When I say limiting trades, I mean naively saying 'I will have at most x positions outstanding'. Each trade has an associated risk (variance), that interacts in complicated ways in a portfolio, which I'm sure you know.
silly example, 100 small positions could be less risky than 1 large position or, 1 long, and 1 short trade will cancel each other out and create a riskless portfolio (with 0 return).
You need to have a risk budget, account for each trade, and work out the risk for the composite portfolio. Obviously this is not fool proof, but it's a way better approximation of the real world.
> interacts in complicated ways in a portfolio, which I'm sure you know.
Yes. And assumptions about this are bound to break at the most inopportune moment, see e.g. AIG, which I already referred to. Read about the "copula model" disaster, as your statement indicates you are unaware of its details. https://en.wikipedia.org/wiki/David_X._Li#CDOs_and_Gaussian_...
> 1 long, and 1 short trade will cancel each other out and create a riskless portfolio (with 0 return)
This is true if and only if the long and short are in the same exchange, AND exchange rules allow netting long vs. short deterministically. Otherwise, you have counterparty risk. E.g., you can be long SPY and short SP contract (in equal underlying), which would theoretically mean your only exposure is interest rate changes (and sometimes not even that!)
However, since this is in different exchanges, it might happen that during a flash crash, your SPY position will be liquidated for insufficient margin at a low price, but then the price bounces back, and you've lost money on a perfectly hedged position.
OP's model (limiting exposure and assuming the worst, if I understand correctly) is not statistically efficient use of margin, but it's way better at actually managing risk than any statistical model.
silly example, 100 small positions could be less risky than 1 large position or, 1 long, and 1 short trade will cancel each other out and create a riskless portfolio (with 0 return).
You need to have a risk budget, account for each trade, and work out the risk for the composite portfolio. Obviously this is not fool proof, but it's a way better approximation of the real world.