Portfolio selection with a systematic skewness constraint

This paper investigates portfolio selection within a mean-variance-systematic skewness framework. We derive the composition of efficient portfolios in our model, and analyze the properties of these efficient portfolios. We show that the required systematic skewness is achieved at the expense of traditional mean-variance efficiency, and that a more stringent systematic skewness constraint induces a greater loss in mean-variance efficiency. Our numerical analysis demonstrates that the presence of the systematic skewness constraint helps improve the skewness of efficient portfolios in our model over the skewness of traditional efficient portfolios.     

Assessing skewness in financial markets

It is a matter of common observation that investors value substantial gains but are averse to heavy losses. Obvious as it may sound, this translates into an interesting preference for right-skewed return distributions, whose right tails are heavier than their left tails. Skewness is thus not only a way to describe the shape of a distribution, but also a tool for risk measurement. We review the statistical literature on skewness and provide a comprehensive framework for its assessment. Then, we present a new measure of skewness, based on the decomposition of variance in its upward and downward components. We argue that this measure fills a gap in the literature and show in a simulation study that it strikes a good balance between robustness and sensitivity.     

Skewness preference,mean–variance and the demand for put options

This paper compares the mean–variance and the mean–variance–skewness approaches to modelling expected utility. Attention is focused on a problem encountered in risk management: determining the optimal demand for a put option hedging the return on an asset with a negatively skewed return distribution. It is demonstrated theoretically that incorporating positive skewness preference into the decision‐maker's objective function typically produces a reduction in the demand for put options when compared with the mean–variance solution. A state‐dependent example is provided to illustrate how a mean–variance–skewness objective can result in a significant reduction in the optimal amount of crop insurance demanded when compared with the mean–variance solution. Copyright © 1999 John Wiley & Sons, Ltd.     

Extreme risk transmission channels between the stock index futures and spot markets: Evidence from China

We develop a skewness-dependent multivariate conditional autoregressive value at risk model (SDMV-CAViaR) to detect the extreme risk transmission channels between the Chinese stock index futures and spot markets. The proposed SDMV-CAViaR model improves the forecast performance of extreme risk by introducing the high-frequency realized skewness. Specifically, the realized skewness has a significant impact on the spillovers, but the realized volatility and realized kurtosis do not, which implies that the jump component plays an important role in extreme risk spillovers. The empirical results indicate there are bidirectional extreme risk spillovers between the stock index futures and spot markets, the decline of one market has direct and indirect channels to exacerbate the extreme risk of the other market. Firstly, the market decline will directly increase the extreme risk of related markets by decreasing market returns. Besides, the decline will indirectly increase the extreme risk by increasing the negative realized skewness and extreme risk spillovers.     

Priced risk and asymmetric volatility in the cross section of skewness

We investigate the sources of skewness in aggregate risk factors and the cross section of stock returns. In an ICAPM setting with conditional volatility, we find theoretical time series predictions on the relationships among volatility, returns, and skewness for priced risk factors. Market returns resemble these predictions; however, size, book-to-market, and momentum factor returns are not always consistent with our predictions. We find evidence that size and book-to-market may be priced post-crisis but not in the decade before. Momentum does not appear priced by our test. We link aggregate risk and skewness to individual stocks and find empirically that the risk aversion effect manifests in individual stock skewness. Additionally, we find several firm characteristics that explain stock skewness. Smaller firms, value firms, highly levered firms, and firms with poor credit ratings have more positive skewness.     

Limited attention,salient anchor,and the modified MAX effect: Evidence from Taiwan’s stock market

The literature documents that investors overweighing the right-tail probability pursue positively skewed assets, leading to lottery-like stocks overpriced. We find that the lottery anomaly primarily exists among stocks further away from their 52-week high prices. After attention-grabbing events with gambling features, inattentive retail investors become aware of certain stocks’ gambling traits and then net buy more lottery-like stocks, which further promotes the lottery anomaly. However, when such stocks are near their 52-week high price, retail investors tend to place little weight on the likelihood that the stock price will rise beyond the 52-week high, thereby reducing the skewness preference. Overall, our findings suggest that the perception of the 52-week high price as a price ceiling influences skewness preference, and that investor attention is the main determinant of whether anchoring bias affects skewness preference.     

