premium in the cross-section of expected returns. We also demonstrate that CER explains the premia to downside beta, coskewness, and cokurtosis. CER provides distinct information regarding black swan hedging that cannot be captured by co-crash-based tail dependence measures. As we find that the pricing effect is stronger among black swan hedging stocks, this distinction helps explain the absence of premium to tail dependence.     

Conditional coskewness and asset pricing

We explore the empirical usefulness of conditional coskewness to explain the cross-section of equity returns. We find that coskewness is an important determinant of the returns to equity, and that the pricing relationship varies through time. In particular we find that when the conditional market skewness is positive investors are willing to sacrifice 7.87% annually per unit of gamma (a standardized measure of coskewness risk) while they only demand a premium of 1.80% when the market is negatively skewed. A similar picture emerges from the coskewness factor of Harvey and Siddique (Harvey, C., Siddique, A., 2000a. Conditional skewness in asset pricing models tests. Journal of Finance 65, 1263–1295.) (a portfolio that is long stocks with small coskewness with the market and short high coskewness stocks) which earns 5.00% annually when the market is positively skewed but only 2.81% when the market is negatively skewed. The conditional two-moment CAPM and a conditional Fama and French (Fama, E., French, K., 1992. The cross-section of expected returns. Journal of Finance 47,427465.) three-factor model are rejected, but a model which includes coskewness is not rejected by the data. The model also passes a structural break test which many existing asset pricing models fail.     

Extreme downside risk and expected stock returns

We propose a measure for extreme downside risk (EDR) to investigate whether bearing such a risk is rewarded by higher expected stock returns. By constructing an EDR proxy with the left tail index in the classical generalized extreme value distribution, we document a significantly positive EDR premium in cross-section of stock returns even after controlling for market, size, value, momentum, and liquidity effects. The EDR premium is more prominent among glamor stocks and when high market returns are expected. High-EDR stocks are generally characterized by high idiosyncratic risk, large downside beta, lower coskewness and cokurtosis, and high bankruptcy risk. The EDR premium persists after these characteristics are controlled for. Although Value at Risk (VaR) plays a significant role in explaining the EDR premium, it cannot completely subsume the EDR effect.     

Asset pricing: A tale of two days

We show that asset prices behave very differently on days when important macroeconomic news is scheduled for announcement. In addition to significantly higher average returns for risky assets on announcement days, return patterns are much easier to reconcile with standard asset pricing theories, both cross-sectionally and over time. On such days, stock market beta is strongly related to average returns. This positive relation holds for individual stocks, for various test portfolios, and even for bonds and currencies, suggesting that beta is after all an important measure of systematic risk. Furthermore, a robust risk–return trade-off exists on announcement days. Expected variance is positively related to future aggregated quarterly announcement day returns, but not to aggregated non-announcement day returns. We explore the implications of our findings in the context of various asset pricing models.     

Are extreme returns priced in the stock market? European evidence

This paper revisits some recently found evidence in the literature on the cross-section of stock returns for a carefully constructed dataset of euro area stocks. First, we confirm recent results for US data and find evidence of a negative cross-sectional relation between extreme positive returns and average returns after controlling for characteristics such as momentum, book-to-market, size, liquidity and short term return reversal. We argue that this is the case because these stocks have lottery-like characteristics, which is attractive to certain investors. Also, these stocks tend to be very volatile so that arbitrageurs are discouraged from correcting potential mispricing. As a consequence, these stocks are often overpriced and hence face lower expected returns. Second, when we control for extreme returns, the recently found negative relationship between idiosyncratic risk and future returns is less robust. In our models, after adding maximum returns, the relationship is insignificant and sometimes even positive. We also find that idiosyncratic skewness and coskewness play an important role for asset pricing, as predicted by several theoretical models.     

IS THE BOOK‐TO‐MARKET RATIO A MEASURE OF RISK?

We develop a leverage‐based alternative to traditional asset pricing models to investigate whether the book‐to‐market ratio acts as a proxy for risk. We argue that the book‐to‐market ratio should act as a proxy because of the expected relations between (1) financial risk and measures of capital structure based on the market value of equity and (2) asset risk and measures of capital structure based on the book value of equity. We find no relation between average stock returns and the book‐to‐market ratio in all‐equity firms after controlling for firm size, and an inverse relation between average stock returns and the book‐to‐market ratio in firms with a negative book value of equity.     

Option Coskewness and Capital Asset Pricing

This article shows how the market coskewness model of Rubinstein(1973) and Kraus and Litzenberger (1976) is altered when a nonredundantcall option is optimally traded. Owing to the option’snonredundancy, the economy’s stochastic discount factor(SDF) depends not only on the market return and the square ofthe market return but also on the option return, the squareof the option return, and the product of the market and optionreturns. This leads to an asset pricing model in which the expectedreturn on any risky asset depends explicitly on the asset’scoskewness with option returns. The empirical results show thatthe option coskewness model outperforms several competing benchmarkmodels. Furthermore, option coskewness captures some of thesame risks as the Fama–French factors small minus big(SMB) and high minus low (HML). These results suggest that thefactors that drive the pricing of nonredundant options are alsoimportant for pricing risky equities.(JEL G11, G12, D61)     

The coskewness puzzle

We propose a novel approach to testing non-linear stochastic discount factor (SDF) specifications that arise in rational representative investor models. Our approach does not require overly-restrictive assumptions about the shape of investors’ preferences, typically imposed by the extant literature, and is based instead on restrictions that rule out “good deals”, i.e., arbitrage opportunities as well as unduly large Sharpe ratios. We apply this framework to test the empirical admissibility of 3 and 4-moment versions of the CAPM. We find that, while coskewness and cokurtosis risk help price a number of stock strategies and portfolios, including static strategies based on a fine industry-level diversification, momentum strategies and portfolios managed on the basis of available information, the CAPM and its 3 and 4-moment versions cannot provide an exhaustive account of observed asset returns.     

