Skewness Risk Research Articles

Kurtosis and Skewness on Lagged Market Risk Premium in Indonesian Market During Covid 19 Pandemic

This study investigates the impact of return distribution such as skewness and kurtosis on lagged market risk premium to risk premium in Indonesia capital market during COVID-19 pandemic. Data are monthly, from january to December 2020, and 674 firms. Panel data predictive regression is used The method For this study, I first looked for market risk premium and risk premium desripitives. Second, I used monthly panel data predictive regression from lagged market risk premium and risk premium in 2020. Third, I incorporate skewness and kurtosis simultaneously. Fourth, I exclude kurtosis or skewness in previous model. The results are market risk premium and risk premium having negative return. Risk premium has lower returns than market risk premium. The beta lagged market risk premium is significant to risk premium. The skewness and kurtosis market risk premium do not signify to risk premium together but significant separately. I can clonclude that the movement market risk premim and risk premium during COVID-19 pandemic are average negative. Beta lagged market risk premium can explain the future monthly risk premium. Contrary skewness and kurtosis, those can not be run together. When the model used to beta lagged market risk premium and skewness, partially the skewness was significant and the direction was positive. However, only beta lagged market risk premium and kurtosis were staying negative to the previous model. Incorporating lagged assumptive distribution only explain the risk premium under 1 % about 0.24%.

Frequency-Dependent Higher Moment Risks

Based on intraday data for a large cross-section of individual stocks and exchange traded funds, we show that short-term as well as long-term fluctuations of realized market and average idiosyncratic higher moments risks are priced in the cross-section of asset returns. Specifically, we find that market and average idiosyncratic volatility and kurtosis are significantly priced by investors mainly in the long-run even if controlled by market moments and other factors, while skewness is mostly short-run phenomenon. A conditional pricing model capturing the time-variation of moments confirms downward-sloping term structure of skewness risk and upward-sloping term structure of kurtosis risk, moreover the term structures connected to market skewness risk and average idiosyncratic skewness risk exhibit different dymanics.

Managing Forward Volatility and Skew Risk

The forward start dual volatility swap is introduced. It can be regarded as the analog for volatility of what the entropy contract is for variance. Under the risk neutral measure it is shown that the difference between the forward start volatility swap and its dual is approximately the difference between two specific forward start implied volatilities. A dynamic replicating strategy is given which enables practitioners to approximately but robustly hedge forward start (dual) volatility swaps and the forward start skew using no more than two forward start options.

Modeling Skewness in Portfolio Choice

Despite half a century of research, we still do not know the best way to model skewness of financial returns. We address this question by comparing the predictive ability and associated portfolio performance of several prominent skewness models in a sample of ten international equity market indices. Models that employ information from the option markets provide the best outcomes overall. We develop an option-based model that accounts for the skewness risk premium. The new model produces the most informative forecasts of future skewness, the lowest prediction errors and the best portfolio performance in most of our tests.

Salient Cues and Complexity

Economic decisions are often influenced by cues that stand out in the choice context and attract attention. Intuitively, through channeling attention to a subset of the relevant information, salience thereby reduces the dimensionality of a decision problem. Building on this intuition, we hypothesize that people behave more consistently across differently complex problems if there is a common salient cue that guides their attention and, consequently, behavior. We experimentally test and confirm this hypothesis in the context of choice under risk: while revealed attitudes toward skewed risks — which have extreme and salient outcomes — are consistent across differently complex problems, revealed attitudes toward symmetric risks — where such a salient cue is missing — vary significantly with complexity. We provide suggestive evidence that these findings are driven by the extreme outcomes of skewed risks attracting a subject's attention and guiding choices. To rationalize our experimental results, we propose a variant of Bordalo et al.'s (2012) salience theory.

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.

The Price of the Smile and Variance Risk Premia

Using a new specification of multifactor volatility, we estimate the hidden risk factors spanning S&P 500 index (SPX) implied volatility surfaces and the risk premia of volatility-sensitive payoffs. SPX implied volatility surfaces are well-explained by three dependent state variables reflecting (i) short- and long-term implied volatility risks and (ii) short-term implied skewness risk. The more persistent volatility factor and the skewness factor support a downward sloping term structure of variance risk premia in normal times, whereas the most transient volatility factor accounts for an upward sloping term structure in periods of distress. Our volatility specification based on a matrix state process is instrumental to obtaining a tractable and flexible model for the joint dynamics of returns and volatilities, which improves pricing performance and risk premium modeling with respect to recent three-factor specifications based on standard state spaces. This paper was accepted by Gustavo Manso, finance.

