# How to determine ratios for mean-reverting basket

Suppose I have a basket of 3 securities A, B, and C. I believe that the basket is cointegrated and I want to create a mean-reverting trade. I fit the model: $\log(A)=\beta_b*\log(B)+\beta_c*\log(C)+\alpha$ where A, B, and C are the prices of the securities.

This gives me estimates of $\alpha$, $\beta_b$ and $\beta_c$.

Now suppose that I believe that the spread is out of line. I want to sell \$1 of A and buy \$1 of the B and C basket. How should I allocate that dollar to B and C? Is it simply $\beta_b*\$1$units of B and$\beta_c*\$1$ units of C or is it more complex?

Related, is it more correct to regress log prices or raw prices when fitting the model?

(I know that this is related to How to build a mean reverting basket? but the answers there weren't very detailed and this is a more specific question).

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You generally regress returns, not prices... – assylias May 2 '13 at 21:39
The classic pairs trading paper Gatev & Goetzmann 2006 regresses prices – Thomas Johnson May 2 '13 at 22:46
Can get it out with a mass simulation if you can't figure it out. – user2763361 Nov 18 '13 at 12:42