An In-Depth Guide to Using Standard Deviation in Trading

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Photo by Anna Nekrashevich: https://www.pexels.com/photo/person-holding-mug-and-mobile-phone-6802052/

Trading is difficult and nearly impossible. If anyone tells you otherwise they’re lying. Luckily, there are tools and methods to give you an edge. There are different types of trading but we won’t get into that here.

What we will dive into is a mathematical approach, or statistical approach rather, that’ll help you gain an understanding of where the markets may move.

The main driver in this process is standard deviation, or STD DEV for short.

Now, if you’re looking for a 100% win rate tool, you’re in the wrong place. If you’re looking for something you have to put no work into, you’re in the wrong place. Like anything, you have to put in the work to understand the tools you’re implementing.

Using this STD DEV analysis of the market, there’s going to be a manual process to it.

Luckily, the information needed is available in the evening, before the next market open, giving you plenty of time to plot the data.

Product wise, we’ll be using these on the e-mini futures contracts for the 4 major U.S. indices.

Without further delay, let’s jump in!

Definitions

To begin, it’s important to understand the definitions behind what we’re working with. Without an understanding of what you’re implementing, you’re simply following the ideas of another. That’s no good.

Standard Deviation

For this, we’ll borrow the Investopedia definition.

A standard deviation is a statistic that measures the dispersion of a dataset relative to its mean. The standard deviation is calculated as the square root of variance by determining each data point’s deviation relative to the mean.

If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.

Value Area

The Value Area is a range of prices where the majority of trading volume took place on the prior trading day. In specific, this area is the range where 70% of the prior day’s volume happened. The value area is approximately one standard deviation above and below the average highest volume price.

This definition comes from Towards Data Science.

Point of Control (POC)

The point of control is simple. It’s where the most trading at a price point occurred. Meaning if trading between 100 and 105 happened, and at 102 is where the most volume is, then 102 price is the point of control.

This data point can be found using the volume profile tool, which also gives us the value area.

Contract Settlement

Contract settlement is important because it gives us the last trade price for the security. We need this to determine the STD DEV for the next day. I’ll provide you with a link, but you can find this on the CME website shortly after the end of the trading day.

Purpose of Standard Deviation Analysis

The real purpose of STD DEV analysis is this — to remove as much human emotion as possible. Really, the only human emotion aspect of this whole thing is implied volatility. Luckily, we don’t need to manually quantify that and it’s easily obtained.

Using this analysis allows us to use certain data. No guesswork, no what-if’s, just cold hard data.

Of course once the data is plotted on your charts, it’s up to you to find the proper entry and exit points. That’s true with any trading or investing analysis. But what this does give you is a guide to where those entry and exit points should be.

Another purpose of STD DEV is by nature, it provides you with probabilities of certain events happening. Below is a chart illustrating how it works.

0 is the middle, the mean. A 1 STD DEV means that any occurrence has a 68.2% chance of staying within 1 STD DEV. Then a 2 STD DEV move has a 95.4% of staying within 2 STD DEV.

The goal is to use STD DEV to give us an area where the market might trade the next day, and use probability to help us make an informed decision about entries and exits.

Calculation

Here’s the fun part, knowing how to build the data yourself. This is the hardest part because with any equation, you need to test it out to ensure the inputs are correct. Good news is I’ve done that already.

Just know that with any analysis, understanding the inputs is critically important.

For this example, we’ll just say we’re using the S&P 500 e-mini futures contract.

First you’ll need the settlement price for the previous day. You can find that data point on the CME website, which I’ve linked for you. At the end I’ll link all the data points and information for easy reference.

Secondly, you’ll need to find the implied volatility for the next day (the day you’re setting up for). Now I use ThinkorSwim as my charting platform. You can add a data point that’ll tell you the implied volatility for the upcoming trading day.

Unfortunately I don’t have a website that provides that information so the best I can tell you is to dig into your charting or brokerage provider and see if they provide you with that data.

Lastly, you’ll need the amount of time you’re building out the STD DEV calculation for. For this, it’ll be 1 day. Now this is where you have to pay attention a bit. The equation is the square root of 1/# of trading days. In 2021 there were/are 252 trading days.

So the equation is the square root of 1 divided by 252. Which equates to 0.06299407883.

Now that we have the data points, you multiply them together.

SETTLEMENT PRICE x IMPLIED VOLATILITY x DURATION = EXPECTED STD DEV MOVE

Above you can see an example of how it would look at the end. I like to break out the calculations into half deviations because it helps identify potential entry/exit levels. We’ll go over that in detail shortly.

Implementation

Now, we have to take the data we just solved for and put it on the chart.

This is generally how it’ll look. You can set the colors, fonts, etc. to fit your needs. I always bold the settlement and I’ll also use green for positive STD DEV and red for negative.

