Standard deviation explained

Downward trend
By :  ,  Financial Writer

What is standard deviation?

Standard deviation is a measurement of variation within a set of data points relative to the dataset’s mean average. A higher standard deviation indicates greater variability, while a lower standard deviation suggests less variability from the mean.

To understand standard deviation as it applies to trading, you can think of the data points as closing prices and the average mean as representative of the average price for the period you’re analysing.

For traders, standard deviation is frequently used to assess the volatility or risk associated with an asset. A stock with high volatility has a wider range of price fluctuations, resulting in a higher standard deviation. On the other hand, a stock with lower price fluctuations will have a lower standard deviation.

How to use standard deviation in your trading strategy

Standard deviation is used in several different trading indicators to calculate risk vs return when conducting risk management. It can be applied to a single asset, an index or an entire market. When applied specifically to the rate of return, standard deviation can measure a trade or investment’s historical volatility.

Evaluating a market using standard deviation

Deviation can also be used to measure a market’s current price action. For example, market tops with growing standard deviation can indicate indecisive traders, while market tops with low standard deviation may indicate a more mature bull market. On the other hand, market bottoms with high standard deviation indicate panicked sell-offs while low standard deviation demonstrates traders may currently be disinterested in the market.

  • Market tops + decreasing volatility = maturing bull market
    • Evaluating longer time frames, a maturing bull market displays low standard deviation during recurring price tops
  • Market tops + growing volatility = hesitant traders
    • Traders may be unsure of where the market is going next when price tops occur with increasing standard deviation
  • Market bottoms + decreasing volatility = traders losing interest
    • An extended period of low standard deviation and recurring market bottoms often signals a flat market
  • Market bottoms + growing volatility = panicked selloffs
    • Mass selloffs are often indicated by high standard deviation and recurring market bottoms
Example of standard deviation in shares trading

In the EUR/USD chart above, a period of losing interest is indicated by recurring market bottoms while the price drifts downwards and standard deviation falls.

Standard deviation has many uses beyond measuring current market momentum. Keep reading to learn how standard deviation is calculated and the many ways it can be applied to your trading strategy.

How to calculate standard deviation

Standard deviation is calculated in these steps:

  1. Find the mean average closing price for every period in the timespan you’re analysing
  2. Determine the deviation for each period (closing price – average price)
  3. Square each deviation
  4. Add the total sum of all squared deviations
  5. Divide the total by the number of periods (the same number of deviations you squared)
  6. Take the square root of the quotient found in step 5

Thankfully, most trading platforms will automatically calculate the standard deviation of any timeframe. On the City Index web trader platform, you can apply standard deviation from the dropdown list of indicators.

Start trading with the standard deviation

Follow these steps to start using standard deviation with City Index today:

  1. Open your City Index account, or log in if you already have one
  2. Add some funds
  3. Choose a market to trade
  4. Select ‘Standard Deviation’ from the list of indicators
  5. Open your buy or sell position

Alternatively, you can practise trading with a cost-free City Index demo account. You’ll get full access to our platform, preloaded with virtual funds. So, you can test out your trading strategy with zero risk.

Standard deviation formula

The formula for calculating standard deviation looks like this:

standard deviation formula

Trading strategies with standard deviation

Standard deviation can be used on its own to measure volatility in a market, but it is also used in the calculation of several other indicators to give a more comprehensive analysis. Below, we go through several ways you can apply standard deviation to your trading plan.

However, like other measures of volatility, standard deviation does not differentiate positive and negative deviation in its calculation. So, a high deviation could be from a market outperforming its average or underperforming. 

Risk assessment

Standard deviation is a key tool for measuring volatility, which is a crucial factor in assessing risk. A higher standard deviation indicates greater price swings and potential losses. For example, commodities will typically have higher standard deviations while a balanced stock index will display less deviation.


Diversification is a strategy aimed at reducing risk by investing in a variety of assets. Standard deviation plays a role here by allowing investors to compare the volatility of different assets in their portfolios. A well-diversified portfolio consists of assets with varying standard deviations to mitigate the impact of a single highly volatile asset.


Some traders specialize in volatility trading, which involves profiting from price fluctuations regardless of the market's direction. Volatility trading strategies often rely on options and derivatives, and standard deviation is used to assess the expected magnitude of price movements.

Stop loss and take profit orders

You can use standard deviation to place appropriate stop loss and take profit levels. A high standard deviation might require wider stop loss and take profit ranges to account for the asset's volatility, while a lower standard deviation might require tighter ranges.

Bollinger Bands

Other technical analysis indicators like Bollinger Bands incorporate standard deviation to make trend predictions based on price momentum. Using this information, Bollinger Bands can help identify potential trend reversals and breakout points.

Bollinger Bands consist of a moving average line and two lines plotted above and below the moving average at a certain number of standard deviations. The ranges indicated by standard deviations suggest when a market is overbought or oversold compared to its average price. 

Mean reversion

Mean reversion is a trading theory in fundamental analysis that posits the price of an asset will revert to its historical mean, or equilibrium. Standard deviation aids in identifying situations where an asset's price has deviated significantly from its mean, potentially signalling an opportunity to enter a trade based on the assumption that the price will revert to its average.

Detecting flat markets

Standard deviation can be used to gain insight into what is causing a flat market. Flat markets are often caused by low trading volume, but they can also exist in markets like indices where different assets performing both positively and negatively cancel each other out. While you typically want to avoid a flat market with little trading volume, a flat market with high volume may be poised for a breakout.

Downsides of standard deviation

We’ve covered a lot of ways standard deviation can be used to improve your trading strategy, but there are a few pitfalls to watch out for when using standard deviation. For one, standard deviation doesn’t indicate which direction the price is moving. A stock can perform exceptionally compared to past performance, and another can do poorly, but both could display the same degree of variation.

In addition, a single outlier can have a strong impact on the average mean, making the standard deviation seem more severe than it would be if that one data point was removed. When using standard deviation, you should keep in mind that the indicator gives more weight to extreme values. 

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