*Standard deviation* is a term derived from the statistical branch of mathematics and is a method used to describe the distribution of a set of data values. Standard deviation ascribes a value to how spread out the distribution of those values are from the mean value for the data set. The greater the standard deviation, the more widely spread the values in the data set are. The lower the standard deviation, the more narrowly spread the values are.

This article will discuss the Standard Deviation indicator, which applies this statistical concept to Forex and other financial prices in order to reveal details about market volatility.

### Standard Deviation in Forex and Finance

Specifically in the world of financial markets, standard deviation is used as one of several ways of quantifying volatility, and, therefore, risk. Do bear in mind, when we talk about volatility, that it is a term with multiple meanings. To read more about volatility in general, and the various different ways of defining it, have a read through our article that discusses Using a Forex Volatility Indicator.

Why Care About Volatility?

Fund managers are very interested in volatility, and therefore standard variation, as a means of making a more like-for-like comparison of different funds and their continuously compounded returns over a set period of time. When comparing managed funds, one of the most common measures is the *Sharpe ratio*. The Sharpe ratio takes the differential return for the investment (that is, the return of the investment minus a risk-free rate of return) and divides it by the standard deviation of the returns being measured. This form of standard deviation investing allows pensions funds to compare different mutual funds by adjusting for risk. Long-term investors also care about volatility because it is a useful guide to help guide expectations of how losses may swing against you over the life of an investment.

When it comes to Forex trading, how widely prices are ranging from the mean price over a time period is useful for a number of reasons. It can inform a trader's thinking on how close or far to place a stop-loss, or provide clues on whether prices are breaking out of a range or about to return towards a recent mean.

If the standard deviation for a currency pair is large, then price values are scattered and the price range is wide. In other words, volatility is high. For a low standard deviation, prices are less scattered and volatility is low.

So the Standard Deviation indicator is basically a volatility indicator. For Forex traders, the effect of volatility is double-edged: greater volatility offers greater opportunity for profit, but also greater risk of prices moving against you. Really, how much volatility you want as a trader depends on your style of trading. A swing trader will actively seek out more volatile markets, as steeper fluctuations in the price allow for substantive profits over shorter periods. A trader using a long-term, trend-following strategy would prefer a less volatile instrument, as the 'noise' of price fluctuations may make trends harder to recognise and less smooth of a ride when holding a position.

So how do we actually calculate the standard deviation for a group of prices?

### Calculating the Standard Deviation

There are a number of steps involved in calculating the standard deviation of a price set. These steps are as follows:

decide on a specific window of observation (for example, 20 periods); calculate the average (arithmetic mean) for prices over the course of the window; calculate how much price for each period deviates from the mean (that is, price – mean); square the deviation values from step 3; sum the values from step 4; divide by the number of periods to give the*variance*; take the square root of the variance to give the standard deviation.

We can sum this all up with the standard deviation equation for N periods:

= i=1N[x - x]2

Where σ is the standard deviation, xis the price, and x is the mean of the price values. This standard deviation formula is the method used by the indicator in MT4.

The Standard Deviation indicator, therefore, looks at prices over a given number of periods and plots a histogram that represents the standard deviation for the window of observation. The window of observation is constantly moving as time progresses, the earliest data point being ousted by a new one each time we get a new price bar. This allows us to see at a glance how volatility has been changing with time for our instrument of choice. Furthermore, it also helps us to shape our expectations for the future of that instrument. Let's take a look at using the Standard Deviation indicator in MT4.

### Using the Standard Deviation Indicator in MT4

The Standard Deviation indicator is one of the tools that come bundled as standard when you download MT4. The standard indicators in MT4 are divided up into four broad categories of *Trend*, *Oscillators*, *Volumes*, and *Bill Williams*. The Standard Deviation indicator is labelled in MetaTrader 4 as a trend indicator and you will therefore find it in the *Trend *folder within the *Navigator*, as shown below:

*Image source: MetaTrader 4 platform, 11 September 2017*

Bear in mind, that although it's designated here as a trend tool, it is one of the key volatility indicators in MT4. You can also see in the screenshot above the parameters that you are able to set. The default period is 20, and it is applied as default to *Close* (closing price of each bar). A variety of other price values can be used, including open, high, low, or median. The default method is *Simple*, which refers to the averaging method. A number of other averaging methods are available, including exponential. As you can see, there are a large number of variations that you can play around with, but the default values are always a sensible place to start.

Shown below is the Standard Deviation indicator added to an hourly USD/JPY chart. The Forex standard deviation values are shown by the green histogram plotted below the main price chart.

*Image source: MetaTrader 4 platform, price data from Admiral Markets, hourly USD/JPY chart, 4 September 2017 to 11 September 2017*

In the green histogram above of standard deviation for USD/JPY, we see that the highest value over the whole chart is lower than 0.5. In other words, prices were not particularly volatile over the observed period. If prices start to move enough to push the indicator up above 1.0 standard deviations, we should start to take notice. This is a significant price move, suggesting above-average strength or weakness.

How can we use this?

In statistics, we expect in a normal distribution to see around two-thirds of values varying by less than one standard deviation from the mean. Around 95% of all values vary by less than two standard deviations and nearly all values lie within three standard deviations of the mean. Now, we cannot say that prices traded for an instrument obey a normal distribution. However, there may be times when it is a reasonable assumption, for example, in a market moving sideways, when short-term price fluctuations are effectively random. In such a circumstance, you might assume reversion to the mean to be a likely behaviour and trade accordingly. Of course, different traders may use the same information in different ways, according to their trading styles. A trend-following trader may look at a high standard deviation value and see it as a possible formation of a new trend, as prices break out of the old range.

The use of standard deviation as a standalone indicator is somewhat limited though, and there are more applications when using it as building block in combination with other tools. For example, standard deviation is used as a key part when constructing the Bollinger Bands, probably the most famous type of volatility channel indicator. With this indicator, a moving average acts as a centre-line and then volatility channels – the Bollinger Bands – are plotted a number of standard deviations above and below.

John Bollinger, who invented the indicator, suggested that when bands narrow, there is a high chance of a subsequent spike in volatility. Trend-following traders also use the bands as a breakout signal.

There are plenty of other ways in which you could use standard deviation in combination with other indicators. For example, you could use a trend-confirming tool, such as a moving average or moving averages, to establish the overall trend as a first step. You could then use the Standard Deviation indicator as a second step, trading on the basis of reversion to the mean — but only when such a trend was in the direction of the larger trend. Really, there are an almost endless number of permutations you can choose to put into practice.

Whatever you do decide, you can optimise your choice by expanding the number of indicators at your disposal. MetaTrader 4 Supreme Edition is a custom plugin that makes available a larger number of tools all in a single, free download.

So is the Standard Deviation indicator a tool you should be using? Well, the ultimate judgement on this should come down to what is effective for you in practice. The best indicator of market volatility may differ from trader to trader according to their own experiences and needs. So, try it out with our Demo Trading Account and see how it goes for you. All the other volatility indicators in MT4 can be used in our demo account with real market prices, but without any risk, making it the perfect environment for trying out trading strategies.

### Standard Deviation Indicator Conclusion

If you're looking for something that is easy to use and understand, Standard Deviation is one of the best volatility indicators you'll find in MT4. It uses well-established statistical theory to calculate its values and helps you easily see whether volatility is high or low.

We hope you enjoyed this discussion of the Standard Deviation indicator. If so, you may also like our article on Getting To Grips With The Most Volatile Currency Pairs.