Menu-dependent self-control

The literature on self-control problems has typically put forth models that imply behavior that is consistent with the weak axiom of revealed preference (WARP). We argue that when choice is the outcome of some underlying internal conflict, the resulting choices may not be perfectly consistent across choice problems: an agent’s ability to resist temptation may well depend on what alternatives are available to him. We generalize Gul and Pesendorfer (2001) so that self-control weakens in the presence of temptation. To model choices from menus explicitly, we consider a choice correspondence as well as a preference over menus and relax both the Independence axiom for the preference and the WARP condition for the choice correspondence. The model is shown to unify a range of well-known findings in the experimental literature on choice under risk and over time within a single specification.     

Skewness Risk and Bond Prices

This paper uses extreme value theory to study the implications of skewness risk for nominal loan contracts in a production economy. Productivity and inflation innovations are drawn from generalized extreme value distributions. The model is solved using a third‐order perturbation and estimated by the simulated method of moments. Results show that the data reject the hypothesis that innovations are drawn from normal distributions and favor instead the alternative that they are drawn from asymmetric distributions. Estimates indicate that skewness risk accounts for 12% of the risk premia and reduces bond yields by approximately 55 basis points. For a bond that pays 1 dollar at maturity, the adjustment factor associated with skewness risk ranges from 0.15 cents for a 3‐month bond to 2.05 cents for a 5‐year bond. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling time-varying higher-order conditional moments: A survey

Since the introduction of the Autoregressive Conditional Heteroscedasticity (ARCH) model, the literature on modeling the time-varying second-order conditional moment has become increasingly popular in the last four decades. Its popularity is partly due to its success in capturing volatility in financial time series, which is useful for modeling and predicting risk for financial assets. A natural extension of this is to model time variation in higher-order conditional moments, such as the third and fourth moments, which are related to skewness and kurtosis (tail risk). This leads to an emerging literature on time-varying higher-order conditional moments in the last two decades. This paper outlines recent developments in modeling time-varying higher-order conditional moments in the economics and finance literature. Using the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) framework as a foundation, this paper provides an overview of the two most common approaches for modeling time-varying higher-order conditional moments: autoregressive conditional density (ARCD) and autoregressive conditional moment (ARCM). The discussion covers both the theoretical and empirical aspects of the literature. This includes the identification of the associated skewness–kurtosis domain by using the solutions to the classical moment problems, the structural and statistical properties of the models used to model the higher-order conditional moments and the computational challenges in estimating these models. We also advocate the use of a maximum entropy density (MED) as an alternative method, which circumvents some of the issues prevalent in these common approaches.     

Factor pricing of cryptocurrencies

In this paper, we study the cryptocurrency pricing factors. We review the literatures which state that the cryptocurrency market is weakly efficient. We use the Fama–MacBeth method to investigate the pricing factors. The classical equity-based risk factors including size, momentum, and value to growth from the Fama–French three factor model are studied. We use crypto-unique coin-to-token as a proxy for value-to-growth. For volatility risk factor category, we investigate realized volatility, skewness and jump. We also investigate liquidity factors including bid–ask, volume growth and Roll’s measure. The macro factors are found not to be an explanatory factor. The attention factor works sometimes. The factor model constructed by the significant factors explain most of the excess return of cryptocurrencies.     

