Sigma moves - annualize return or no?

CFA General
#1

This might be a very simple dumb question. But when you look at a security’s annualized volatility over a 3 year period, assuming the security has an annualized vol of 5% and the drawdown over three year period is -15%. Is it fair to say that it is a 3 sigma move or should you annualize that -15% and claim its ~ 1 sigma move?

What is the appropriate way to do this?

#2

I’d keep it consistent: annual standard deviation vs. annual return.

#3

You mean 15% drawdown in a single day? If so, let’s assume there are 252 business days in a year. A 1 standard deviation move for one day (t = 1/252) is 5%*(1/252)^0.5 = 0.31%. A 15% move is 15%/0.31% standard deviations. Adjust accordingly if the drawdown occurs over a different length of time.