Forex statistical analysis

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In order to be successful, forex traders need to know the basic mathematics of probability. After all, it’s difficult to achieve and maintain trading gains without first having the ability to understand the numbers and measure them. Many traders use a combination of black box indicators to develop and implement trading rules. Probability and statistics are the key to developing, testing and profiting from forex trading. By knowing a few probability tools, it’s easier for traders to set trading goals in mathematical terms, create and operate effective trading strategies, and assess results. It’s helpful to review the most basic concepts of probability and statistics for forex trading. This is the sort of distribution that would result from artificially spreading objects as evenly as possible across an area, with a uniform amount of spacing between them.

However, instead of a uniform distribution, a currency-pair’s price will likely be found within a certain area at any given time. Normal distribution offers forex traders predictive power regarding the likelihood that a currency-pair price will reach a certain level during a certain time frame. If a large number of sample prices are checked, the normal distribution will form the shape of a bell curve when plotted graphically. The greater the number of samples, the smoother the curve will be. The rules of simple averages are helpful to traders, yet the rules of normal distribution offer more useful predictive power. Yet, the normal distribution can also tell the trader the likelihood that a certain daily price move will fall between 30 and 50 pips, or between 50 and 70 pips. Yet, traders should be cautious when using the concept of normal distribution alone for purposes of risk management.

So, for testing a forex-trading strategy by estimating the results from sample trades, the system developer must analyze at least 30 trades in order to reach statistically-reliable conclusions regarding the parameters being tested. Likewise, the results from a study of 500 trades are more reliable than those from an analysis of only 50 trades. Mathematical expectation for a series of trades is easy to calculate: Just add up all the trade results and divide that amount by the number of trades. If the trading system is profitable, then the mathematical expectation is positive.

If the mathematical expectation is negative, the system is losing on average. The relative steepness or flatness of the distribution curve is shown by measuring the spread or dispersion of price values within the area of mathematical expectation. Dispersion and standard deviation are critically important for risk management in forex trading systems. The higher the value of the standard deviation, the higher will be the potential drawdown, and the higher the risk. Likewise, the lower the value for standard deviation, the lower will be the drawdown while trading the system. In the above example based on the minimum number of thirty trades for an adequate sample, it’s important to note that the mathematical expectation is positive, so the forex trading strategy is indeed profitable. Here’s the rest of the math: To determine the mathematical expectation for this group of trades, add together all the trades’ gains and losses, then divide by 30.

Thus far, the system looks promising. 26 is subtracted from the results of each trade, then it’s squared, and the sum of all these squares is added together. The sum is divided by 29, which is the total number of trades minus 1. The same calculation is performed for each trade in the test series. In this example, the dispersion over the series equals 9,353. 26 per trade, yet the standard deviation is high when compared with that profit.

This risk may be acceptable, or the trader may choose to modify the system in search of lower risk. For example, let’s assume the average expected profit from a given forex trading system is four times less than the expected loss amount from each stop-loss order triggered while trading this system. Some traders may assume that the system will win over time, as long as there is an average of at least one profitable trade for each four losing trades. Yet, depending upon the distribution of wins and losses, during real-world trading this system may draw down too deeply to recover in time for the next winner. A positive Z-score represents a value above the mean, and a negative Z-score represents a value below the mean.

To obtain this value, the trader subtracts the population mean from an individual raw value then divides the difference by the population standard deviation. Where μ is the population mean and σ is the population standard deviation. It’s important to understand that calculating the Z score requires that the trader know the parameters of the population, not merely the characteristics of a sample taken from that population. Z represents the distance between the population mean and the raw score, expressed in units of the standard deviation.

R counts the number of such series. Z can offer an assessment of whether a forex trading system is operating on-target, or how far off-target it may be. In other words, whether the outcomes of consecutive trades are dependent upon each other. If the Z-score is near 0, then the distribution of trade results is near the normal distribution. The score of a sequence of trades may indicate a dependency between the results of those trades. Whether the Z value is positive or negative will inform the trader about the type of dependence: A positive Z value indicates that the profitable trade will be followed by a loser.

And, positive Z indicates that the profitable trade will be followed by another profitable one, and a loser will be followed by another loss. This observed dependency lets the forex trader vary the position sizes for individual trades in order to help manage risk. As with the methods described above, it relies on applying the concepts of normal distribution and standard deviation. It gives traders a method to check the performance of a trading system by adjusting for risk. Likewise, HPR can be calculated by dividing the after-trade balance amount by the before-trade amount.

AHPR by itself produces an arithmetic average which may not properly estimate the performance of a forex trading system over time. Instead, a trading system’s investment efficiency can be more closely estimated by using the Sharpe Ratio, which shows how AHPR minus the risk-free rate of long-term investment returns relates to the standard deviation of the trading system. T-bond rates, and SD is the standard deviation. Sharpe Ratio, the more efficient the trading system. The concepts of normal distribution, dispersion, Z-score and Sharpe Ratio are already incorporated into the logarithms of EAs and mechanical trading systems, and their usefulness is invisible to most traders.