A Simple Econophysics Model of the Stock Market as a Nonequilibrium Open System
Mathematical modeling of a stock market functioning is one of the actual and at the same time complex task of the modern theoretical economics. From our point of view, building such mathematical models “ab initio”, by using analogy between the stock market and a certain physical system (in our work, laser), is the most promising approach. This paper proposes a simple econophysical model of stock market as an open nonequilibrium system in form of Lorenz–Haken equation. In this system, variation of ask price, variation of bid price, and instantaneous difference between numbers of agents in active and passive state are intensity of external information flow is a control parameter. This model explains the impossibility of existence of an equilibrium state of the market and shows the presence of deterministic chaos in a stock market.
We consider essentially nonlinear dynamical systems with the ability to implement a chaotic behavior and deterministic solutions of various kinds. Among the deterministic solutions, we will highlight a variety of periodic solutions of different periods. This work is devoted to numerical algorithms for constructing and analyzing the stability of periodic solutions of strongly nonlinear dynamical systems.
The article describes proposed by the authors methodology of analysis of the Russian mutual funds. The aim of this methodology is to find out how attractive they are to investors and if they are able to provide the possibility of obtaining higher returns with less risk than the market in general. The study determines what type of fund management (active or passive) is more optimal. It also explains the effectiveness of focusing on past performance of the funds for making future investments. In addition, the ability of the management companies to repeat their past results is analyzed. Moreover, it is shown if it makes sense to focus on management companies that achieved the best results in the past while making decisions about future investments. These and other results achieved in this article reveal the features of the Russian market of collective investments and allow investors to form more competent policy of mutual funds’ investments. The methodology proposed by the authors is universal. Its application for the analysis of the other markets of collective investments will allow revealing their features.
The present article is devoted to consideration of investment strategy in stock market. The questions connected with designing of such strategy are systemically considered in it. The emphasis is thus placed on adaptation of the general (managerial) theory of engineering to engineering of investment strategy. Engineering of investment strategy is considered in indissoluble interrelation with the analysis of their typology. The most actual types and directions of engineering of investment strategy are characterized in the conclusion of article.
Hedging is one of the most popular strategies for market risk management. Hedging is aimed at decreasing the volatility, or variability, of portfolio returns. The portfolio usually consists of the spot assets and hedging instruments. The latter can be represented by futures, options and over-the-counter assets such as forwards and swaps. While futures’ hedging is rather simple it’s quite widespread in practice. This paper is aimed at comparison of four hedging strategies, where the spot asset is stock and hedging instrument is futures. For this purpose five Russian stocks from Moscow Exchange are selected and analyzed for the period from the 1st of December 2015 till the 29th of February 2016.
The key element of the hedging strategy is the calculation of the hedging coefficient. The latter shows what part of the stocks’ value in the portfolio should be covered by futures. In this paper the hedging coefficient is computed through internal rate of return, ordinary least squares (OLS) and maximum likelihood. The latter is able to estimate hedging coefficient taking into account heteroskedasticity, because the regression errors follow GARCH model. Further hedging strategies are compared by such criteria as standard deviation of portfolio returns, portfolio Value-at-Risk and hedging efficiency.
According to the results the most efficient strategy is one based on internal rate of returns. The other criteria show that the same strategy together with OLS demonstrates better results. Correction for heteroskedasticity made through maximum likelihood did not allow improving hedging efficiency.
The research can be extended in the several directions, namely considering options’ hedging; adding to the portfolio other spot assets, for example, commodities and currencies; taking into account investors’ risk aversion in the calculations of hedging coefficients; introducing transaction costs in the model.