4. Quantifying Downside Risk

Standard deviation is an adequate measure of risk if the underlying distribution is normal; because the normal distribution is symmetric, the probability of observing a positive deviation from the mean is exactly equal to the probability of observing a negative deviation, equal to 0.5. In other words, half of the time we would observe negative deviations and half of the time positive deviations from the mean. If you want a measure of the negative deviations from the mean for a normal distribution, you can simply divide the standard deviation by 2.

However, the standard deviation is not an adequate measure of risk if the underlying distribution is not normal. In such cases, other measures of the shape of a distribution, such as skewness and kurtosis, will be informative in assessing risk.