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We 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 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 contract...

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-adjust...

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).

Using an equilibrium asset and option pricing model in a production economy under jump diffusion, we derive an analytical link between the equity premium, risk aversion and the systematic variance and skewness risk premium. In an empirical application of the model using more than 20 years of data on S&P500 index options, we find that, in line with theory, risk-averse investors demand risk-compensation for holding equity when the systematic skewness risk premium is high. However, when we differentiate between market conditions proxied by investor sentiment, we find that in up-markets (high sentiment) risk aversion is low, while in down-markets (low sentiment) risk aversion is high. We show that in line with theory, the skewness-risk-premium-return 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. Therefore, we also provide new evidence that helps to disentangle sentiment from risk aversion.

This paper investigates the role of realized and implied and their risk premia (variance and skewness) for commodities’ future returns. We estimate these moments from high frequency and commodity futures option data that results in forward-looking measures. Risk premia are computed as the difference between implied and realized moments. We highlight, from a cross-sectional and time series perspective, the strong positive relation between commodity returns and implied skewness. Moreover, we emphasize the high performance of skewness risk premium. Additionally, we show that their portfolios exhibit the best risk-return tradeoff. Most of our results are robust to other factors such as the momentum and roll yield.

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.

The variance risk premium defined as the difference between risk neutral variance and physical variance is one of the most crucial information recovered from option prices. It does not, however, reflect the asymmetry in upside and downside movements of underlying asset returns, and also has limitation in reflecting asymmetric preference of investors over gains and losses. In this sense, this paper decomposes variance risk premium into downside - and upside-variance risk premium, and then derives the skewness risk premium and examines its effectiveness in predicting future underlying asset returns. Using KOSPI200 option prices, we obtained the following results. First, we found out that the estimated skewness risk premium has meaningful forecasting power for future stock returns, while the estimated variance risk premium has little forecasting power. Second, by utilizing our results of skewness risk premium, we developed a profitable investment strategy, which verifies the effectiveness of skewness risk premium in predicting future stock returns. In conclusion, the empirical results of this paper can contribute to the literature in that it helps us understand why variance risk premium, in most global markets except the US market, has not been successful in forecasting future stock returns. In addition, our results showing the profitability of investment strategies based on skewness risk premium can also give important implications to practitioners.

This paper studies the positive and normative implication of extreme shocks for monetary policy. The analysis is based on a small-scale new Keynesian model with sticky prices and wages where shocks are drawn from asymmetric generalized extreme value (GEV) distributions. A nonlinear perturbation of the model is estimated by the simulated method of moments. Under both the Taylor and Ramsey policies, the central bank responds nonlinearly and asymmetrically to shocks. The trade-off between targeting a gross inaation rate above 1 as insurance against extreme shocks and strict price stability is unambiguously decided in favour of strict price stability.

This paper investigates the determinants of the corporate credit spreads changes in the Japanese bond markets. We show that the business cycle risk and market skewness risk affect changes in the credit spread in Japan even after controlling for the frequently used variables. We also find that the magnitude of market skewness risk is relatively higher for low-rated bonds. Our results are robust to changes in credit ratings, different maturity groups and time periods around the recent global financial crisis.

We propose that the “risk” of a portfolio has three components: variance, skewness, and kurtosis. Whereas most previous papers have focused on how variance is diversified, we use both analysis and simulations to investigate how skewness and kurtosis are diversified when the number of stocks in a well-diversified portfolio is increased. We find that, first, when a portfolio is skewed and fat-tailed, its variance, skewness, and kurtosis are simultaneously reduced as the number of risky assets in the portfolio increases. When the risky assets in a portfolio are moderately correlated, the three components tend to decrease and eventually converge to nonzero values, which define the portfolio's true multidimensional systematic risk and hence allow diversification of its multidimensional nonsystematic risk. Second, the skewness risk of a portfolio tends to decrease more slowly than variance and kurtosis risk, indicating that, among the three, skewness is the hardest to diversify.

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.