The use of option prices to assess the skewness risk premium

ABSTRACT The aims of this study are twofold. First, to determine the sign and magnitude of the skewness risk premium (SRP) in the Italian index option market using two procedures: (i) skewness swap contracts, (ii) option trading strategies consisting of positions in options and their underlying assets. Second, to investigate the term structure of the SRP for 30, 60 and 90-day maturities to provide investors with a proper time horizon for profitable skewness trading strategies. Several results are obtained. First, the SRP, defined as the difference between the physical and the risk-neutral skewness, is positive and statistically and economically significant. These findings indicate that the SRP does exist, it is positive in sign, and it can be quantified. Second, the SRP is higher in magnitude for short-term maturity (€35 for the 30-day maturity) and lower for 60-day and 90-day maturities (both about €27). Third, skewness trading strategies confirm our finding of a positive and economically significant SRP. Fourth, a strategy that sells out-of-the-money puts is more profitable for medium-term maturities compared to short-term maturities. A strategy that takes a long position on out-of-the-money calls, and a short position on out-of-the-money puts, yields a higher return, if near-term options are used.

Two Skewed Risks

We analyze the joint effects of skewness and correlation in a simple two-asset framework. Returns follow the split bivariate normal distribution, which combines bivariate normal distributions with different standard deviations and provides a good empirical fit. We show that equilibrium risk premia deviate from the CAPM if assets differ in skewness. Moreover, if the more positively skewed asset is more volatile, it underperforms and its beta, maximum return, idiosyncratic and systematic skewnesses are all higher—consistent with empirical evidence. We also derive formulas and analyze the role of skewness for portfolio choice and recently proposed conditional risk metrics.

Risk premium spillovers among stock markets: Evidence from higher-order moments

We investigate the volatility and skewness risk premium spillovers among the U.S., U.K., German, and Japanese stock markets. We define risk premia as the difference between risk-neutral and realized moments. Our findings highlight that during periods of stress, cross-market and cross-moment spillovers increase and that these increases are mirrored by a decrease in within-market effects. We document strong bidirectional spillovers between volatility and skewness risk premia and emphasize the prominent role played by the volatility risk premium. Finally, we show that several announcements drive the time-varying risk premium spillovers.

Cross-Asset Skew

We find that realized skewness is a significant indicator of returns across a range of assets from different asset classes, namely commodities, government bonds, equity indices and currencies. Taking on skewness risk is broadly compensated within, but more substantially across asset classes. Portfolios in these four asset classes with long positions on most negatively (or least positively) skewed assets and short positions on least negatively (or most positively) skewed assets generate on average a Sharpe ratio of 0.35 between 1990 and 2017. We find little evidence of a common risk driver among these portfolios, to the extent that their combination benefits substantially from diversification, delivering a Sharpe ratio of 0.72. The patterns are not subsumed by other known factors that drive returns, such as value, momentum or carry factors and, consequently, mean-variance efficient multi-factor portfolios assign a positive weight to skewness. Our results remain robust to different measures of skewness and across sub-samples.

On Taking a Skewed Risk More Than Once

This paper collects results on the repeated risk-taking of skewed risks. An extensive body of theoretical and experimental literature has shown that, in one-time decision situations, humans are skewness-seeking and dislike risks that feature unlikely but large losses (i.e., negatively skewed risks). We show that, contrary to intuition, the often-observed phenomenon of penny-picking—repeatedly taking negatively skewed risks—is not at odds with skewness-seeking, but, to the contrary, may even be caused by it. The skewness of the distribution that results from repeatedly taking a skewed risk depends in non-trivial ways on the risk-taking strategy and may even differ in sign from that of the individual risk. With sufficient time available, every risk—no matter how negatively skewed—can be gambled in such a way that, in total, skewness is positive. Because recent work has shown that skewness is decisive whether risk is taken, this result may be important for economics and finance on a fundamental level.

Measuring skewness premia

We provide a new methodology to empirically investigate the respective roles of systematic and idiosyncratic skewness in explaining expected stock returns. Using a large number of predictors, we forecast the cross-sectional ranks of systematic and idiosyncratic skewness, which are easier to predict than their actual values. Compared to other measures of ex ante systematic skewness, our forecasts create a significant spread in ex post systematic skewness. A predicted systematic skewness risk factor carries a significant and robust risk premium that ranges from 6% to 12% per year. In contrast, the role of idiosyncratic skewness in pricing stocks is less robust.

