A few key concepts to take note of regarding standard deviation are:

• The standard deviation of a stock determines the dispersion of a dataset in relation to its mean.
• A high standard deviation represents volatile stocks, while a low standard deviation usually points to consistent blue-chip stocks.
• The greater the standard deviation, the riskier the stock.

What Is the Standard Deviation of a Stock?

The standard deviation is a statistical measurement that analyzes the dispersion of a dataset in relation to its mean. It’s quantified as the square root of the variance. To calculate the standard deviation as the square root of the variance, the variation must be evaluated between the various data points in relation to the mean. When the data points are a greater distance from the mean, the dataset has a higher deviation. In other words, the more scattered the data points, the higher the standard deviation.

When using the standard deviation in a financial setting, such as applying it to stock market returns, it can assist in providing insight on past volatility of that stock. When the standard deviation is higher, it points to a larger variance between the stock’s prices and the mean. This points to a more vast price range. For example, a high standard deviation will appear for volatile stocks, while a lower standard deviation is present in stocks that are more consistent

Calculating the Standard Deviation of a Stock

When calculating the standard deviation, you first need to determine the mean and variance of the stock. To calculate the mean, you add together the value of all the data points and then divide that total by the number of data points.

To determine the variance, you take the mean less the value of the data point and square each individual result. Then you add up the squared results for one single total, which is then divided by the number of data points minus one. This result is known as the square root of the variance. This result is used to calculate the standard deviation. While these calculations can be completed on paper, the easiest way to perform them is by using Excel.

When it comes to stock prices, the data set is viewed in dollars and the variance in dollars squared. The standard deviation comes into play because dollars squared is not a helpful unit of measurement. In calculating the standard deviation of the stock, you get the square root of the variance, which returns the value back to its original form, making the data much easier to apply and evaluate.

Standard Deviation Risk

When it comes to stock returns and investments, the standard deviation is used to determine market volatility and, therefore, risk. A higher risk stock will demonstrate an unpredictable price and a wider range. Stocks that stick close to their means, or range-bound stocks, are considered lower risk because investors can assume, with a fair amount of confidence, that the stocks practice a consistent behavior. When a stock has a wider range and tends to increase, decrease, or gap unpredictably, it’s viewed as a higher risk stock with the potential for a more significant loss.

While a greater risk can sound intimidating, it’s important to remember that when it comes to the stock market, risk isn’t necessarily a bad thing. The greater a stock’s risk, the greater the possibility of a hefty profit.

The use of standard deviation to determine risk in the stock market is applied assuming that most of the market’s stocks’ price activities follow a normal distribution pattern. When stocks are following a normal distribution pattern, their individual values will place either one standard deviation below or above the mean at least 68% of the time. A stock’s value will fall within two standard deviations, above or below, at least 95% of the time.

For instance, if a stock has a mean dollar amount of $40 and a standard deviation of $4, investors can reason with 95% certainty that the following closing amount will range between $32 and $48. This also means that 5% of the time, the stock’s price can experience increases or decreases outside of this range. When the stock’s standard deviation is high, it is most likely a highly volatile stock. When its standard deviation is low, it’s usually a reliable blue-chip stock.

In taking all this to mind, investors can assume that a low standard deviation points to a less risky investment, while a greater variance and standard deviation reflects a higher risk stock. While 95% of the time, investors can reasonably assume that a stock’s price will stay within two standard deviations of the mean, this is still a decent-sized range. The key idea to remember is that more potential outcomes, the more potential risk.

Standard Deviation Investments

Standard deviation in investing usually appears in the likeness of Bollinger bands. Bollinger bands, created by John Bollinger in the 1980s, are a number of lines that assist in determining trends in specific stocks. The exponential moving average (EMA) is found at the center of these trend lines, and it shows the average price of the stock over a given period of time. The lines on both sides of this center range anywhere from one to three standard deviations away from the mean. When the stock’s price changes, the outer trend lines also change with the moving average.

While Bollinger bands can be applied in many useful ways, they are commonly used to determine the market’s volatility. Whenever a stock tends to experience significant volatility, the bands will appear further apart. When the volatility lessens, the bands will fall closer together and appear nearer to the exponential moving average. It’s not uncommon for charts that typically see narrow bands to experience random spikes in volatility — for example, after earnings reports or products are released.

