Standard Deviation and Mean

What is Standard Deviation and Mean? How can these arithmetic formulas help with your own portfolio or selection of stocks?

DEFINITION of 'Standard Deviation'

1. A measure of the dispersion of a set of data from its mean. The more spread apart the data, the higher the deviation. Standard deviation is calculated as the square root of variance.

2. In finance, standard deviation is applied to the annual rate of return of an investment to measure the investment's volatility. Standard deviation is also known as historical volatility and is used by investors as a gauge for the amount of expected volatility.

Standard deviation is a statistical measurement that sheds light on historical volatility. For example, a volatile stock will have a high standard deviation while the deviation of a stable blue chip stock will be lower. A large dispersion tells us how much the return on the fund is deviating from the expected normal returns.

Applying asset class returns to this curve, it is accepted that 68% of the returns will fall within one standard deviation of the mean, which is between -1% and 1%. It is then accepted that 95.5% of the returns will fall within two standard deviations of the mean, a range of -2% and 2%. Finally, with the tails included, 99.7% of the returns fall between -3% and 3%, or within three standard deviations of 0%.

DEFINITION of 'Mean Reversion'

A theory suggesting that prices and returns eventually move back towards the mean or average. This mean or average can be the historical average of the price or return or another relevant average such as the growth in the economy or the average return of an industry

To summarize with an example - The Rubber Band Effect

Markets tend to overshoot, similar to a rubber band that’s stretched to its extreme and snapped back to its normal tension; so, too, do the markets. In mathematics, it’s known as reversion to the mean. This theory is based on a phenomenon stating that when the price of any market deviates substantially away from its medium price, the odds are enhanced that it will revert or move back towards the average. This pattern is repeated quite often in the markets and is extremely worthwhile in identifying, as it may uncover some very attractive risk/reward opportunities.