Liquidity skewness premium

Risk-averse investors may dislike decrease of liquidity rather than increase of liquidity, and thus there can be asymmetric preference in variation of liquidity. In addition, investors are likely to avoid extreme illiquidity. This paper examines whether the skewness of an individual firm’s liquidity capturing asymmetric distribution of liquidity and extreme illiquidity is priced in the US stock market. Using the skewness of the daily price impact, we find that it is positively priced, and this positive relation is significant up to eight months after controlling for other effects. Moreover, we find our results remain significant with the skewness of alternative liquidity measures, i.e., dollar-volume, and turnover.     

An analysis of the capital asset pricing model in the Egyptian stock market

This paper offers evidence confirming the validity of applying modern portfolio theory and capital asset pricing models to the emerging stock market of Egypt. The results indicate that market risk, as measured by beta and preference for skewness, seems to play a significant role in the returns dynamics in the Egyptian stock market. There is a significant and positive premium for companies with positive skewness. With regard to the return-risk trade off, the results indicate that a portfolio that was based on consumer staples and financial companies (mainly banks) with low betas had outperformed a portfolio containing construction, materials, hotels, and weaving companies with larger betas. Historically, the government's nationalizations that took place, between the mid fifties to the mid sixties, had adversely affected companies in the industrial and construction sectors more than consumer staples companies and banks. This could explain why lower beta companies were observed more in consumer staples, banks, and pharmaceuticals.     

The ‘wrong skewness’ problem: a re-specification of stochastic frontiers

In this paper, we study the ‘wrong skewness phenomenon’ in stochastic frontiers (SF), which consists in the observed difference between the expected and estimated sign of the asymmetry of the composite error, and causes the ‘wrong skewness problem’, for which the estimated inefficiency in the whole industry is zero. We propose a more general and flexible specification of the SF model, introducing dependences between the two error components and asymmetry (positive or negative) of the random error. This re-specification allows us to decompose the third moment of the composite error into three components, namely: (i) the asymmetry of the inefficiency term; (ii) the asymmetry of the random error; and (iii) the structure of dependence between the error components. This decomposition suggests that the wrong skewness anomaly is an ill-posed problem, because we cannot establish ex ante the expected sign of the asymmetry of the composite error. We report a relevant special case that allows us to estimate the three components of the asymmetry of the composite error and, consequently, to interpret the estimated sign. We present two empirical applications. In the first dataset, where the classic SF has the wrong skewness, an estimation of our model rejects the dependence hypothesis, but accepts the asymmetry of the random error, thus justifying the sign of the skewness of the composite error. More importantly, we estimate a non-zero inefficiency, thus solving the wrong skewness problem. In the second dataset, where the classic SF does not yield any anomaly, an estimation of our model provides evidence for the presence of dependence. In such situations, we show that there is a remarkable difference in the efficiency distribution between the classic SF and our class of models.     

Time-varying higher-order conditional moments and forecasting intraday VaR and Expected Shortfall

We estimate several GARCH- and Extreme Value Theory (EVT)-based models to forecast intraday Value-at-Risk (VaR) and Expected Shortfall (ES) for S&P 500 stock index futures returns for both long and short positions. Among the GARCH-based models we consider is the so-called Autoregressive Conditional Density (ARCD) model, which allows time-variation in higher-order conditional moments. ARCD model with time-varying conditional skewness parameter has the best in-sample fit among the GARCH-based models. The EVT-based model and the GARCH-based models which take conditional skewness and kurtosis (time-varying or otherwise) into account provide accurate VaR forecasts. ARCD model with time-varying conditional skewness parameter seems to provide the most accurate ES forecasts.     

On compensation for risk aversion and skewness affection in wages

This paper presents extensive empirical testing of the hypothesis that greater post-schooling earnings risk requires higher expected returns. Expanding on this notion, on the basis of utility theory, we predict that workers not only care about risk but also about the skewness in the distribution of the compensation paid: workers exhibit risk aversion and skewness affection. To test these hypotheses, this paper carefully develops various measures of risk and skewness by occupational/educational classification of the worker and finds supportive evidence: for men, wages rise with occupational earnings variance and decrease with skewness, for women only the negative effect of skewness is significant.     