A Bollinger band can be a useful chart in investing because it provides a visualization of the standard deviation and makes the identification of highly volatile stock as easy as a quick glance.

Applying the Standard Deviation of a Stock

Standard deviation can be used throughout the financial world, but it is especially useful when it comes to investing in stocks and determining trading strategies. The use of standard deviation assists in measuring the volatility of the market and stocks as well as predicting stocks’ performance trends.

When it comes to investing, investors can reasonably expect an index fund to have a low standard deviation because the whole goal of an index fund is to match the index. Conversely, investors can expect an aggressive growth fund to have a higher standard deviation compared to standard stocks because the whole point of these funds is to generate exceptionally high returns.

There isn’t necessarily a better level of standard deviation. Some investors may prefer a low standard deviation, while others are attracted to stocks with a high standard deviation. The preferred standard deviation simply depends on the type of investment investors are looking for as well as the amount of risk they are willing to accept. When it comes to applying the standard deviation of a stock to a portfolio, investors should determine how much volatility they are comfortable with as well as their ultimate investment goals. Aggressive investors are typically more eager to take on high volatility stocks, while the more reserved investors tend to avoid them.

Analysts, advisors, and portfolio managers all use standard deviation as one of their top methods of measuring risk. The standard deviation is also listed by investment firms for their mutual funds and other various products. When a significant dispersion is evident, it means that the stock’s return is not sticking to expectations. The standard deviation is a very simple statistic to understand; therefore, it is commonly reported to investors and end clients.

Each moving average looks slightly different when charted, with varying degrees of significance in regards to trading setups. Common similarities and differences include:

• Both SMAs and EMAs measure stock trends.
• Both SMAs and EMAs are interpreted in the same way.
• Technical traders use both SMAs and EMAs to smooth out price fluctuations.
• SMAs give all prices equal weight, while EMAs put more weight on more recent data.
• EMAs react faster to current price changes, while SMAs are true indicators for the average price of a security over a specific period of time.

It’s important to understand moving essentials as there are many trade situations where a sell or buy signal is confirmed, supported, or triggered by this important technical indicator. In addition, the moving average is the basis for many other technical indicators and is a stock market indicator that can assist in cutting through the chaos of big price fluctuations.

What Are Moving Averages?

A moving average (MA) collects the closing price of a specific stock for a set period of time, usually over a couple of days, and then averages the price and plots it as a line on the chart. Rolling average, trailing average, and moving average all mean the same thing. Different industries will use one term over the others. While moving average is most commonly used, the rolling average is often used in statistics, while trailing average is preferred by MS Excel experts.

While common moving average collection periods are 10, 20, 50, and 200-days, modern charting software allows you to establish the number of days along with intraday periods for calculation. For example, a trader may use a nine-day moving average based on the daily close then compare it with another technical indicator, such as the volume weighted average price, to determine if a specific trade meets their criteria.

There are many types of moving average with the three most common being:

• Simple moving average (SMA) – The most common type of moving average takes the sums of past closing prices over a set period of time and divides that number by the number of data or price points.
• Exponential moving average (EMA) – This MA gives more weight to the most recent prices or data points by adding a weighted multiplier into the equation. While a little more complicated, it keeps the moving average line close to the price changes seen on a chart.
• Weighted moving average (WMA) – The weighted moving average also assigns more weight to recent data points like EMA, but the distribution of weighting is equal where with EMA, weighting is exponential.

Simple Moving Average

Simple moving average allows you to select the number of days you want within your established time period. To calculate SMA, simply add a securities closing price for the predetermined number of days, and then divide that number by the number of days in the established time period. This gives you the average price of that security for that time period.

SMA smooths out volatility and makes viewing a security’s price trend easier. When the SMA average points up, it means the price of a security is increasing, while a downward-pointing SMA indicates the security’s price is decreasing. The longer time frame a moving average has, the smoother the SMA will be. While a shorter-term MA is more volatile, it’s reading is closer to source data.

