# How to Use Standard Deviation for Profitable Investing

A stock price fluctuates up and down based on the company or economic news. It is difficult to ascertain with a high accuracy in the long-run the probable direction of a stock price. However, you can make some possible profitable investment decision in a short term time frame using standard deviation. Standard deviation shown as Sigma is a measure of variability or dispersion of a data point from the mean or average of a set of data or time series. A high value denotes more variance from the mean. Conversely, a low number indicates the closeness of a data point from the mean or expected value.

If you assume a stock’s closing prices are random and submit to a normal distribution, then you can utilize stock price vacillations around its mean to make some profitable trading decisions. Standard deviation which is expressed as the same unit of the data set, can project probability of a stock price movement around its mean price. For instance, if the mean of closing prices for stock A is \$25 and its sigma is \$1, then one sigma indicates 68 percent of probability that the next closing price may be between \$24 and \$26. While two sigmas projects with 95 percent probability that next closing price may be at \$23 to \$27. Finally, three sigmas states with 99 percent probability that the next closing price can be between \$22 and \$28.

You may use this information about a stock closing price in three different techniques to make some possible profitable investment decisions; to purchase a stock to initiate a new long position, to sell your holding position to exit a profitable investment, and to protect your position by placing a stop loss order.

Consider the above example, stock A with an average daily closing price for \$25 in the past year. When the stock price sells off to two sigmas below the mean price to \$23, you may initiate a buy order and purchase the stock. To protect your position against a possible loss due to a downward move, you can place a stop loss order to sell your stock at \$22 which is three standard deviations away from the mean. Accordingly, you can place a sell order to exit some of your long position at your first profit target which is \$25, the average price. You may sell all of your holdings at \$27 or even \$28 price levels which are two and three sigmas respectfully.

It should be noted since stock closing price gyrates up and down on a daily basis; you should monitor its daily move and adjust your stop loss or target profit accordingly.

If you have a high risk tolerance for aggressive trading, you may use standard deviation method to short sell a stock. By short selling a stock you hope to buy back the stock at a lower price for a profit. In other words, if a stock is in a downward trend you look to short sell the price when it moves up to unusual price levels like two or three standard deviations above its mean. If you short sell a stock at two standard deviations price level, then you may place your stop loss order at the price corresponding to three standard deviations. Accordingly, your target profits can be at the average price level or one or two standard deviations below its mean.

Many internet financial website which provide live data and charts for stocks, let you use different technical indicators. Bollinger Bands is a technical indicator developed based on standard deviation concept. However, it uses a simple moving averages to replace the mean value. Accordingly, you can adjust the outer bands around the moving averages value to one, two, or three standard deviations. Conversely, if you like to utilize all three standard deviations, you may insert the same indicator into your stock price chart three times and change the bands for one, two and three standard deviations values.

To augment your trading decisions for better accuracy and higher winning probability for using standard deviation method, you may use another tool like 50 or 200 days moving averages. For instance, if stock price is above its 50-day moving averages, then you may attempt to purchase the stock at two standard deviations below its daily mean price. However, if the stock closing price falls below the 50-day moving averages, it may signal the beginning of a trend reversal. Accordingly, you should be very careful to purchase the stock since it may continue to sell off and keep on falling further down. Conversely, if you decide to short sell a stock then, you should use the 50-day moving averages, as an example, to confirm the downward trend direction.

It is much easier to use any spread sheet program to calculate a time series mean price and standard deviation than manually. Enter the past year daily prices of a stock, and use the program’s formulas to calculate its daily mean price and standard deviation. However, these price levels can alter depending on new daily closing prices for your stock. Nevertheless, you can add the new closing prices each day to your Excel spread sheet and obtain the new values for the mean and standard deviation. By doing so you create a dynamic flow of price levels that help you monitor and invest in the stock for better profits.

You may decide to make your trading more or less active by adjusting your time frame. For instance, if you decide to swing (short term) or day trade, then you may use different intraday periods like 30 or 100 minutes. By using 100-minute closing prices, as an example, you can apply the above method to trade your favorite stocks more frequently.