Utility is the fundamental variable thought to underlie economic choices. In particular, utility functions are believed to reflect preferences toward risk, a key decision variable in many real-life situations. To assess the validity of utility representations, it is therefore important to examine risk preferences. In turn, this approach requires formal definitions of risk. A standard approach is to focus on the variance of reward distributions (variance-risk). In this study, we also examined a form of risk related to the skewness of reward distributions (skewness-risk). Thus, we tested the extent to which empirically derived utility functions predicted preferences for variance-risk and skewness-risk in macaques. The expected utilities calculated for various symmetrical and skewed gambles served to define formally the direction of stochastic dominance between gambles. In direct choices, the animals' preferences followed both second-order (variance) and third-order (skewness) stochastic dominance. Specifically, for gambles with different variance but identical expected values (EVs), the monkeys preferred high-variance gambles at low EVs and low-variance gambles at high EVs; in gambles with different skewness but identical EVs and variances, the animals preferred positively over symmetrical and negatively skewed gambles in a strongly transitive fashion. Thus, the utility functions predicted the animals' preferences for variance-risk and skewness-risk. Using these well-defined forms of risk, this study shows that monkeys' choices conform to the internal reward valuations suggested by their utility functions. This result implies a representation of utility in monkeys that accounts for both variance-risk and skewness-risk preferences.

In this study, we investigate the skewness risk premium in the financial market under a general equilibrium setting. Extending the long-run risks (LRR) model proposed by Bansal and Yaron (J Financ 59:1481–1509, 2004) by introducing a stochastic jump intensity for jumps in the LRR factor and the variance of consumption growth rate, we provide an explicit representation for the skewness risk premium, as well as the volatility risk premium, in equilibrium. On the basis of the representation for the skewness risk premium, we propose a possible reason for the empirical facts of time-varying and negative risk-neutral skewness. Moreover, we also provide an equity risk premium representation of a linear factor pricing model with the variance and skewness risk premiums. The empirical results imply that the skewness risk premium, as well as the variance risk premium, has superior predictive power for future aggregate stock market index returns, which are consistent with the theoretical implication derived by our model. Compared with the variance risk premium, the results show that the skewness risk premium plays an independent and essential role for predicting the market index returns.

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.

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.

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.

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 risk premium that ranges from 7% to 12% per year and is robust to the inclusion of downside beta, size, value, momentum, profitability, and investment factors. In contrast to systematic skewness, the role of idiosyncratic skewness in pricing stocks is less robust. Finally, we document how the determinants of systematic and idiosyncratic skewness differ.

We show that exposure to the risk of kurtosis in oil market drives the cross-section of stock returns from 1996 to 2014. The average monthly difference between the return of portfolio of stocks with low exposure and high exposure to the risk of kurtosis is -0.37%, showing that higher exposure to oil’s kurtosis risk will be penalized by lower average returns. We are able to confirm the significance of kurtosis risk within the statistical framework of Carhart 4-factor model. In contrast to the skewness risk, which is only a significant player in some of the sub-periods, kurtosis risk is keeping its significance through all sub-periods, as well as after taking market moments into account and within different maturities. The significance of the risk of skewness gets more evident moving from shorter to longer maturities. The risk of volatility, which has been shown to be a significant-priced risk in the cross-section of stock returns in literature, loses its significance after controlling for the third and fourth moments.

Using the model-independent approaches of Trolle and Schwartz (2008) and Kozhan et al (2013), we estimate the Variance Risk Premium and Skew Risk Premium for oil market. After estimation, the contribution of the paper is twofold. First, we try to figure out which variables can describe the variation in variance and skew risk premium and the risk-neutral Skewness. The results show that we are able to describe a considerable portion of the variation in all three variables using speculative and macroeconomic factors and most of the variation is being described by by the latter group of variables. We also try to capture the effect of fundamentals of oil market on these variables. The results show that the fundamentals are able to describe big portion of variation in these three variables. Second, we try to predict the return of delta-hedged and delta-vega hedged option portfolios and also oil futures return. The results show that variance risk premium is a significant predictor of delta-hedged portfolio cumulative return with a positive sign while skew risk premium can describe the cumulative return of the delta-Vega Hedged portfolio with negative sign. The results also show that both variance and skew risk premia are significant predictors of cumulative futures return with different signs.

