Calculating Cumulants of a Taylor Expansion of a Multivariate Function

A method, which we believe is simpler and more transparent than the one due to McCullagh (1984) , is described for obtaining the cumulants of a scalar multivariate stochastic Taylor expansion. Its generalisation is also suggested. An important feature, previously not reported, is that the expansion of every cumulant of order ≥ 2 is made up of separate subseries.
In order to handle certain frequently occurring sums over permutations of members of compound index sets, we introduce a new notation  [ m ]_*,  where   m   is a positive integer.     

Mean reversion in annual earnings and its implications for security valuation

This article documents the long-horizon mean reverting character of annual earnings and tests the implications of such mean reversion for security valuation. First, both theory-based and nonparametric measures of earnings persistence decrease as the estimation order increases, revealing 40 percent less long-horizon persistence than expected under the commonly used random walk model. Second, the return responses to the earnings shocks are more closely related across firms to the higher-order measures of persistence that reflect significant long-horizon mean reversion. Third, the persistence measure derived from classical valuation theory outperforms the generic measure in explaining the return responses. Taken as a whole, these results provide evidence for significant mean reversion in the higher-order properties of earnings and for the stock market incorporating these properties in a manner consistent with classical valuation theory.     

Helping Disadvantaged Students: Findings from the Thuthuka Programme

Abstract

Drawing on social closure theory, this study achieved a deep understanding of the perceptions and experiences of the first cohort of candidates passing through the Thuthuka support programme. Using semi-structured interviews as part of a qualitative approach, currently prevalent modes of professional closure were considered by taking the backgrounds of these students into account, together with their perceptions of the accounting profession. Their views on whether the Thuthuka programme as an intervention had been successful in removing post-apartheid professional closure were determined by taking into account the Thuthuka students’ readiness to sit for professional examinations and to enter the workplace. The findings of the study suggest features that could be considered in support programmes intended for socio-economically disadvantaged students to facilitate their entry into a restrictive and restricted market.     

Leveraging the power of experiential learning to achieve higher-order proficiencies

Although experiential learning approaches, such as service-learning, have been shown to increase student motivation and academic achievement, faculty concerns about the costs of developing and implementing such courses have limited their adoption within economics. One cost that can be eliminated is the opportunity cost typically associated with “required” reflection exercises that are often perceived as taking time away from economic instruction. This article contributes to the existing literature by introducing a reflection mechanism based on programmatically appropriate project-management reports. This approach not only links experience and course content, essential elements of service-learning best-practice, but also facilitates the successful management of a complex project, thereby contributing to the development of higher-order proficiencies.     

Does country risks predict stock returns and volatility? Evidence from a nonparametric approach

We use the k-th order nonparametric causality test at monthly frequency over the period of 1984:1–2015:12 to analyze whether aggregate country risk, and its components (economic, financial and political) can predict movements in stock returns and volatility of eighty-three developed and developing economies. The nonparametric approach controls for the existing misspecification of a linear framework of causality, and hence, the weak evidence of causality obtained under the standard Granger tests cannot be relied upon. When we apply the nonparametric test, we find that, while there is no evidence of predictability of squared stock returns barring one case, at times, there are nearly 50 percent of the countries where the aggregate risks and its components tend to predict stock returns and realized volatility.     

基于高阶矩风险防范的银行资产负债组合优化模型研究——以A银行为例

资产负债管理能力是现代商业银行的基本能力,其核心在于风险控制和价值创造。商业银行资产负债组合优化是现代商业银行信贷管理框架中的核心内容,它对于保持银行资产流动性、安全性和赢利性的＂三性＂的最佳组合、优化配置资源、提高银行的生存能力和竞争能力,具有重要的现实意义。本文通过以贷款组合的VaR约束控制贷款组合的二阶矩,即控制了资产组合的风险;以贷款组合收益率的偏度约束控制贷款组合的三阶矩,即控制了贷款组合收益率发生总体损失的可能性;以组合收益率的峰度约束控制贷款组合的四阶矩,即减少了组合收益率发生极端损失的可能性,建立了资产分配的收益率均值-方差-偏度-峰度模型。     

Higher-Order Systematic Comoments and Asset Pricing: New Evidence

We provide evidence supporting Rubinstein's (1973) model that if returns are not normal, measuring risk requires more than just measuring covariance. Higher-order systematic comoments should be important to risk-averse investors who are concerned about the extreme outcomes of their investments. Our paper shows that the Fama-French factors [SMB (return on small stocks less the return on big stocks), HML (return on high book-to-market stocks less the return on low book-to-market stocks)] as well as the momentum and market liquidity factors can be explained by the higher-order systematic comoments, and it lends support to the traditional covariance risk-based theory without having to resort to behavior assumptions.     

Properties of Multinomial Lattices with Cumulants for Option Pricing and Hedging

In this paper, we analyze properties of multinomial lattices that model general stochastic dynamics of the underlying stock by taking into account any given cumulants (or moments). First, we provide a parameterization of multinomial lattices, and demonstrate that mean, variance, skewness, and kurtosis of the underlying may be matched using five branches. Then, we investigate the convergence of the multinomial lattice when the basic time period approaches zero, and prove that the limiting process of the multinomial lattice that matches annualized mean, variance, skewness and kurtosis is given by a compound Poisson process. Finally, we illustrate the effect of higher order moments in the underlying asset process on the price of derivative securities through numerical experiments using the multinomial lattice, and provide a comparison with jump-diffusion models.     

‘Enhancing the Creative Process for Learning in Primary Technology Education’

When undertaking design and technology activities, children are provided with opportunities to create solutions to problems in new and innovative ways. The mental processes involved in the generation of new ideas may be enhanced when children’s attention is not focussed and is allowed to wander in a relaxed and uncompetitive environment. Research indicates that the two mental states, generative and non-generative, cannot exist simultaneously. This paper reports on a research project which investigated the impact on children’s thinking when a period of non-focussed thinking became part of the technology process. The results support the previous proposition that a child’s non-generative/analytical mental state needs to give way to a generative state so that a child can be more fully creative. Moreover, from this study that documented children’s ideas during their involvement in a design and technology activity, teachers are urged to provide an incubation period as part of the technological process in the classroom, so that children’s creativity can be fostered.     

运用高阶累积量和SVM的调制自动识别

针对数字信号调制模式识别问题,提出了运用高阶累积量和二叉树支持向量机（SVM）进行 自动识别的算法。该算法首先使用信号的四阶、六阶、八阶累积量构造了5个新的分类特征 ,然后利用二叉树支持向量机分类器实现了8种信号的有效分类。仿真结果表明,该算法优 于直接多类分类支持向量机算法,在信噪比大于5 dB时,识别率达到90%以上。