Bad news and Dow Jones make the Spanish stocks go round

This paper is a data-based attempt to analyse what kind of information basically affects close-to-open returns, open-to-close returns, volatility and volume in actively traded individual securities on the Spanish stock market. Specifically, we are interested in detecting how these variables react to specific pieces of news considered as exogenous information. However, as volume itself could be interpreted as a proxy of the information flow, we first apply the linear and nonlinear Granger causality tests from volume to return and to volatility. We do not find evidence supporting this latter hypothesis. Furthermore, we only find significant evidence of linear causality from volume to volatility. The other major finding is that both bad news and the Dow Jones play a significant informational role in explaining price changes and volatility. As a consequence of these findings, we also test the residual role of volume as a proxy for noise/liquidity trading after filtering for news, although we do not find evidence in favour of this argument.     

Sample period selection and long-term dependence: New evidence from the Dow Jones index

This study employs the classical and modified rescaled adjusted range statistic (R/S statistic) to investigate the sensitivity of the long-term return anomaly observed on the Dow Jones Industrial Average (DJIA) to sample and method bias. Daily data from 1/1/1970 to 17/3/2004 is used with sub-periods identified based on sign shifts in the mean returns as well as the October 1987 crash. The return series are also filtered to accommodate autoregressive conditional heteroskedastic (ARCH) innovations and short-term dependencies. Hurst exponent and V-statistic values for each of the filtered series for the whole sample and sub-periods are estimated, while polynomial regression techniques are applied to plot the V-statistics. These plots show oscillating cycles of varying lengths. Overall, we find the null hypothesis of no long-term dependence is accepted for the whole sample and every sub-period using the modified rescaled range test, but not necessarily using the classical rescaled adjusted range test. The later test does, however, reveal episodes of both positive and negative dependence over the various sample periods, which have been reported by other researchers.     

Predicting DAX trends from Dow Jones data by methods of the mathematical theory of democracy

The mathematical theory of democracy operates on the indices of popularity and universality which are used to find socially optimal representatives and representative bodies. Regarded mathematically, neither the ‘society’, nor its ‘representatives’ are necessarily human, so that some objects can represent the behavior of other objects. This idea is applied to predicting the DAX-trends (German stock index) from the actual Dow-Jones data; the current fluctuations of stock prices in New York are regarded as representative indicators of future stock price fluctuations in Frankfurt. In particular, it is found that American Express anticipates on the average the price ±fluctuations of 2/3 of the DAX stocks. The statistical significance of the null hypothesis that such a bias from the uncertainty 50% can occur by chance is only 3.5%.     

Portfolio optimization based on downside risk: a mean-semivariance efficient frontier from Dow Jones blue chips

To create efficient funds appealing to a sector of bank clients, the objective of minimizing downside risk is relevant to managers of funds offered by the banks. In this paper, a case focusing on this objective is developed. More precisely, the scope and purpose of the paper is to apply the mean-semivariance efficient frontier model, which is a recent approach to portfolio selection of stocks when the investor is especially interested in the constrained minimization of downside risk measured by the portfolio semivariance. Concerning the opportunity set and observation period, the mean-semivariance efficient frontier model is applied to an actual case of portfolio choice from Dow Jones stocks with daily prices observed over the period 2005–2009. From these daily prices, time series of returns (capital gains weekly computed) are obtained as a piece of basic information. Diversification constraints are established so that each portfolio weight cannot exceed 5 per cent. The results show significant differences between the portfolios obtained by mean-semivariance efficient frontier model and those portfolios of equal expected returns obtained by classical Markowitz mean-variance efficient frontier model. Precise comparisons between them are made, leading to the conclusion that the results are consistent with the objective of reflecting downside risk.     

Ball,sphere, and all,all, all

The relationship of multidimensional geometry with statistical thermodynamics and with laws of large numbers is described.     

Kepler, Kugeln, Cluster, Katastrophen

Zusammenfassung. Dieser Überblick skizziert Theorie und Anwendungen von Kugelpackungen, ausgehend von den klassischen Problemen von Kepler und Newton. Der weitaus wichtigste Bereich der regelmäßigen, gitterförmigen Kugelpackungen einschließlich der Anwendungen auf Codes wird kurz gehalten, weil es dazu ausgiebig Literatur gibt. Dagegen wird ausführlicher auf die in den letzten Jahren stark entwickelten endlichen Kugelpackungen eingegangen, die gute Modelle für die in der Nanotechnik wichtigen Microcluster sind. In jeder der relativ knapp gehaltenen Sektionen wird das zum Verständnis Unerlässliche an Theorie angegeben, sowie mindestens ein überraschendes oder im Wortsinn merkwürdiges Phänomen. Außerdem wird auf weiterführende Literatur verwiesen. Für Einsteiger sei insbesondere M. Leppmeiers Buch [L] empfohlen.     

When is an L(B, m, n, r, s, t, z, w) loop SRAR?

In [5, 6], the second author and D. A. ROBINSON initiated a study of non-Moufang Bol loops with the property that over a field, necessarily of characteristic 2, their loop rings satisfy the right, but not the left, Bol identity. They called such loops SRAR and showed that the family of SRAR loops includes those Bol loops which have a unique non-identity commutator/associator. In [4, 2], the current authors presented a construction for a new class of Bol loops denoted L(B,m,n,r,s,t,z,w) with initial data a given (possibly associative) Bol loop B, elements, r, s, t, z and w in the centre of B, and integers m and n.     

Woodhouse, babbage, peacock, and modern Algebra

In a recent article, J. M. Dubbey [Historia Mathematica 4 (1977), 295–302] showed that George Peacock's A Treatise on Algebra (1830) was similar to an unpublished work written by Charles Babbage in 1821. Evidently perplexed about the absence of a dispute over priority, Dubbey concluded that Peacock had unconsciously assimilated Babbage's ideas, and that Babbage was too busy with other activities to be concerned. The thesis of this article is that the innovative aspects of the work of both Babbage and Peacock are extensions of ideas put forth in 1803 by Robert Woodhouse, and that probably neither Babbage nor Peacock was overly concerned with acknowledgments because their approach to algebra was not unique at Cambridge.     

A three-stage, VSVO, Hermite-Birkhoff-Taylor, ODE solver

The new variable-step, variable-order, ODE solver, HBT(p) of order p, presented in this paper, combines a three-stage Runge-Kutta method of order 3 with a Taylor series method of order p-2 to solve initial value problems , where y:R→R^d and f:R×R^d→R^d. The order conditions satisfied by HBT(p) are formulated and they lead to Vandermonde-type linear algebraic systems whose solutions are the coefficients in the formulae for HBT(p). A detailed formulation of variable-step HBT(p) in both fixed-order and variable-order modes is presented. The new method and the Taylor series method have similar regions of absolute stability. To obtain high-accuracy results at high order, this method has been implemented in multiple precision.