- 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.
Statistical Risk Measures
TradingThe entire study of statistics originated from Gauss and allowed us to understand markets, prices and probabilities, among other applications.
InvestingDiscover a few of the most popular probability distributions and how to calculate them.
InvestingCheck out how the assumptions of theoretical risk models compare to actual market performance.
Financial AdvisorAdvisors can help clients avoid required minimum distribution mistakes in their retirement plans.
InvestingThis simple ratio will tell you how much that extra return is really worth.
Financial Advisor401(k)s, pensions and profit-sharing plans can be a source of cash, but there are consequences to this option.
InvestingLearn about three ways to measure the performance of alternative investments. See how the commonly used Sharpe ratio has drawbacks in measuring volatility.