The Distribution of 
Stock Prices 
Much of the work that has been done in statistics and related areas regarding the 
stock market has made the assumption that stock prices are distributed normally, or 
more specifically, lognonnally. In actual practice, this is usually an incorrect assump­
tion. For the option strategist, this means that some of the things one might believe 
about certain option strategies having an advantage over certain other option strate­
gies might be incorrect. In this chapter, a number of facts concerning stock price dis­
tribution will be brought to light, including how it might affect the option strategist. 
MISCONCEPTIONS ABOUT VOLATILITY 
Statistics are used to estimate stock price movement (and futures and indices as well) 
in many areas of financial analysis. Many authors have written extensively about the 
use of probabilities to aid in choosing viable option strategies. Stock mutual fund 
managers often use volatility estimates to help them determine how risky their port­
folios are. The uses are myriad. Unfortunately, almost all of these applications are 
wrong! Perhaps wrong is too strong a word, but almost all estimates of stock price 
movement are overly conservative. This can be very dangerous if one is using such 
estimates for the purposes of, say, writing naked options or engaging in some other 
such strategy in which volatile stock price movement is undesirable. 
As a review for those not familiar with mathematical distributions, the lognor­
mal distribution is what's commonly used to describe stock prices because its shape 
is intuitively similar to the way stocks behave - they can't go below zero, they can rise 
to infinity, and most of the time they don't go much of anywhere. On top of that, the 
distribution's shape is based on the historical volatility of the underlying instrument. 
In a lognormal distribution (and normal distribution, too), stocks remain within 3 
standard deviations of their current price 99. 7 4% of the time. A standard deviation 
783