COMMENT ON “SKEWNESS‐AWARE ASSET ALLOCATION”

This paper discusses risk measures proposed by Low et al. One of their new risk measures is skewness‐aware deviation, which is closely related to constant absolute risk aversion utility functions. This measure captures downside risk more effectively than traditional variance does. The authors also propose a second measure, skewness‐aware variance, which is derived from skewness‐aware deviation. This measure simplifies asset allocation problems and empirical results indicate that it captures risk better than traditional variance. However, this measure is also found to be inconsistent due to factor selection. Additionally, in the aspect of skewness‐aware deviation, optimal portfolios based upon skewness‐aware variance are sometimes less efficient than optimal portfolios that base themselves on traditional variance.     

Portfolio selection with skewness in emerging market industries

In the presence of skewness, portfolio selection requires to consider competing and conflicting objectives. We utilize polynomial goal programming to determine the optimal portfolio from emerging markets industries. This paper is concerned with an industry level analysis of the effects of portfolio selection when the skewness is taken into account. We have found that the incorporation of skewness into an investor's portfolio decision provokes a great change in the resulting optimal portfolio allocation. This evidence suggests that individuals trade expected return for skewness.     

进口竞争与企业产品专业化--基于中国多产品企业的研究

本文以企业内部资源配置为视角,检验了进口竞争对企业内部产品专业化的影响。研究发现,进口竞争显著地促进了中国企业的产品专业化程度。进口竞争的加剧促使企业缩小产品生产范围,使其将资源集中到少数核心产品的专业化生产和销售上来。这一过程伴随着企业产品种类的减少和企业整体产品范围偏度的集中。本文利用中国对外反倾销冲击作为进口竞争程度下降的拟自然实验,考察了企业是否受反倾销保护对其产品专业化程度影响的因果效应。进一步的异质性检验表明,相比加工贸易而言,一般贸易产生的进口竞争对企业产品专业化的促进作用更大;相比低收入国家而言,来自高收入国家的进口竞争对企业产品专业化的促进作用更大。本研究对如何理解进口竞争对中国经济发展的影响,提供了来自企业内部产品配置的证据。     

Average skewness in global equity markets

This paper examines the predictive power of average skewness, defined as the average of monthly skewness values across stocks, documented by the prior literature for US market returns in an international setting. First, we confirm the validity of the results in the original study and show that the intertemporal relation between average skewness and aggregate returns becomes weaker in an alternative sample period. Second, when we repeat the analysis in 22 developed non-US markets, we find that average skewness has no robust predictive power for future market returns. The loss of forecasting power in the international sample does not depend on the method used to calculate average skewness or the regression specification and is supported by additional out-of-sample tests and subsample analysis.     

Can skewness of the futures-spot basis predict currency spot returns?

This paper examines the relationship between skewness of the futures-spot basis and expected currency spot returns. The empirical results show that the expected spot returns are negatively correlated with the basis skewness. We find that the basis skewness exhibits statistically significant in-sample and out-of-sample forecasting power. Furthermore, the basis skewness beat the random walk (without drift) in economic measures. The impacts of the basis skewness on spot returns barely vary with time and have no structural breaks. We also find that the basis skewness can really improve the predictability of spot returns, even when the futures-spot basis is considered.     

The impact of skewness in the hedging decision

The impact of skewness in the hedger's objective function is tested using a model of hedging derived from a third‐order Taylor Series approximation of expected utility. To determine the effect of price skewness upon hedging and speculation, analytical results are derived using an example of cotton storage. Findings suggest that when forward risk premiums and price skewness in the spot asset have opposite signs, speculation increases relative to the mean‐variance model. When the signs are identical, speculation will decrease, contradicting findings of mean‐variance models. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:503–520, 2006     

Morphology of asset asymmetry

Although many financial paradigms are predicted on the assumption that security returns are symmetrically distributed, relatively little research has been conducted into the legitimacy of the presumption. This effort is intended to present the results of a thorough investigation of the subject, where two measures of skewness have been computed and compared. Roughly, the major conclusion is that regardless of how skewness is measured, securities have displayed a persistent propensity to positive asymmetry during the last three decades, although the evidence is less unambiguous when evaluated over the last 50 years.     

The Relation between Physical and Risk‐neutral Cumulants

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.     

