Risk and Return Measures - Distribution of Returns
Statistical Risk Measures
- Normal Distribution - A symmetrical return distribution, its mean and median are equal, approximately 68% of its observations lie between plus and minus one standard deviation from the mean; 95% lie between plus and minus two standard deviations; and 99% lie between plus and minus three standard deviations.
- Lognormal Distribution - Closely related to normal distribution. Its use is widespread in modeling probability distribution of asset prices.
- Skewness - The statistical measure of skew or asymmetry of distributions. An asymmetrical distribution is skewed. Positive skew is where the return distribution has frequent small losses and a few extreme gains; negative skew is the opposite.
- Kurtosis - The statistical measure indicating when a distribution is more or less peaked than a normal distribution.
- Mesokurtosis - a normal (symmetrical) distribution.
- Leptokurtosis - where the distribution of returns is more peaked than normal, i.e. returns cluster closely around the mean.
- Platykurtosis - a less than normal peaked distribution, e.g. returns are dispersed more widely around the mean.