Volatility is a time-based statistical measurement of price variation for an investment. It can be used to quantify the level of uncertainty or risk for price changes of an investment. Commonly speaking, the higher the volatility, the riskier the investment.
Volatility is a non-directional measurement of dispersion. Investments with similar expected returns can have different volatilities, meaning one would fluctuate by a larger amount over the same time period.
Historic volatility is calculated using price information from previous time periods.
Implied volatility is calculated using price information for derivative investments, and is used to approximate an option's value.
The standard deviation of the return rate is the difference between the actual value and the average value.
The reason people like to use standard deviation as the measurement of volatility is that it is relatively easy to calculate. However, it may not accurately measure the risk since it is based on the assumption that investment performance data follows a normal distribution.
In practice, this is not always true. Historical data shows that most investment returns have skewness or kurtosis, meaning that investment performances have exhibited many periods of extremes, both positive and negative.
Skewness is when the return of investment is asymmetrical, but it tends to have abnormally high and low periods of performance.
Kurtosis describes if the returns all cluster near the mean or toward the tails of the distribution. In certain types of investments, such as a retirement savings account, investors want to have as little uncertainty as possible, meaning they want the returns to be clustered around the average return.
Heteroskedasticity occurs when the variance of a dataset is inconsistent over time. When the time period used to calculate the standard deviation changes in length or period, the standard deviation fluctuates.
All of the above may cause confusion about the unrealized volatility of an investment, meaning the true risk may be higher than the anticipated risk.