Hedging and value at risk: A semi‐parametric approach

The non‐normality of financial asset returns has important implications for hedging. In particular, in contrast with the unambiguous effect that minimum‐variance hedging has on the standard deviation, it can actually increase the negative skewness and kurtosis of hedge portfolio returns. Thus, the reduction in Value at Risk (VaR) and Conditional Value at Risk (CVaR) that minimum‐variance hedging generates can be significantly lower than the reduction in standard deviation. In this study, we provide a new, semi‐parametric method of estimating minimum‐VaR and minimum‐CVaR hedge ratios based on the Cornish‐Fisher expansion of the quantile of the hedged portfolio return distribution. Using spot and futures returns for the FTSE 100, FTSE 250, and FTSE Small Cap equity indices, the Euro/US Dollar exchange rate, and Brent crude oil, we find that the semiparametric approach is superior to the standard minimum‐variance approach, and to the nonparametric approach of Harris and Shen (2006). In particular, it provides a greater reduction in both negative skewness and excess kurtosis, and consequently generates hedge portfolios that in most cases have lower VaR and CVaR. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:780–794, 2010     

Optimal pricing, production rate, and quality under learning effects

This study investigates the marketing and production problem for a monopolist firm where price, quality and production rate are simultaneous dynamic decision variables under the condition of a dynamic demand that depends on price, quality and cumulative sales. The formulated continuous profit maximization model follows the steps for dynamic optimization to derive optimal price, quality and production policies, wherein a unit production cost that decreases with cumulative production reflects the cost learning effect. Through the differentiable multiplicatively separable demand function, this study analyzes optimal trajectories for determining price, quality, and production rate. The results specify several optimal policies and policy makers would gain insight into the consequence of their decisions that otherwise might have been obscured by sub-optimal analysis.     

The economic significance of conditional skewness in index option markets

This study examines whether conditional skewness forecasts of the underlying asset returns can be used to trade profitably in the index options market. The results indicate that a more general skewness‐based option‐pricing model can generate better trading performance for strip and strap trades. The results show that conditional skewness model forecasts, when combined with forward‐looking option implied volatilities, can significantly improve the performance of skewness‐based trades but trading costs considerably weaken the profitability of index option strategies. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:378–406, 2010     

多哈回合分层公式对中国农产品税率分布的影响效应分析

在新一轮多哈回合农产品谈判中,关税削减是市场准入部分的核心议题,本文在《中华人民共和国进出口税则》(2006)的基础上模拟了5个主要的分层削减公式对中国农产品税率分布的影响。采用了均值、中位数、众数、标准差系数、极大值、偏度系数和峰度系数衡量削减效果。模拟结果显示,G20模拟方案(三)和美国模拟方案的降税幅度较大,而G10模拟方案和G20模拟方案(一)的降税幅度较小,后者对中国农业带来的冲击相对较弱。     

Ability parity model for optimal fund allocation: Evidence from China's mutual fund markets

We propose in this article a novel ability parity model for optimal fund allocation. Compared with the traditional portfolio selection methods which directly work on asset returns and/or risk (volatility), the proposed ability parity method focuses mainly on the allocation between the stock selection ability and market timing ability of fund managers, which essentially determines fund performance (Fama, 1972). Using the data of China's mutual fund markets, we find strong and robust evidence that the proposed ability parity model delivers significantly higher return, skewness, and Sharpe ratio than traditional models and the benchmark index, while having volatilities comparable with traditional models.     

Skewness and index futures return

In this paper, we show that the individual skewness, defined as the average of monthly skewness across firms, performs very well at predicting the return of S&P 500 index futures. This result holds after controlling for the liquidity risk or for the current business cycle conditions. We also find that individual skewness performs very well at predicting index futures returns out-of-sample.     

Option pricing under extended normal distribution

This article proposes a closed pricing formula for European options when the return of the underlying asset follows extended normal distribution, that is, any different degrees of skewness and kurtosis relative to the normal distribution induced by the Black‐Scholes model. The moment restriction is suggested, so that the pricing model under any arbitrary distribution for an underlying asset must satisfy the arbitrage‐free condition. Numerical experiments and comparison of empirical performance of the proposed model with the Black‐Scholes, ad hoc Black‐Scholes, and Gram‐Charlier distribution models are carried out. In particular, an estimation of implied parameters such as standard deviation, skewness, and kurtosis of the return on the underlying asset from the market prices of the KOSPI 200 index options is made, and in‐sample and out‐of‐sample tests are performed. These results not only support the previous finding that the actual density of the underlying asset shows skewness to the left and high peaks, but also demonstrate that the present model has good explanatory power for option prices. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:845–871, 2005     

SKEWNESS‐AWARE ASSET ALLOCATION: A NEW THEORETICAL FRAMEWORK AND EMPIRICAL EVIDENCE

This paper presents a new measure of skewness, skewness‐aware deviation, that can be linked to prospective satisficing risk measures and tail risk measures such as Value‐at‐Risk. We show that this measure of skewness arises naturally also when one thinks of maximizing the certainty equivalent for an investor with a negative exponential utility function, thus bringing together the mean‐risk, expected utility, and prospective satisficing measures frameworks for an important class of investor preferences. We generalize the idea of variance and covariance in the new skewness‐aware asset pricing and allocation framework. We show via computational experiments that the proposed approach results in improved and intuitively appealing asset allocation when returns follow real‐world or simulated skewed distributions. We also suggest a skewness‐aware equivalent of the classical Capital Asset Pricing Model beta, and study its consistency with the observed behavior of the stocks traded at the NYSE between 1963 and 2006.     