In this article, we show how to take into account skewness risk in portfolio allocation. Until recently, this issue has been seen as a purely statistical problem, since skewness corresponds to the third statistical moment of a probability distribution. However, in finance, the concept of skewness is more related to extreme events that produce portfolio losses. More precisely, the skewness measures the outcome resulting from bad times and adverse scenarios in financial markets. Based on this interpretation of the skewness risk, we focus on two approaches that are closely connected. The first one is based on the Gaussian mixture model with two regimes: a normal regime and a turbulent regime. The second approach directly incorporates a stress scenario using jump-diffusion modeling. This second approach can be seen as a special case of the first approach. However, it has the advantage of being clearer and more in line with the experience of professionals in financial markets: skewness is due to negative jumps in asset prices. After presenting the mathematical framework, we analyze an investment portfolio that mixes risk premia, more specifically risk parity, momentum and carry strategies. We show that traditional portfolio management based on the volatility risk measure is biased and corresponds to a short-sighted approach to bad times. We then propose to replace the volatility risk measure by a skewness risk measure, which is calculated as an expected shortfall that incorporates a stress scenario. We conclude that constant-mix portfolios may be better adapted than actively managed portfolios, when the investment universe is composed of negatively skewed financial assets.

This paper characterizes the equilibrium demand and risk premiums in the presence of skewness risk. We extend the classical mean-variance two-fund separation theorem to a three-fund separation theorem. The additional fund is the skewness portfolio, i.e. a portfolio that gives the optimal hedge of the squared market return; it contributes to the skewness risk premium through co-variation with the squared market return and supports a stochastic discount factor that is quadratic in the market return. When the skewness portfolio does not replicate the squared market return, a tracking error appears; this tracking error contributes to risk premiums through kurtosis and pentosis risk if and only if preferences for skewness are heterogeneous. In addition to the common powers of market returns, this tracking error shows up in stochastic discount factors as priced factors that are products of the tracking error and market returns.

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.

Variance swaps are natural instruments for investors taking directional bets on volatility and are often used for portfolio protection. The empirical observation on skewness research suggests that derivative professionals may also desire to hedge beyond volatility risk and there exists the need to hedge higher-moment market risks, such as skewness and kurtosis risks. We study two derivative contracts – skewness swap and kurtosis swap – which trade the forward realized third and fourth cumulants. Using S&P 500 index options data from 1996 to 2005, we document the returns of these swap contracts, i.e., skewness risk premium and kurtosis risk premium. We find that the both skewness and kurtosis risk premiums are significantly negative.

This paper estimates skewness risk premia on individual stocks using synthetic skew swaps and shows that there is a considerably large variation of monthly realized skewness risk premia across a representative set of portfolios which are sorted by skewness risk premium payoffs in the prior period. It then focuses on investigating the determinants of such cross-sectional variation and documents that consumption risk does not seem to be priced with respect to skewness risk premia. The market excess return and, especially, the market variance risk premium are shown to be key risk factors that drive the cross-sectional variation of skewness risk premium payoffs. The market variance risk premium factor is significantly priced with respect to skewness risk premia even if I allow for potential model misspecification. The success of the market variance risk premium factor can be potentially explained by the very different risk exposures of skewness risk premium-based portfolios to the risk proxied by the market variance risk premium. I further show that the higher the exposure of the skewness risk premium-based portfolio to such a risk, the larger skewness risk premium payoff is required in the cross section.