Oil Risk Exposure: The Case of the U.S. Oil and Gas Sector

We estimate oil price risk exposures of the U.S. oil and gas sector using the Fama‐French‐Carhart's four‐factor asset pricing model augmented with oil price and interest rate factors. Results show that the market, book‐to‐market, and size factors, as well as momentum characteristics of stocks and changes in oil prices are significant determinants of returns for the sector. Oil price risk exposures of U.S. oil and gas companies in the oil and gas sector are generally positive and significant. Our study also finds that oil price risk exposures vary considerably over time, and across firms and industry subsectors.     

Liquidity and asset pricing: Evidence from the Hong Kong stock market

This study investigates the role of liquidity in pricing stock returns in the Hong Kong stock market. Our results show that liquidity is an important factor for pricing returns in Hong Kong after taking well-documented asset pricing factors into consideration. The results are robust to adding portfolio residuals and higher moment factor in the factor models. The results are also robust to seasonality, and conditional-market tests. We also compare alternative factor models and find that the liquidity four-factor model (market excess return, size, book-to-market ratio, and liquidity) is the best model to explain stock returns in the Hong Kong stock market, while the momentum factor is not found to be priced.     

Low-Risk Anomalies?

This 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.     

A conditional higher-moment CAPM

This paper investigates whether dynamic and moment extensions to the traditional CAPM can improve its empirical performance and offer some alternative explanation to the cross-section of average returns on portfolios of stocks double sorted on book-to-market ratios and size. We consider three extensions. First, we introduce time-varying factor loadings obtained from a multivariate GARCH and dynamic conditional correlations. Second, we extend the model to a four-moment CAPM, which incorporates coskewness and cokurtosis. Finally, we allow for time-varying risk premia, based on a Markov-switching process. Our results confirm that the higher-moment CAPM does not perform well in its unconditional version, but its performance is significantly improved when we introduce a conditional version that accounts for both time-varying factor loadings and time-varying risk premia. The four-moment CAPM tests lead to a positive total risk premium estimate of 0.67% per month over the period 1926–2021, with all risk premia (beta, coskewness, and cokurtosis) exhibiting the expected theoretical signs.     

Profitability,Value, and Stock Returns in Production‐Based Asset Pricing without Frictions

In a production‐based asset pricing model without adjustment costs and with decreasing returns to scale following Brock (1982), stock returns at the firm level are determined by profitability, the book‐to‐market ratio, and the change in future profitability prospects. Although firms with low book‐to‐market ratios are normally more profitable and profitable firms are predicted to have higher returns, the stylized fact that book‐to‐market ratios positively forecast returns still holds theoretically, but with specific predicted exceptions. These implications are confirmed empirically.     

Do industries matter in explaining stock returns and asset-pricing anomalies?

Industry returns cannot be explained fully by well-known asset pricing models. This study reveals that common factors extracted from industry returns carry significant risk premiums that go beyond the explanatory power of size, book-to-market (BM) ratios, and momentum. In particular, this study shows that (1) the small-firm effect is significant only for firms whose market capitalization is below their industry average; (2) the BM effect is an intra-industry phenomenon; (3) a one-year momentum effect is significant only for firms whose BM ratio is smaller than the industry average and limited to non-January months; and (4) there is seasonality in all effects that cannot be explained by risk-based asset-pricing models. Neither rational nor behavioral theories alone can explain industry returns, and it is perhaps too hasty to attribute asset pricing anomalies to a single driving force.     

An alternative measure of the “world market portfolio”: Determinants, efficiency, and information content

The world market portfolio plays an important role in international asset pricing, but is unobservable in practice. We first propose a framework for constructing a market proxy that corresponds to the “market portfolio” of financial theory. We then construct this proxy, analyze its determinants and test its efficiency and explanatory power over the period 1975-2007 with respect to the return generating processes of a broad asset universe. We show that its major determinants are traded assets and that it is not efficient. However, it is significant for explaining individual asset returns over an asset universe that includes stocks, bonds, money markets and commodities. The explanatory information is incremental to what is available in traded asset prices and the significance of this information is robust with respect to diversified portfolios generated by factor analysis and to characteristic-sorted portfolios as well as to various model specifications, including the single-index model, the Fama-French (1992) three factor model for stocks, and various specifications of multi-index models hedged and unhedged for foreign currency risk.     

Joint tests of contagion with applications

Joint tests of contagion are derived which are designed to have power where contagion operates simultaneously through coskewness, cokurtosis and covolatility. Finite sample properties of the new tests are evaluated and compared with existing tests of contagion that focus on a single channel. Applying the tests to daily euro zone equity returns from 2005 to 2014 shows that contagion operated mainly through higher order moment channels during the GFC and the European debt crisis, which were not necessarily detected by traditional tests based on correlations. The empirical results have important implications for pricing risk and constructing well diversified portfolios.     

Firm characteristics and the impact of emerging market liberalizations

We provide a firm level analysis of the impact of capital market liberalization in 18 emerging markets. Consistent with models of international asset pricing, we find that firms’ stock returns increase during liberalization and that a majority of firms have lower mean returns and lower dividend yields after liberalization. We also find that emerging market firms have increased exposure to the world market and decreased exposure to the home market following liberalization. These changes in returns and exposures support the predictions of theoretical international asset pricing models. We also test and find support for the importance of size, local risk, foreign exchange risk, and cross-listing status in explaining the cross-section of changes in returns.