The Shape of a Lognormal Distribution
Prices are said to have a lognormal distribution if the logarithm of the price has a normal distribution. To illustrate, if a stock is priced at $100 per share and prices have a normal distribution, the distribution of prices is the familiar bell- shaped curve centered at $100, but if the prices have a lognormal distribution, then it is the logarithm of the price which has a bell-shaped distribution about logn 100 = 4.6051702. The logarithm of the prices is equally likely to be 5.2983174 or 3.912023, i.e., 4.6051702 ± .6931472 corresponding to prices of $200 and $50, respectively. If the lognormal probability density curve is plotted as a function of price rather than as a function of the logarithm of price, the curve will appear positively skewed with tails more nearly depicting the observed behavior of stock prices. Lognormality arises from the process of return compounding. See also Normal Distribution, Brownian Motion, Fat- Tailed Distribution (diagram), Distribution.
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