A momentum trading approach is presented to examine the Dow Jones industrial components for a period of about past 10 years (1992–2002). An analogy between the classical dynamics in physics and the stock trade dynamics is used with the momentum, P=mv, where the velocity (v) is a relative price change in a period (τ) and the inertial mass (m) is a normalized trade volume. Extrema in the momentum time series, i.e., the singularities in the driving force provide the signals for executing trades, minima with negative momentum to buy and maxima with positive momentum to sell. Trades are implemented using a momentum threshold (Pc). A range of periodic cycles (τ=5–240 days) in time series and trading momentum thresholds (|Pc|=0.01–0.5) are considered and returns (maximum, minimum, accumulative, and average) are examined in detail on the historical DJI data for about a decade (1992–2002). Frequency of trade is generally higher with smaller periods with the high probability of higher returns at |Pc|=0.02–0.1 for nearly all stocks in DJI.
Technical analysis of moving averages and momentum based on the assumption of an efficient market is an important part of trading tools in major stock markets [1], [2], [3], [4], [5] and [6]. The hypothesis of pure random stock market is common in econometry [7] while it is not considered as explicitly in empirical finance. It is well known that the efficiency of the market varies and econophysics is an attempt to develop a better understanding of econo-dynamics [8], [9], [10], [11], [12], [13] and [14]. Numerous variables affect the econo-dynamics and are reflected into the price index of the stock market. These variables include interest rates, sales signals for goods, consumer confidence, deficits, surplus, emergence of emerging tools and perceived potentials and breakthroughs, the evolving socio-economic dynamics, etc. [15], and probability of unexpected disasters (flood, earthquakes, accidents, etc.). A variety of practices are exercised in current stock market [1], [2] and [3] with an enormous range of technical details some of which appear ad hoc and based on pure visual judgment of graphs and charts on the part of the analysts. Availability of data, statistics, and charts have led to a rather very fast dissemination of opinions with a long list of terminology for various indicators [1]. A scientific analysis, however, requires a systematic observation of trends and relates it to basic laws, fundamental or empirical.
In a series of papers, Ausloos and Ivanova [16], [17] and [18] have recently investigated the stock price, active volume, moving averages, and presented an elegant analogy with the fundamental quantities of mechanical physics. For example, they extended the definition of the classical momentum, the average price change during the moving average period to a more technical footing by introducing the generalized momentum. Momentum is defined as P=mv, where mass (m) is the normalized volume transaction and velocity (v), the average rate of price change during the moving average period. Using the stock price of IBM for a decade (1990–2000), they pointed out sign of appropriate signals for the transactions. The analogy between the stock dynamics and the classical mechanics of particles’ dynamics is an appealing concept to pursue. We would like to follow the same terminology with somewhat different definitions for mass, velocity, and momentum. A momentum trading approach is presented to analyze a sector represented by the Dow Jones industrial (DJI) stocks which may help understanding signals for selecting specific stocks from the DJI group. Method and definitions are presented in the next section followed by detailed analysis and conclusions.
A technical analysis of DJI stocks based on the historical data during 1992–2002 is presented with a momentum trading approach. Price change of each stock in a unit time (τ), normalized by the stock price defines the velocity u(t) ( Eq. (2)). The relative velocity v(t) ( Eq. (3)) is obtained by normalizing u(t) by the maximum value uh(t) among all 30 components during the span of unit cycle time (τ); a set of periods are used, τ=5,20,30,60,120 and 240 days. This normalization uh(t) is important factor to correlate relative speed of stocks prices within a sector, i.e., those in DJI. It varies with time and changes from one stock to another for t⪢τ. Normalized trade volume of each stock is the measure of its inertia (mass). The market momentum is the product of mass and relative velocity ( Eq. (5)). The rate of momentum change is the driving force for trading and price change. The extrema in time series of momentum, i.e., the singularities in the driving force provide opportunities for trade which is controlled by the momentum trading threshold Pc. The threshold is an excellent tool for the limit orders (p(t)⩾Pc (sell), p⩽−Pc (buy)). Returns are examined for a range of threshold Pc=0.01–0.5 for the DJI data for a period of 10 years (1992–2002); the interesting range are found to be Pc=0.02–0.1. The probability of return is found to be high with such momentum trading based on these historical data. The choices of period (τ) for the momentum time series and trading threshold (Pc) depend on the objectives (i.e., long to short term trading horizon). Although, all our analyses are based on the market data, the probability of return is not an exact science. This is an academic exercise to see that the basic law of classical dynamics in physics is applicable in stock analysis with some modifications.