The momentum risk premium is one of the most important alternative risk premia alongside the carry risk premium. However, it appears that it is not always well understood. For example, is it an alpha or a beta exposure? Is it a skewness risk premium or a market anomaly? Does it pursue a performance objective or a hedging objective? What are the differences between time-series and cross-section momentum? What are the main drivers of momentum returns? What does it mean when we say that it is a convex and not a concave strategy? Why is the momentum risk premium a diversifying engine, and not an absolute return strategy? The goal of this paper is to provide specific and relevant answers to all these questions. The answers can already be found in the technical paper "Understanding the Momentum Risk Premium" published recently by Jusselin et al. (2017). However, the underlying mathematics can be daunting to readers. Therefore, this discussion paper presents the key messages and the associated financial insights behind these results. Among the main findings, one result is of the most importance. To trend is to diversify in bad times. In good times, trend-following strategies offer no significant diversification power. Indeed, they are beta strategies. This is not a problem, since investors do not need to be diversified at all times. In particular, they do not need diversification in good times, because they do not want that the positive returns generated by some assets to be cancelled out by negative returns on other assets. This is why diversification may destroy portfolio performance in good times. Investors only need diversification in bad economic times and stressed markets. This diversification asymmetry is essential when investing in beta strategies like alternative risk premia. On the contrary, this diversification asymmetry is irrelevant when investing in absolute return strategies. However, we know that generating performance with alpha strategies is much more difficult than generating performance with beta strategies. Therefore, beta is beautiful, but convex beta is precious and scarce. Among risk premia, momentum is one of the few strategies to offer this diversification asymmetry. This is why investing in momentum is a decision of portfolio construction, and not a search for alpha.

The concept of alternative risk premia is an extension of the factor investing approach. Factor investing consists in building long-only equity portfolios, which are directly exposed to common risk factors like size, value or momentum. Alternative risk premia designate non-traditional risk premia other than a long exposure to equities and bonds. They may involve equities, rates, credit, currencies or commodities and correspond to long/short portfolios. However, contrary to traditional risk premia, it is more difficult to define alternative risk premia and which risk premia really matter. In fact, the term "alternative risk premia encompasses" two different types of systematic risk factor: skewness risk premia and market anomalies. For example, the most frequent alternative risk premia are carry and momentum, which are respectively a skewness risk premium and a market anomaly. Because the returns of alternative risk premia exhibit heterogeneous patterns in terms of statistical properties, option profile and drawdown, asset allocation is more complex than with traditional risk premia. In this context, risk diversification cannot be reduced to volatility diversification and skewness risk becomes a key component of portfolio optimization. Understanding these different concepts and how they interconnect is essential for improving multi-asset allocation.

In this study, I implement a novel methodology to extract crash risk premia from options and stock markets. I document a dramatic increase in crash risk premia after the 2008/2009 financial crisis, indicating that investors are willing to pay high insurance to hedge against crashes in individual stocks. My results apply to all sectors but are most pronounced for the financial sector. At the same time, crash risk premia on the market index remained at pre-crisis levels. I theoretically explain this puzzling feature in an economy where investors face short-sale constraints. Under short-sale constraints, prices are less informationally efficient which can explain the increase in downside risk in individual stocks. In the data, I document a strong link between proxies of short-sale constraints and crash risk premia.

Intuition suggests that constraint investment strategies will result in losses due to a limited portfolio allocation. Two types of constrained assets have been particularly growing over the last few decades: Islamic Mutual Funds and Socially Responsible Mutual Funds. Although research regarding the performance of these types of constrained investments has been performed, little attention has been given to their relative performance. In this paper we assess, and rank, the relative performance of Islamic, Socially Responsible, and conventional mutual funds from 11 Islamic markets and the United States by expanding the traditional mean-variance frontier to account for higher moments; constrained assets tend to be smaller and skewed in nature, thus violating the normality assumption under the mean-variance frontier. We find that controlling for skewness risk, by using an unconditional coskewness measure, has the power to improve asset pricing tests by expanding the mean-variance frontier specification. We find supporting evidence suggesting that Islamic mutual funds perform better than Socially Responsible Investing, which in turn outperform conventional mutual funds.

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).

