We have all gone through the example of finding the probabilities of a dice roll. Now, we know that there are only six outcomes on a dice roll, i. This kind of probability is called discrete, where there are a fixed number of outcomes. Now, as the name suggests, the probability distribution is simply a list of all outcomes of a given event. Thus, the probability of the dice roll event is the following:.
Listing all the values here works because we have a limited set of outcomes, but if the outcomes are large, we use functions. If the probability is discrete, we call the function a probability mass function. For discrete probabilities, there are certain cases which are so extensively studied, that their probability distribution has become standardised.
We write its probability function as px 1 — p 1 — x. Now, there are cases where the outcomes are not clearly defined. For example, the heights of all high school students in one grade. While the actual reason is different, we can say that it will be too cumbersome to list down all the height data and the probability. It is in this situation that the functions are essential. Earlier, we said that for discrete values, the probability function is the probability mass function. In comparison, for continuous values, the probability function is known as a probability density function.
In the data set taken, the minimum value of the closing price is Now, we will move towards standard deviation.
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In simple words, the standard deviation tells us how far the value deviates from the mean. Let us use the full dataset and try to understand how the standard deviation helps us in the arena of trading. We are taking into account the closing price for our calculations. As specified previously, the mean of our dataset is The python code for Plotting the graph with the closing price and the mean should give us the following figure.
Now we will plot the above graph with one standard deviation on both sides of the mean.
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Well, a quick look tells us that most of the closing price values are in between the two standard deviations. Thus, this gives us a rough idea about the majority of the price action. But you might still be wondering, what is the use of knowing a certain range of price values? Well, for one thing, standard deviation plays an important role in Bollinger Bands , which is a quite popular indicator. You can use the upper standard deviation as a sign of a breakout. And initiate a buy trade when the price moves above the upper band.
The volatility of the stock can be calculated using the standard deviation. The stock volatility is an important feature used in many machine learning algorithms. It is also used in Normal probability distribution, which we will cover in a while.
Normal distribution is a very simple and yet, quite profound piece in the world of statistics, actually in general life too. The basic premise is that given a range of observations, it is found that most of the values centre around the mean and within one standard deviation away from the mean. Wait, we are going ahead of ourselves now. Let us first take the help of something called the histogram to understand this. Now there might be students who have heights of Sometimes we are not looking for that level of detail and would like just to find out how many students have a height of 60 - 61 inches.
That is exactly what a histogram does. It gives us the frequency distribution of the observed values. When it comes to trading, we usually use the daily percentage change instead of the closing prices. Recall how we said that the majority of the values are situated close to the mean.
Forex Patterns and Probabilities: Trading Strategies for Trending and Range-Bound Markets
You can see it clearly in the histogram plotted above. We call this a bell curve, which is another name for the normal probability distribution, or normal distribution for short. You can see the majority of the values lying between the standard deviations, i. Moving further, we will say that When the distribution of your data meets certain requirements, such as symmetry around the mean and bell-shaped curve, we say your data is normally distributed.
For example, say, your data sample X represents marks obtained out of in an entrance test for a sample of students. When plotted, this data would look as follows:. If you increase the number of observations in your sample data set from to , this is what happens:. Now that we know, X has normally distributed data with mean at 50 and standard deviation of 10, we can predict the marks of the entire student population or future students from the same population with a certain confidence.
With almost Statistically speaking, distribution functions give us the probability of expecting the value of a given observation between two points. Before we try to answer the question, let us take another dataset and see how its histogram looks like. Here, the mean Closing price is So what conclusion can you draw from the above histogram?
To sum it up, probability distribution functions are used in every step of technical analysis, and it is the core of the quantitative analysis. These analyses constitute the core part of any strategy building process. So far, we have gone through some basic concepts in the world of statistics.
Now, we shall try to go a bit further in this fascinating world and see its application in trading. We will first start with correlation. Well, in a way, correlation tells us about the relationship between two sets of values. Until now, we have taken the data set of Apple from Dec 26, to Dec 26, Correlation is a unit free number lying between -1 and 1 which gives us the measurement of the relationship between variables. A highly positive correlation value lying between 0.
That means, if one variable increases, there is a high probability that other one will increase as well. The behavior will be consistent in other cases of decrease or no change in value as well. This does not matter. What does matter though is understanding that each individual trade should, as long as you keep to your trading rules and money management strategy, have little effect on the collective outcome.
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Do we panic if we have a loss, do we panic if we have two, or even three consecutive losses? Absolutely not. Remember, there is no way of knowing the outcome of each trade you take! Do you think the trader who managed the account pictured above panicked when the equity curve started to turn south see black arrows? Highly unlikely given the results.
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In our humble opinion, trading a method that has a clear edge and following it religiously, while thinking in probabilities, is key to a successful trading career. This type of thinking will not happen overnight. Empowering the individual traders was, is, and will always be our motto going forward. Contact us: contact actionforex. Necessary cookies are absolutely essential for the website to function properly.