The analytical significance of simple moving averages is that they allow individuals to quickly identify uptrends and downtrends of a security. Comparing two SMAs, each covering different periods of time, is another popular analytical tool, although, it’s a slightly more complex process. When a shorter-term SMA is above a longer-term average, you can usually expect an uptrend, while a long-term average above a shorter-term average usually signals a downtrend.

The death cross and golden cross are two popular trading patterns that utilize SMAs. Death happens when the 50-day SMA crosses below the 200-day MA, this is considered a bearish signal and predicts further losses are likely. The golden cross happens when a short-term MA moves above a long-term MA. When combined with high trading volumes, this can indicate further gains are possible.

Exponential Moving Average

The most popularly analyzed or quoted short-term averages are the 12-day and 26-day exponential moving averages. Both are used to create indicators like the percentage price oscillator and the moving average convergence divergence. Likewise, the 50-day and 200-day EMAs are used as long-term trends signals. Once the price of a stock crosses it’s 200-day MA, it’s a technical indicator that a reversal has happened.

When applied correctly, traders who routinely use technical analysis find MAs very insightful and useful, however, when they are misinterpreted or used improperly, they often create havoc. All MAs routinely used in technical analysis are lagging indicators. Consequently, conclusions drawn from applying an MA to a particular market chart should be used to indicate its strength or confirm a market move.

Most often, by the time an MA indicator line makes a change, it reflects a significant move in the market, meaning the optimal point of market entry has passed. To some extent, an EMA helps alleviate this dilemma, as the exponential market average calculation places more weight on the most recent data “hugging” the price action more tightly and reacting more quickly. This is a desirable action when an EMA derives a trading entry signal.

Like all MA indicators, EMAs are better suited for trending markets. When the market is in a sustained and strong upward trend, the exponential moving average indicator line will also show an uptrend. When the market is in a downward trend, the EMA indicator will indicate the same downtrend.

A vigilant trader not only pays attention to the EMA line direction, but also the relationship between the rate change from one bar to the next. For example, if the price action of a solid uptrend starts to flatten and reverse, the exponential moving average change rate from one bar to the next will also begin to diminish until the indicator line completely flattens and there is a zero rate of change.

Due to the lagging effect at this point or a few bars before even, the price action should have already reversed. Therefore, when you observe an EMAs rate of change diminishing, it could also be an indicator that could further address the dilemma created by the lagging effect of MAs.

Exponential moving averages are routinely used together with other indicators as a way to confirm significant market moves and to determine their validity. For individuals who trade fast-moving and intraday markets, the EMA is very applicable. Usually, traders utilize EMAs to determine trading biases. For example, if an EMA shows a strong upward trend on a daily chart, the strategy of an intraday trader may be to only trade from the long side of an intraday chart.

Limitations of SMA and EMA

Both the simple moving average and exponential moving average rely entirely on historical data. Many people, including economists, believe they are efficient and the current market price reflects all available information. If this is true, historical data does not provide useful information on the future direction of prices.

Differences Between EMA and SMA

Deciding which moving average to use typically depends on the objectives and time horizons of the investor. When carefully looking at an exchange-traded fund chart or stock, many investors use the moving average as an effective tool in navigating an investment strategy. However, investors may notice slight variations between the simple moving average and the exponential moving average.

The SMA is a security’s average price over a set period of time. For example, a 20-day moving average is calculated by adding the closing prices for the last 20-days and then diving that amount by 20. This number is re-calculated as new data becomes available which makes it a “moving average.”

The exponential moving average adds another component to the process by giving more the most current prices more weight in an attempt to more accurately reflect new market data. The difference between the SMA and the EMA is most noticeable when comparing long-term averages.

The 200-day EMA reacts faster to the most current price changes in indexes including the S&P 500 due to its shorter or more responsive lag-time when compared to the SMA. However, the simple moving average is a true indicator for the average price over a specific period of time. Because of this, many technical analysts use the SMA to identify resistance or support levels.

Similarities between EMA and SMA

Simple moving average and exponential moving average are similar in that they both measure stock trends, are interpreted in the same manner, and technical traders commonly use both to smooth out price fluctuations.