What is Standard Deviation?
Definition
Standard deviation measures the dispersion of returns around the average return. In investing, it quantifies volatility—a higher standard deviation means returns vary more widely, indicating greater risk and uncertainty.
Detailed Explanation
Standard deviation is the most common statistical measure of investment risk. For a normally distributed set of returns, approximately 68% of returns fall within one standard deviation of the mean, and about 95% fall within two standard deviations.
For the S&P 500, the annualized standard deviation has historically been about 15-16%. This means that in roughly two-thirds of years, returns have been within 15-16 percentage points of the average return. Individual stocks have higher standard deviations (25-40%+ is common), which is why diversification reduces portfolio risk.
Standard deviation is used in the Sharpe ratio (excess return divided by standard deviation) and in calculating Bollinger Bands (price bands at standard deviation intervals from a moving average). It is also a key input for options pricing models like Black-Scholes.
Limitations include that it treats upside and downside deviations equally (investors only dislike downside), assumes a normal distribution (markets exhibit fat tails), and is based on historical data (past volatility may not predict future volatility).
Formula
SD = sqrt(Sum of (Return_i - Mean Return)^2 / (N - 1))Example
A stock has annual returns of +15%, -5%, +20%, +10%, -10% over 5 years. The mean is 6%, and the standard deviation is approximately 12.6%. About 68% of the time, returns should fall between -6.6% and +18.6%.
Frequently Asked Questions
Is a lower standard deviation always better?
How does diversification reduce standard deviation?
What is the standard deviation of the S&P 500?
Related Terms
Beta
Beta measures a stock's volatility relative to the overall market. A beta of 1.0 means the stock moves in line with the market. A beta above 1.0 indicates higher volatility than the market, while a beta below 1.0 indicates lower volatility.
Volatility
Volatility measures the degree of variation in a stock's price over time. Higher volatility means larger and more frequent price swings, indicating greater uncertainty and risk. It is commonly expressed as the annualized standard deviation of returns.
Bollinger Bands
Bollinger Bands are a technical analysis tool consisting of a middle band (20-period SMA) and two outer bands set at two standard deviations above and below the middle band. They dynamically adjust to volatility, widening during volatile periods and narrowing during calm periods.
Sharpe Ratio
The Sharpe Ratio measures the risk-adjusted return of an investment by calculating excess return per unit of volatility. Developed by Nobel laureate William Sharpe, it allows investors to compare the return of different investments relative to the risk taken to achieve those returns.
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Disclaimer: The information on this page is provided for educational and informational purposes only and does not constitute investment advice. AI-generated analysis may contain errors or inaccuracies. Always conduct your own research and consult a qualified financial advisor before making investment decisions.
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