In general, investors prefer positively skewed distributions over negatively skewed ones (it is much more fun to own an investment that generates a +10% return versus an investment that delivers say a negative 40% return. See, positive distribution is all the rage.) Also, when it comes to kurtosis, the fatness of the tail, investors prefer a lower likelihood of jumps (lower kurtosis) than an investment with a higher likelihood of skipping around (higher kurtosis).
And now, just for the hell of it, standard deviation:
An investment with an average return of 5%, a standard deviation of 7% and a variance of 40%
Definitions Just for You
Standard Deviation: “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.”[i] In a normal distribution, 68.37% of the values lie within one standard deviation, 95.45% within two and 99.73% lie within three standard deviations. For example, 99.73% of the returns would lie in the range of -16% to 26% for our investment example with an average return of 5% and a standard deviation of 7%.
Here’s the math:
7% * 3 = 21%
5% + 21% = 26%
5% - 21% = -16%
Variance, the Nerdy Math Definition: A measure of the dispersion of a set of data points around their mean value.
The Explanation: “Variance measures the variability (volatility) from an average. Volatility is a measure of risk, so this statistic can help determine the risk an investor might take on when purchasing a specific security.”[ii]
Annualized Standard Deviation = 7% x the square root of 12 = 24%
Annualized Variance = 40% x 12 = 480%
Bottom line:
“Without making comparisons to the standard deviations in stock returns of other companies, we cannot really draw any conclusions about the relative risk of [a stock] by just looking at its standard deviation.”[iii]
Semi-variance just give you the downside to the investment. In other words, it is a measurement of only the negative returns from the average return. Think of semi as semi-under average or as “Oh my god that semi is coming straight towards us and soon we will be underneath it.” In general, a stock or investment with small positive returns and large negative returns will have a semi-variance that is higher than the variance.
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