# Units of Risk: Variance vs Standard Deviation

Suppose you are trading two mean-reverting assets, A and B, and that $Covar(A, B) > 0$. You are currently long one unit of A, and are considering buying one unit of B. Compared to the situation where you have no position, should you be...

That is: $\sigma_{A+B} - \sigma_B < \sigma_A$
That is: $\sigma_{A+B}^2 - \sigma_B^2 > \sigma_A^2$
If (B), then why do people use $2\sigma$ as a rule of thumb for entering a spread rather than $X \sigma^2$ ?
• I donlt understand the question. A spread bigger than $2\sigma$ where $\sigma$ is the standard deviation of the spread (not of a A's return or B's return) only occurs 5% of the time, so its a rare situation that warrants going long one stock and short the other in the hope that the spread will mean revert. – noob2 Jun 27 '17 at 18:40
• Suppose that normally you would enter the B spread at $2\sigma$. Are you saying that you wouldn't change that entry point regardless of any other correlated position you hold? (Edit: Or equivalently, you wouldn't change the size of B you would want to put on at $2\sigma$?) – Thomas Johnson Jun 27 '17 at 18:44