position sizing when you have short positions in your portfolio

Benoît Zuber

I have a conceptual question regarding position sizing. So far I have not been margin trading. I have calculated new position sizing as a function of my account value. Namely I have sized each position to risk 0.2 % of my account value.
Now I want to add shorting to my strategy. I am not too sure how to calculate new position sizing if I have some short positions in my account. Let us take an example.

I start with $1000 cash. My account value is therefore $1000.
Then I get a short position for $400 of asset A.
My new account value is $600, and my new cash value is $1400.

Let us now consider that I want to get a long position of asset B. If I bought it before I shorted asset A, asset B position size would have been, say, $200.
If I bought i after I shorted asset A, asset B position size would have been 200*600/1000 = $120.

Do you guys think this is the right thing to do, or should I have bought in both cases for $200 of asset B? If you think the latter is better, how would you calculate position sizing? would you calculate it as a function of (account value + absolute value of all short postions) ?

Thanks