Statistics for Crypto Traders Part 2: Standard Deviation and Expected Move
When most traders talk about price, they usually do so in terms of direction. Bullish, bearish, their view on the markets is directional. For all their good intentions and thoughts, future market movements are impossible to predict and are assumed to follow the random walk hypothesis.
What can be derived from markets though are beliefs on how far and how fast price will move in a certain period using Standard Deviation to calculate the expected move over a given time period.
Variance & Standard deviation
Standard deviation is a way to calculate volatility: the degree to which asset prices fluctuate.
A coin with little price movement has a low standard deviation. Conversely, a coin whose prices can move a lot has much larger deviation. Standard deviation is an extremely important figure to know and understand, as it can guide traders in how much they risk, their stops and a multitude of other factors.
To find SD, first, calculate the mean, then find the variance, then take the square root of the average of all variances. Here is the formula for SD:
- Calculate the mean (μ) for the whole price range
- Subtract each individual price point (xi) from the mean
- Square the results from (2) and add them up
- Divide your result from (3) by the total number of price points
Of course, you can just let Adara’s widgets and indicators do the whole calculation for you automatically. Once you get the S.D. for a data set, you can use it on its own or with other data.
Think about it like this, let’s take two sets of price data:
Set 1: 3018, 3669, 2575, 3738
Set 2: 1575, 1977, 3,696, 5782
Both sets of data have the same mean of 3,250. However, looking at the data sets, it’s pretty clear that the price data in Set 2 contains values which are further away from the mean than data Set #1. Variance is used for this, to calculate it, find the difference between each price point, square it, then find the average of the results.
Formula for Variance of Data Set 1 & 2
Data Set 1
2= (-232)2 + (419)2 + (-675)2 + (488)24
2= 53,824 +175,561 + 455,625 + 238,1444= 230,788.5
Data Set 2
2= (-1,675)2 + (-1,273)2 + (446)2 + (2532)24
2= 2,805,625 + 1,620,529 + 198,916 + 6,411,0244=2,759,023.5
Now that we know the variance, to find standard deviation, simply take the square root of each number.
Std Dev of Data Set 1 = 480
Std Dev of Data Set 2 = 1,661
So what does this mean?
SD provides a statistical representation of the dispersion of returns. For assets with higher SD, the dispersion from the mean increases. Put differently, higher SD means that an asset’s price will move farther and faster from it’s mean than an asset with a lower standard deviation.
If you were throwing darts, a beginner player would probably not be able to hit close to the bullseye every single time. The dispersion of their throws would be high in relation to the bullseye. With practice, their shots might place closer to each other. On the other hand, a professional might be able to hit the bullseye 80% of the time and his dispersion would be significantly less.
Look at the chart below to see the differences in how dispersion and standard deviation are charted. The green area represents the beginner player who’s shots are not usually on target and sometimes veer wildly away from the bullseye. With practice, his shot dispersion gets tighter, as he starts to hit near to the bullseye more often. The blue area is representative of a professional who rarely misses shots and almost never throws far from the bullseye.
If we take the above graph and we rotate it 90 degrees, it can be overlaid crudely on a candlestick price chart to show how different dispersions can be represented for price.
Ok, so now you understand what high versus low SD is and how it is represented on a stock chart.
When talking about SD, you will usually hear people say “it’s a one SD move,” or “the probability for Bitcoin to reach X price is 3 SD.” This is because different SD levels represent the probability of price occurring within the normal distribution curve. SD follows what’s called the 65–95–99.7 rule, the “percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively.”
So when someone says “this is a one SD move,” what they really mean is “this move had a 68.27% probability of occurring.” If they say “the probability for Bitcoin to reach X price 3 SD,” they really mean “there is less than 1% chance that the price of Bitcoin will reach X price before a certain time.”
SD is used as a measure of volatility or the price dispersion from the mean for any given asset. While there are issues with using SD solely as a measure of volatility, until we have a functioning, liquid options market for Bitcoin, it will be the best measure of it.
Knowing volatility allows for an expected 1 SD move to be calculated. This will be the topic of the next lesson.
The key to using standard deviation effectively is understanding how it represents real-life price variance. If you’re unsure, try using the Standard Deviation indicator to see how S.D. changes with chart prices. (If you don’t know how to use indicators, check out our free lessons on Technical Analysis in Adara Academy).
Before we close this article, let’s cover one more important thing.
If you’d like to know more about all these formulas and technical analysis in general, we invite you to our Intermediate trading lessons, available for free at Adara Academy.
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