Standard Deviation

The standard deviation is a measure of volatility. It is commonly used to measure the volatility of investments (i.e., stocks). Volatility is associated with the riskiness of an investment. The higher an investment’s volatility, the higher its risk and vice versa. Investors generally prefer lower risk (lower volatility) investments. The standard deviation is a statistical measure of dispersion relative to the mean. It can be calculated by taking the square of variance based on each data point relative to the mean. To perform the calculation step-by-step for a stock, add up its returns across a period of time (i.e., monthly returns across 6 months) and divide by the number of observations to get the historical return. Subtract those returns from the average, square them, and add up those results. Now divide that sum by the number of observations minus one. Finally, take the square root of the last result to get the standard deviation.

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