We use a sample of option prices, and the method of Bakshi, Kapadia and Madan (2003), to estimate the ex ante higher moments of the underlying individual securities’ risk-neutral returns distribution. We find that individual securities’ volatility, skewness and kurtosis are strongly related to subsequent returns. Specifically, we find a negative relation between volatility and returns in the cross-section. We also find a significant relation between skewness and returns, with more negatively (positively) skewed returns associated with subsequent higher (lower) returns, while kurtosis is positively related to subsequent returns. To analyze the extent to which these returns relations represent compensation for risk, we use data on index options and the underlying index to estimate the stochastic discount factor over the 1996-2005 sample period, and allow the stochastic discount factor to include higher moments. We find evidence that, even after controlling for differences in co-moments, individual securities’ skewness matters. However, when we combine information in the risk-neutral distribution and the stochastic discount factor to estimate the implied physical distribution of industry returns, we find little evidence that the distribution of technology stocks was positively skewed during the bubble period–in fact, these stocks have the lowest skew, and the highest estimated Sharpe ratio, of all stocks in our sample.

The cross section of stock returns has substantial exposure to risk captured by higher moments of market returns. We estimate these moments from daily Standard & Poor's 500 index option data. The resulting time series of factors are genuinely conditional and forward-looking. Stocks with high exposure to innovations in implied market skewness exhibit low returns on average. The results are robust to various permutations of the empirical setup. The market skewness risk premium is statistically and economically significant and cannot be explained by other common risk factors such as the market excess return or the size, book-to-market, momentum, and market volatility factors, or by firm characteristics.

This paper explores the impacts of a water right's allocative priority—as an indicator of farmers' risk‐bearing ability—on land irrigation under water supply uncertainty. We develop and use an economic model to simulate farmers' land irrigation decision and associated economic returns in eastern Idaho. Results indicate that the optimal acreage of land irrigated increases with water right priority when hydroclimate risk exhibits a negatively skewed or right‐truncated distribution. Simulation results suggest that prior appropriation enables senior water rights holders to allocate a higher proportion of their land to irrigation, 6 times as much as junior rights holders do, creating a gap in the annual expected net revenue reaching up to $141.4 acre−1 or $55,800 per farm between the two groups. The optimal irrigated acreage, expected net revenue, and shadow value of a water right's priority are subject to substantial changes under a changing climate in the future, where temporal variation in water supply risks significantly affects the profitability of agricultural land use under the priority‐based water sharing mechanism., Key Points Develops a theoretical framework to explicitly model the influence of water institution on a farmer's land irrigation decision under water supply uncertaintyThe optimal acreage of land irrigated increases with a water right's priority when water supply uncertainty exhibits a left‐skewed or right‐truncated distributionSignificant differences exist in agricultural productivity between senior and junior water right holders

The shape of the volatility smirk has significant cross-sectional predictive power for future equity returns. Stocks exhibiting the steepest smirks in their traded options underperform stocks with the least pronounced volatility smirks in their options by 10.9% per year on a risk-adjusted basis. This predictability persists for at least 6 months, and firms with the steepest volatility smirks are those experiencing the worst earnings shocks in the following quarter. The results are consistent with the notion that informed traders with negative news prefer to trade out-of-the-money put options, and that the equity market is slow in incorporating the information embedded in volatility smirks.

This article examines the role of nonnormality risks in explaining the momentum puzzle of equity returns. It shows that momentum profits are not normally distributed and, relatedly, that the momentum profitability is partly a compensation for systematic negative skewness risk in line with market efficiency. This finding is pervasive across nine trading strategies that combine different holding and ranking periods and is reinforced when time dependencies in abnormal returns and risks are explicitly modelled. The analysis also reveals that the market and skewness risks of momentum portfolios evolve over the business cycle in a manner that is consistent with market timing and risk aversion. While nonnormality risks matter, a large proportion of the momentum profits remains unexplained which may provide comfort to behavioural theorists.

