Standard Deviation
Standard deviation is a statistical-based index that shows the dispersion of data sets relative to the average value. It is calculated as the square root of the dispersion by determining the deviation of each data from the average.
The farther the data points are from the average value, the higher the dispersion of the data set. The greater the data spread, the higher the standard deviation.
Understanding Standard Deviation
The standard deviation is statistical financial measurement data. If you apply it to the annual rate of investment return, you can trace the volatility of that investment. An increase in the standard deviation of securities affects an increase in the difference between each price and the average. This indicates a larger range of prices. For example, the dispersion of blue-chip stocks is usually quite low, while volatile stocks have a high standard deviation.
Standard Deviation formula
To determine the standard deviation, you should first calculate the value when comparing data points to the average of the population, and then extract the square root from it. The formula as follows:
xi – the value of the ith point in the data set;
x – the average value of the data set;
n – the number of data points in the data set.
Standard Deviation calculating algorithm:
1. To calculate the average of all data units by summing up all of them and dividing them by the data point number.
2. To calculate the dispersion for each data unit by subtracting the average from the data point value.
3. To square the dispersion of each data unit (from clause 2).
4. To sum the squared dispersion values (from clause 3).
5. To divide the sum of squared dispersion values (from clause 4) by the number of data points in the data set minus 1.
6. To take the square root of the result (from clause 5).
Using Standard Deviation
The main useful data for investments and trading strategies are the volatility of the market and securities. Using the standard deviation, investors can measure them and predict trends. For example, an index fund has a small standard deviation in comparison with its benchmark index, because the fund tries to duplicate the index.
Another thing to keep in mind is that aggressively growing funds will have a higher standard deviation in comparison with the relative stock indexes, because their portfolio managers are trying to get above-average profitability, so they make aggressive bets.
A low standard deviation is not always a good thing. It often depends on the investment and the investor's decisions to take the risk. A portfolio's tolerance for volatility and investment purposes determine the deviation value. If the volatility of investment instruments is above average, then this strategy is specific for aggressive investors. If an investor is more conservative, he or she needs investment instruments with average volatility.
Analysts, advisors and portfolio managers use a standard deviation as one of the main risk indicators. Mutual funds share data on investment firms' standard deviations. The deviation of a fund's return from the expected normal return is shown by the dispersion. These statistics are always available to investors and end clients.
Standard Deviation vs. dispersion
The standard deviation is the dispersion square root. It is easier to understand and apply. Standard deviation has units as the data. It is not always typical for a dispersion. Standard deviation can show statisticians a normal curve or other mathematical dependence.
The dispersion is taking the average of the data points, subtracting the average from each data point individually, squaring each of those results, and then taking another average of those squares. The dispersion is needed to determine the spread of the data compared to the average value. The closer the data values are to each other, the smaller the dispersion. The greater the dispersion, the greater the spread in the data values. The range between two data values may also be larger. This indicator is a bit more difficult to understand than the standard deviation. Dispersion cannot be meaningfully expressed on a graph of the original data set. It is the value of the squared result.
If 68% of the data points belong to the standard deviation from the average value, or the midpoint of the data, then this is an indicator of the data's normal curve behavior. The larger the deviations, the more points are not under the standard deviation. The smaller the deviations, the more data points are located close to the average.