A symmetric LPM model for heuristic mean-semivariance analysis

While the semivariance (lower partial moment degree 2) has been variously described as being more in line with investors’ attitude towards risk, implementation in a forecasting portfolio management role has been hampered by computational problems. The original formulation by Markowitz (1959) requires a laborious iterative process because the cosemivariance matrix is endogenous and a closed form solution does not exist. There have been attempts at optimizing an exogenous asymmetric cosemivariance matrix. However, this approach does not always provide a positive semi-definite matrix for which a closed form solution exists. We provide a proof that converts the exogenous asymmetric matrix to a symmetric matrix for which a closed form solution does exist. This approach allows the mean-semivariance formulation to be solved using Markowitz's critical line algorithm. Empirical results compare the cosemivariance algorithm to the covariance algorithm which is currently the best optimization proxy for the cosemivariance. We also compare our formulation to Estrada's (2008) cosemivariance formulation. The results demonstrate that the cosemivariance algorithm is robust to a 45 security universe and is still effective at increasing portfolio skewness at a 150 security universe. There are four major benefits to a usable mean-semivariance formulation: (1) managers may engineer skewness into the portfolio without resorting to option strategies, (2) managers will be able to evaluate the skewness effect of option strategies within their portfolio, (3) a workable mean-semivariance algorithm leads to a workable n-degree lower partial moment (LPM) algorithms which provides managers access to a wider variety of investor utility functions including risk averse, risk neutral, and risk seeking utility functions, and (4) a workable LPM algorithm leads to a workable UPM/LPM (upper partial moment/lower partial moment) algorithm.     

贝塔系数是风险的正确度量吗

在经典的投资组合理论中 ,假设所有资产的报酬率服从对数正态分布 ,因而只需要用收益的方差来度量风险就足够了 ,忽略了偏度的影响。资产收益的分布往往不是对称的 ,偏度是客观存在的 ,而且投资者具有正偏度的爱好。所以必须用方差和偏度来共同度量投资的风险 ,在这种情况下 ,贝塔系数不再是风险的正确度量 ,采用有效的修正方法 ,可以用来对资产进行正确的定价     

Reconciling quantile autoregressions of firm size and variance–size scaling

The aim of this paper is to understand what economic mechanisms may cause the Law of Proportionate Effect to break down for fast-growing and shrinking firms. Recent evidence has highlighted that the first-order coefficients of quantile auto-regression of firm size decline across quantiles. Our theoretical results show that negative variance–size scaling is sufficient to yield a decline in quantile auto-regression coefficients if firm log-size is Laplace-distributed, conditional on size one period ahead. However, it is sufficient only for declining auto-regression coefficients for fast-growing firms under Asymmetric Laplace conditional log-size if skewness is decreasing with size. In other words, if the growth of large firms is less dispersed and more left-skewed, size is a disadvantage for the growth of fast-growers, but not necessarily an advantage for fast-decliners. Thus, size-related determinants of negative growth skewness, such as diseconomies of growth, market power, and managerial attention issues, impact on how the LPE is violated. Using data on Dutch manufacturing companies from the Business Register of Enterprises observed between 1994 and 2004, our empirical estimates of quantile regression models confirm the evidence of declining quantile regression coefficients for small–medium firms (20–199 employees) mainly in the right-most quantiles, and for the same subsample, we find that growth rates variance and skewness are decreasing with size. The theoretical propositions of the paper are thus corroborated.     

基于偏度的多期证券投资组合模型研究

在考虑资产收益率分布中正的偏度水平前提下,以风险价值VaR为约束条件,并引入非线性交易费用、税收等市场摩擦因素,建立以累积偏度最大为目标函数的多期投资组合优化模型,用罚函数法和PSO算法结合求解此模型,并给出实证分析。考虑到在买卖资产风险时交易费用等对投资收益的影响,投资者应该在每一期都对其资产组合进行调整分析,确保在每一期的开始都建立起符合需要的最优资产组合,这对投资者的连续投资行为具有一定的指导意义。