On the Nature of Jump Risk Premia

We propose a model-free method for measuring the jump skewness risk premium via a trading strategy. We find that in the S&P 500 option market, the premium is positive and greater in absolute terms than the variance premium. The trading strategy allows for examining the premium in different holding periods: daytime, when markets are open, and overnight, outside of trading hours. We demonstrate that both premia vary considerably between trading and non-trading periods, and also increase in periods of market distress. The daytime return on jump skewness is not spanned by other systematic risk factors, suggesting it is a systematic risk factor itself. Outside of trading hours, skewness risk does not seem to be distinguishable from variance risk. We also decompose total return skewness into a jump component, and a signed variance component, and demonstrate that only the jump component is priced. Our work also sketches a new set of stylized facts about variance and jump skewness premia that option pricing models should match.

The world predictive power of U.S. equity market skewness risk

This study investigates the cross-country impact of U.S. equity market skewness risk. We find that a large decrease in the U.S. market skewness significantly predicts higher future returns on international equity markets. The predictability remains significant after controlling for a set of U.S. and local forecasting variables. Furthermore, we find strong predictability in- an out-of-sample setting and the predictability delivers a large economic value. The U.S. market skewness also forecasts U.S. economic recessions and international market conditions, consistent with the international three-moment capital asset pricing model (three-moment CAPM) and the intertemporal capital asset pricing model (ICAPM).

Bidding for Contracts under Uncertain Demand: Skewed Bidding and Risk Sharing

Procurement projects often involve substantial uncertainty in inputs at the time of contracting. Whether the procurer or contractor assumes such risk depends on the specific contractual agreement. Using auction data from the Florida Department of Transportation, we document evidence of i) risk-balancing behavior through the formation of bid portfolios, and ii) opportunistic behavior via skewed bidding. We develop and estimate a model of bidding for contracts where bidders have multidimensional private information. In equilibrium, bidders balance skewed bidding and risk exposure; both efficient and inefficient bidders bid aggressively via skewed bidding. Counterfactual experiments suggest that the onus of bearing project risk should fall on the procurer (contractor) when project risk is large (small).

Skewness risk premium: Theory and empirical evidence

Using an equilibrium asset and option pricing model in a simple economy under jump diffusion, we show theoretically that the aggregated excess market returns can be predicted by the skewness risk premium, which is constructed to be the difference between the physical and the risk-neutral skewness. In an empirical application of the model using >20 years of data on S&P500 index options, we find that, in line with theory, risk-averse investors demand risk-compensation for holding stocks when the market skewness risk premium is high. However, when we characterize periods of high and low risk aversion, we show that in line with theory, the relationship only holds when risk aversion is high. In periods of low risk aversion, investors demand lower risk compensation, thus substantially weakening the skewness-risk-premium-return trade off.

The World Price of Skewness Risk

This study investigates the cross-country impact of U.S. equity market skewness risk. We find that a large decrease in the U.S. market skewness significantly predicts high future returns on international equity markets. The predictability remains significant after controlling for a set of U.S. and local forecasting variables. Furthermore, we find strong predictability in an out-of-sample setting and the predictability delivers a large economic value. The U.S. market skewness also forecasts U.S. economic recessions and international market conditions, consistent with the international three-moment capital asset pricing model (three-moment CAPM) and intertemporal capital asset pricing model (ICAPM).

Forecasting the oil prices: What is the role of skewness risk?

Crude oil is crucial to the operation and economic well-being of the modern society. Huge changes of crude oil price always cause panics to the global economy. This paper aims to investigate the predictability of the skewness risk of oil to directly forecast oil prices. We find that the skewness risk of oil does exhibit statistically and economically significant in-sample and out-of-sample forecasting power under OLS regressions. Moreover, the strength of the predictive evidence is substantial during recessions, and robust when controlling for a set of variables. Furthermore, the skewness risk of oil reveals substantial economic value for investors, in terms of superior oil risk premium forecasts and sizable utility gains.

Never a Dull Moment: Entropy Risk in Commodity Markets

We develop a new approach to determine investors' risk compensations for all distributional moments of a security. Using the concept of entropy, a summary of all moments of a risky security, we derive the relationship between expected returns and their compensation for entropy risk. Entropy risk premium (ERP), the difference of entropy under the physical and risk-neutral measures, indicates the cost to financially hedge against changes in risks associated with the entire return distribution. We find that ERP carries significant predictive power for the cross-section of commodity returns even after removing its variance, skewness and kurtosis risk components.