Unlevered betas and the cost of equity capital: An empirical approach

The present paper calculates the systematic risk within the context of the capital asset pricing model to investigate the significance of financial leverage on systematic risk. Rather than testing the unlevered beta directly, we develop a multinomial model with theoretically predicted targets in the unleveraged/leveraged process. We find that including tax shields in this process is statistically more robust than omitting them. Our results also suggest that the use of the proxy levered beta to address the lack of market information for both non-traded firms and individual business units is not misleading.     

Complementary information for skewness measures

This paper introduces some new elements to measure the skewness of a probability distribution, suggesting that a given distribution can have both positive and negative skewness, depending on the centred sub‐interval of the support set being observed. A skewness function for positive reals is defined, from which a bivariate index of positive–negative skewness is obtained. Certain interesting properties of this new index are studied, and they are also obtained for some common discrete distributions. We show the advantages of their use as a complement to the information derived by traditional measures of skewness.     

Risk preference heterogeneity in group contests

We analyze the first model of a group contest with players that are heterogeneous in their risk preferences. In our model, individuals’ preferences are represented by a utility function exhibiting a generalized form of constant absolute risk aversion, allowing us to consider any combination of risk-averse, risk-neutral, and risk-loving players. We begin by proving equilibrium existence and uniqueness under both linear and convex investment costs. Then, we explore how the sorting of a compatible set of players by their risk attitudes into competing groups affects aggregate investment. With linear costs, a balanced sorting (i.e., minimizing the variance in risk attitudes across groups) always produces an aggregate investment level that is at least as high as an unbalanced sorting (i.e., maximizing the variance in risk attitudes across groups). Under convex costs, however, identifying which sorting is optimal is more nuanced and depends on preference and cost parameters.     

Regional variation in productivity: a study of the Danish economy

We develop a model of labor productivity as a combination of capital-labour ratio, vintage of capital stock, regional externalities, and total factor productivity (TFP). The skewness of TFP distribution is related to different growth theories. While negative skewness is consistent with the neo-Schumpeterian idea of catching up with leaders, zero skewness supports the neoclassical view that deviations from the frontier reflect only idiosyncratic productivity shocks. We argue that positive skewness is consistent with an economy where exogenous technology is combined with non-transferable knowledge accumulated in specific sectors and regions. This argument provides the framework for an empirical model based on stochastic frontier analysis. The model is used to analyse regional and sectoral inequalities in Denmark.

Dynamic interaction of risk–return trade-offs between oil market and China’s stock market: An analysis from the risk preferences perspective

The risk–return trade-off refers to the compensation required by investors for bearing risks, which can be viewed as the risk preference of investors in a market. The current study investigates the dynamic interdependence of risk–return trade-offs between China’s stock market and the crude oil market from the perspective of risk preference of investors, which is designed to explore the transmission process of investors’ risk preference in both markets. Specifically, this study applies the time-varying parameter GARCH-M model, namely TVP-GARCH-M model, to characterize the time-dependent risk–return trade-offs (investors’ risk preferences) in the crude oil and China’s stock markets, then examines their relationship through Granger causality tests. Results show that a variation in risk preferences of the oil market investors can dramatically cause a variation in risk preferences of the Chinese stock market investors, while the risk preference of investors in the Chinese stock market does not lead to that in the crude oil market, which is in accordance with expectations. The dynamic effect of investors’ risk appetite in the crude oil market is further examined by the TVP-VAR model. The findings of this work suggest that there generally exists a positive impact of investors’ risk preference in the oil market and that the effect is time-varying to a greater degree during the short and medium term. Moreover, responses of the Chinese stock market investors’ risk preference were more significant during the 2008 financial crisis. Additionally, the empirical results remain robust when applying alternative crude oil prices and China’s stock prices.