# Volatility understanding – Reality check

Taleb and Goldstein asked the following question to about 87 people that included portfolio managers, Ivy league graduates and investment professionals :

A stock (or a fund) has an average return of 0%. It moves on average 1% a day in absolute value; the average up move is 1% and the average down move is 1%. It does not mean that all up moves are 1%–some are .6%, others 1.45%, etc. Assume that we live in the Gaussian world in which the returns (or daily percentage moves) can be safely modeled using a Normal Distribution. Assume that a year has 256 business days. The following questions concern the standard deviation of returns (i.e., of the percentage moves), the “sigma” that is used for volatility in financial applications. What is the daily sigma? What is the yearly sigma?

Only 3 of the 87 respondents arrived at the correct answer for the daily sigma and none got it right for the yearly sigma.

What does that say ? Intuitive notions of volatility are incorrect. Volatility always refers to a parameter in a model. But the model being used and parameter being referred to, can be different in different contexts!