The concept of alternative risk premia can be viewed as an extension of the factor investing approach. Factor investing is a term that is generally dedicated to long-only equity risk factors. A typical example is the value equity strategy. Alternative risk premia designate non-traditional risk premia other than long exposure to equities and bonds. They may concern equities, rates, credit, currencies or commodities and correspond to long/short portfolios. For instance, the value strategy can be extended to credit, currencies and commodities. This paper provides an overview of the different alternative risk premia to be found in the academic and professional spheres. Using a database of commercial indices, we estimate the generic cumulative returns of 59 alternative risk premia in order to analyze their risk, diversification power and payoff function. From this, it is clear that the term "alternative risk premia" encompasses two different types of risk factor: skewness risk premia and market anomalies. We then reconsider portfolio allocation in light of this framework. Indeed, we show that skewness aggregation is considerably more complex than volatility aggregation, and we illustrate that the volatility risk measure is less appropriate and pertinent when managing a portfolio with these risk premia. The development of alternative risk premia shall also affect the risk/return analysis of non-linear strategies, e.g. hedge fund strategies. In particular, using alternative risk factors instead of traditional risk factors leads to an extension of the alternative beta framework. Therefore, we apply the previously estimated risk premia to a universe of hedge fund indices. To that end, we develop a model selection based on the lasso regression to identify the most pertinent risk premia for each hedge fund strategy. It appears that many traditional risk factors, with the exception of long equity and credit exposure on developed markets, vanish when we include alternative risk premia.

The carry trade is a zero net investment strategy that borrows in low yielding currencies and subsequently invests in high yielding currencies. It has been identified as highly profitable FX strategy delivering significantly excess returns with high Sharpe ratios. This paper shows that these excess returns are especially compensation for bearing FX variance and negative skewness risk. Additionally, factor risks that affect foreign money changes, foreign inflation changes, as well as changes to a newly developed Carry Trade Activity Index and the VIX index, as a proxy for global risk aversion, make up the carry trade risk anatomy. These findings are not exclusively important for carry traders, but also contribute to the understanding of currency risk in the cross-section. This is directly linked to asset pricing tests from Lustig et al. (2011), which have shown that currency baskets sorted on their interest rate differentials are all exposed to carry trade returns as a risk factor. Furthermore, this paper finds evidence that a decreased level of funding liquidity potentially leads to carry trade unwindings, controlling for equity and FX implied variance and skewness effects, which supports the theoretical model of liquidity spirals developed by Brunnermeier and Pedersen (2009).

This article presents an economic model to examine optimal irrigated land allocation, water rights, and probability distribution of system risk in irrigation water supply. Results indicate that the allocative priority of water rights affects farmers’ irrigation decisions and the skewness of the distribution of the system risk is the key parameter to determine this impact. The optimal acreage of irrigated land increases with the level of the allocative priority when the system risk features a negatively skewed distribution. A higher degree of negative skewness increases divergence in farm income between senior and junior water users and consequently increases the shadow value of the allocative priority.

This paper examines the relationship between currency option's implied skewness and its future realized skewness, where the difference is known as the skewness risk premium (SRP). The SRP indicates whether investors pay a premium to be insured against future crash risk. Past investigations about implied and realized skewness within currency markets showed that both measures are loosely connected or even exhibit a negative relationship that cannot be rationalized by no-arbitrage arguments. Therefore, this paper studies time-series of future and option contract positions data in order to explain the disconnection in terms of investor's position-induced demand pressure. While demand pressures on options do not sufficiently contribute to the disconnection, there is evidence that, surprisingly, demand pressure in currency future markets have the power to explain this market anomaly. Furthermore, currency momentum also plays an important role, which leads to a strong cyclical demand for OTM calls in rising or OTM puts in declining markets. In order to exploit the disconnection of skewness, a simple skew swap trading strategy proposed by Schneider (2012) has been set up. The resulting skew swap returns are relatively high, but the return distribution is extremely fat-tailed. To appropriately compare different skew swap strategy returns, this paper proposes a Higher Moment Sharpe Ratio that also takes higher moments into account.

We examine the impact of default risk on the market skewness risk effect that stocks with low market skewness risk outperform stocks with high risk documented in the previous literature. We find that the effect is strong among large, growth, and low default risk stocks, but vanishes among small, value, and high default risk stocks due to investors’ greater demand for hedging against downside risk. Our results suggest that the positive skewness preference theory is contradicted by investors’ hedging demand for high default risk stocks. The hedging hypothesis is also supported in a sample period after the 2007-2008 financial crisis.

