COMMON MISUNDERSTANDINGS OF A COMMON MEASURE

Dan Goldstein and Nassim Taleb have written a paper called “We don’t quite know what we are talking about when we talk about volatility” which looks at what finance professionals and students do when asked for estimates of standard deviation.In particular, they posed this question:

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?

Find out how many of 87 trained people got it correct.

REFERENCE:
Goldstein, D. G. & Taleb, N. N. (in press). We don’t quite know what we are talking about when we talk about volatility. Journal of Portfolio Management.

UPDATE (May 28, 2007): The aforementioned paper has hit #1 on the SSRN Recent Hits list.