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We consider four very popular indexes of financial markets and in particular, we analyze the following corresponding time series, shown in Fig. See text for further details. In general, the possibility to predict financial time series has been stimulated by the finding of some kind of persistent behavior in some of them [38] , [54] , [55]. The main purpose of the present section is to investigate the possible presence of correlations in the previous four financial series of European and US stock market all share indexes.

In this connection, we will calculate the time-dependent Hurst exponent by using the detrended moving average DMA technique [56]. Let us begin with a summary of the DMA algorithm. The computational procedure is based on the calculation of the standard deviation along a given time series defined as 1 where is the average calculated in each time window of size. In order to determine the Hurst exponent , the function is calculated for increasing values of inside the interval , being the length of the time series, and the obtained values are reported as a function of on a log-log plot.

In general, exhibits a power-law dependence with exponent , i. The case of corresponds to an uncorrelated Brownian process. In our case, as a first step, we calculated the Hurst exponent considering the complete series. This analysis is illustrated in the four plots of Fig. Here, a linear fit to the log-log plots reveals that all the values of the Hurst index H obtained in this way for the time series studied are, on average, very close to 0.

This result seems to indicate an absence of correlations on large time scales and a consistence with a random process. The power law behavior of the DMA standard deviation allows to derive an Hurst index that, in all the four cases, oscillates around 0. See text. On the other hand, it is interesting to calculate the Hurst exponent locally in time. In order to perform this analysis, we consider subsets of the complete series by means of sliding windows of size , which move along the series with time step.

This means that, at each time , we calculate the inside the sliding window by changing with in Eq. Hence, following the same procedure described above, a sequence of Hurst exponent values is obtained as function of time. In Fig. In this case, the values obtained for the Hurst exponent differ very much locally from 0. This investigation, which is in line with what was found previously in Ref. As we will see in the next sections, this feature will affect the performances of the trading strategies considered.

A divergence is a disagreement between the indicator RSI and the underlying price. By means of trend-lines, the analyst check that slopes of both series agree. When the divergence occurs, an inversion of the price dynamic is expected. In the example a bullish period is expected. In this connection we are only interested in evaluating the percentage of wins achieved by each strategy, assuming that - at every time step - the traders perfectly know the past history of the indexes but do not possess any other information and can neither exert any influence on the market, nor receive any information about future moves.

In the following, we test the performance of the five strategies by dividing each of the four time series into a sequence of trading windows of equal size in days and evaluating the average percentage of wins for each strategy inside each window while the traders move along the series day by day, from to.

This procedure, when applied for , allows us to explore the performance of the various strategies for several time scales ranging, approximatively, from months to years. The motivation behind this choice is connected to the fact that the time evolution of each index clearly alternates between calm and volatile periods, which at a finer resolution would reveal a further, self-similar, alternation of intermittent and regular behavior over smaller time scales, a characteristic feature of turbulent financial markets [35] , [36] , [38] , [58].

Such a feature makes any long-term prediction of their behavior very difficult or even impossible with instruments of standard financial analysis. The point is that, due to the presence of correlations over small temporal scales as confirmed by the analysis of the time dependent Hurst exponent in Fig. But this could depend much more on chance than on the real effectiveness of the adopted algorithm.

On the other hand, if on a very large temporal scale the financial market time evolution is an uncorrelated Brownian process as indicated by the average Hurst exponent, which result to be around for all the financial time series considered , one might also expect that the performance of the standard trading strategies on a large time scale becomes comparable to random ones.

In fact, this is exactly what we found as explained in the following. In Figs. From top to bottom, we report the index time series, the corresponding returns time series, the volatility, the percentages of wins for the five strategies over all the windows and the corresponding standard deviations. The last two quantities are averaged over 10 different runs events inside each window.

As visible, the performances of the strategies can be very different one from the others inside a single time window, but averaging over the whole series these differences tend to disappear and one recovers the common outcome shown in the previous figures. In this paper we have explored the role of random strategies in financial systems from a micro-economic point of view. In particular, we simulated the performance of five trading strategies, including a completely random one, applied to four very popular financial markets indexes, in order to compare their predictive capacity.

Our main result, which is independent of the market considered, is that standard trading strategies and their algorithms, based on the past history of the time series, although have occasionally the chance to be successful inside small temporal windows, on a large temporal scale perform on average not better than the purely random strategy, which, on the other hand, is also much less volatile. In this respect, for the individual trader, a purely random strategy represents a costless alternative to expensive professional financial consulting, being at the same time also much less risky, if compared to the other trading strategies.

This result, obtained at a micro-level, could have many implications for real markets also at the macro-level, where other important phenomena, like herding, asymmetric information, rational bubbles occur. In fact, one might expect that a widespread adoption of a random approach for financial transactions would result in a more stable market with lower volatility.

In this connection, random strategies could play the role of reducing herding behavior over the whole market since, if agents knew that financial transactions do not necessarily carry an information role, bandwagon effects could probably fade.

On the other hand, as recently suggested by one of us [59] , if the policy-maker Central Banks intervened by randomly buying and selling financial assets, two results could be simultaneously obtained. Of course, this has to be explored in detail as well as the feedback effect of a global reaction of the market to the application of these actions. This topic is however beyond the goal of the present paper and it will be investigated in a future work. We thank H. Trummer for DAX historical series and the other institutions for the respective data sets.

Browse Subject Areas? Click through the PLOS taxonomy to find articles in your field. Abstract In this paper we explore the specific role of randomness in financial markets, inspired by the beneficial role of noise in many physical systems and in previous applications to complex socio-economic systems.

Funding: The authors have no support or funding to report. Introduction In physics, both at the classical and quantum level, many real systems work fine and more efficiently due to the useful role of a random weak noise [1] — [6]. Expectations and Predictability in Financial Markets As Simon [20] pointed out, individuals assume their decision on the basis of a limited knowledge about their environment and thus face high search costs to obtain needed information.

Detrended Analysis of the Index Time Series We consider four very popular indexes of financial markets and in particular, we analyze the following corresponding time series, shown in Fig. Download: PPT. Figure 1. Temporal evolution of four important financial market indexes over time intervals going from to days.

Figure 2. Detrended analysis for the four financial market series shown in Fig. Figure 3. The random algo did at least as well as the others—and it experienced a lot less day-to-day volatility. Investors probably see patterns in random fluctuations or computer glitches and then pile on.

This herding instinct amplifies mistakes. That's partially how, for example, a single sale of 75, futures contracts by an institutional investor in May turned into a 9 percent drop in the Dow Jones Industrial Average. Biondo and Pluchino have made something of a career out of randomness—they previously used mathematical models to argue that corporate promotions and legislative appointments should be made at random as well.

Nobody took their advice, but considering how dicey the economy has been lately, maybe the Fed should consider investing in darts. More from this issue.

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