This article develops a model that takes into account skewness risk in risk parity portfolios. In this framework, asset returns are viewed as stochastic processes with jumps or random variables generated by a Gaussian mixture distribution. This dual representation allows us to show that skewness and jump risks are equivalent. As the mixture representation is simple, we obtain analytical formulas for computing asset risk contributions of a given portfolio. Therefore, we define risk budgeting portfolios and derive existence and uniqueness conditions. We then apply our model to the equity/bond/volatility asset mix policy. When assets exhibit jump risks like the short volatility strategy, we show that skewness-based risk parity portfolios produce better allocation than volatility-based risk parity portfolios. Finally, we illustrate how this model is suitable to manage the skewness risk of long-only equity factor portfolios and to allocate between alternative risk premia., 48 pages, 23 figures, 21 tables

This paper provides new insights in the skewness risk premium in the stock market. By building strategies which take position in the individual skewness of the constituents of the SP100, we show that the skewness risk premium becomes positive and significant for almost all the stocks after the 2007-2009 financial crisis. We find that this is due to a drastic increase (in absolute value) in the price of the skewness, while we do not find any significant change in the realised skewness of the returns. Consistently, we find that the shape of the average implied volatility smile across stocks becomes steeper after the crisis. Moreover, we find that this pre/post crisis structural change does not apply to the market skewness risk premium, computed as the skew premium of the index SP500.

We develop a one-period model of investor asset holdings where investors have heterogeneous preference for skewness. Introducing heterogeneous preference for skewness allows the model's investors, in equilibrium, to underdiversify. We find suppport for our model's three key implications using a dataset of 60,000 individual investor accounts. First, we document that the portfolio returns of underdiversified investors are substantially more positively skewed than those of diversified investors. Second, we show that the apparent mean-variance inefficiency of underdiversified investors can be largely explained by the fact that investors sacrifice mean-variance efficiency for higher skewness exposure. Furthermore, contrary to the asset-pricing predictions of models that incorporate return skewness in the context of full diversification, we show that idiosyncratic skewness, and not just coskewness, can impact equilibrium prices. Third, the underdiversification of investors does not appear to be coincidentally related to skewness. Stocks most often selected by underdiversified investors have substantially higher average skewness -- especially idiosyncratic skewness -- than stocks most often selected by diversified investors.

Most of existing portfolio models only considered the financial risk or the financial return, and ignored any other risks or any other incomes, such as the skewness or kurtosis characteristics of the portfolio. In this paper, we propose a high moment multi-objective portfolio selection model based on background risk and corporate social responsibility (CSR). Then, we deduce the analytical solution of the portfolio model with the skewness risk and the kurtosis risk, when the risk asset and the financial return of background risk are random numbers. Finally, a numerical example is given based on the Shanghai Stock Exchange data and the Shenzhen Stock Exchange data.

The role of decision support systems in mitigating operational risks in firms is well established. However, there is a lack of investment in decision support systems in emerging markets, even though inadequate operational risk management is a key cause of discouraging external investment. This has also been exacerbated by insufficient understanding of operational risk in emerging markets, which can be attributed to past operational risk measurement techniques, limited studies on emerging markets and inadequate data. In this paper, using current operational risk techniques, the operational risk of developed and emerging market firms is measured for 100 different companies, for 4 different industry sectors and 5 different countries. Firstly, it is found that operational risk is consistently higher in emerging market firms than in the developed markets. Secondly, it is found that operational risk is not only dependent upon the industry sector but also that market development is the more dominant factor. Thirdly, it is found that the market development and the sector influence the shape of the operational risk distribution, in particular tail and skewness risk. Furthermore, an operational risk measurement method is provided that is applicable to emerging markets. Our results are consistent with under investment in decision support systems in emerging markets and imply operational risk management can be improved by increased investment.

This study formalizes the departure between risk-neutral and physical index return volatilities, termed volatility spreads. Theoretically, the departure between risk-neutral and physical index volatility is connected to the higher-order physical return moments and the parameters of the pricing kernel process. This theory predicts positive volatility spreads when investors are risk averse, and when the physical index distribution is negatively skewed and leptokurtic. Our empirical evidence is supportive of the theoretical implications of risk aversion, exposure to tail events, and fatter left-tails of the physical index distribution in markets where volatility is traded.