One thing you might be wondering is how to get the value area. Well, like implied volatility, there’s no website that has that information. Why I like ThinkorSwim is I can have that information automatically calculated for me.

Value area isn’t essential to use STD DEV analysis, but it does provide a complimentary layer of analysis. It also adds another trading opportunity.

You’ll also notice that the value area doesn’t always line up equally with settlement. That’s perfectly fine, sometimes it won’t.

Analysis

The fun part — analysis!

In this section, I’ll highlight how you might want to implement the STD DEV analysis. It’s quite simple and we’ve already done the most difficult part, which is the calculation.

1 STD DEV MOVES

First and most basic is a 1 STD DEV move. Remember in the beginning that about 68% of all data points should remain 1 STD DEV from the mean. For trading, that means according to the rules of STD DEV, the market has a 68% probability of moving only 1 STD DEV.

The key however is a 1 STD DEV may look different. Below are a few examples of how it may look.

The first example above is a straight 1 STD DEV move to either the downside or the upside. Using settlement as the zero point, the probability of the market moving either direction and staying under 1 STD DEV is 68%, according to the rules.

While this is simple and straightforward, it doesn’t tend to happen this way as often as you’d think. Our second example is what you’ll likely see more often.

These next couple of examples are what you’ll likely see happen.

At the beginning the market might move up/down 0.5 STD DEV, and then retrace to the opposite half STD DEV level. While you might think it’s only a half move, the half move up and retracing to the opposite half is in total a 1 STD DEV move.

It’s important to know this because looking at the chart the market may not move much at first glance. Knowing that it’s already moved a full STD DEV is critical though because the probability of that occurring is 68%.

That means if you know the market’s moved 1 STD DEV, odds are in your favor that it won’t move much further and you can analyze your risk to reward appropriately.

In this final example, you can see that the market has moved 1.5 STD DEV in either direction. The probability of the market staying within a 1.5 STD DEV move is north of 80%. This is significant because if the market pushes either direction that far, you have a high probability that it won’t go much further or further at all.

Entry/Exit Examples

Let me provide you now with a few ways to think about entry and exit.

Using a 1 STD DEV move, let us assume the market moved up to the +1 STD DEV level. As we already know, the market moving up that far has a probability of 68%. What that also means is the market has roughly a 32% probability pushing past that.

So, a position might be to go short the market once the move reaches +1 STD DEV. Because if we follow the STD DEV probability rules, we say there’s only a 32% chance the market keeps pushing higher, giving us solid odds.

If you flip it and the market pulls back to -1 STD DEV, you might want to go long. Because there’s roughly a 32% chance the market continues lower.

In our second example, the market pulls back -0.5 STD DEV and retraces to the upside to hit +0.5 STD DEV. This move equals a 1 STD DEV move.

Like our first example, once the market moves back up to the +0.5 STD DEV level, the probabilities are in our favor that the market will not go much higher than that. Same can be said for the other direction.

Between these two examples, we’re simply waiting for a 1 STD DEV move to make an entry/exit decision.

Our last entry/exit example will be the +1.5/-1.5 STD DEV move. These moves are rare, but when they happen can provide you with excellent money making potential.

So let’s say the market moves up/down 1.5 STD DEV. That means you have about a 80% probability of the market staying within that area. As the market moves further away from the middle, the odds become less and less that it reaches further.

An entry would be if the market moves up +1.5 STD DEV, you might want to enter a short position because you have a less than 20% probability the market moves higher.

One thing you might say is well isn’t a move to the upside only covering roughly 40% of the STD DEV area? Yes, but you have to take into account the downside as well, which gives you the other 40%.

As you can see, having the STD DEV levels plotted can help you make higher probability trades. In trading, you need to have winners and ensure your losses are small.

Intuition

It’s important to know that while these data points can help you find solid entry and exit points, you still need intuition. You need sound psychology and trading fundamentals. Lastly, you have to believe in the analysis and tools you implement.

If you don’t believe in standard deviation then odds are this won’t work. Nothing against you.

That’s like using moving averages but thinking they’re unreliable.

You need to know what constitutes a good entry. Is it a candle reversal? What time frame are you using? There are so many inputs beyond this that this alone isn’t enough.

However, it does give you structure the night before. You can set alerts and notices, which gives you freedom to step away from the charts.

There might be some weeks you make 1 or 2 trades if there’s low volatility. Some weeks the market might fly and you can get 5 or more trades. The idea with this analysis is to let the market come to you and not force the trades.

The other advantage is data. You can’t dispute the inputs. It eliminates as much human emotion as possible, which tends to hurt traders in the long run.

Thank you for reading! If you’d like me to write for you, feel free to reach out!