# 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...

(A) More eager to buy B, because it adds some diversification.

That is: $\sigma_{A+B} - \sigma_B < \sigma_A$

(B) Less eager to buy B, because you already have correlated exposure to A.

That is: $\sigma_{A+B}^2 - \sigma_B^2 > \sigma_A^2$

(C) Something else?

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