Diversification does not do what you think inside one account

Splitting risk across uncorrelated strategies is real and large. Adding strategies to an account is a different thing entirely, and it makes the drawdown worse.

This is the first objection we get, and it deserves a straight answer: doesn't running several strategies in one account reduce the drawdown?

Partly yes. We are going to concede that before arguing with it, because the honest version is more useful than the convenient one. None of what follows depends on whose strategies they are. Ours, someone else's, or three you wrote yourself — it is arithmetic about a sum.

Where the received wisdom is right

If you hold your total risk fixed and split it across uncorrelated strategies, the protection is real and large. What ends an account under a trailing limit is the range of the equity path — the fall from a running high to the next trough — and range scales with the square root of variance. Split one risk budget four ways and you cut variance while keeping expected return.

Simulated. One account, a $2,000 trailing limit, 250 trading days, $400 of risk per day held constant and divided between strategies. Probability of breaching:

99.5% — all $400 in one strategy
0.5% — $100 each in four uncorrelated strategies

So when someone tells you diversification lowers drawdown, they are not making it up. On that arrangement it is overwhelming.

Two reasons you will not get that arrangement

1. You cannot actually split the risk

That result depends entirely on holding total risk constant — on each new strategy making the others smaller. In practice nobody re-sizes. They add.

And on a small account they often cannot re-size even if they want to, because the contract is the floor. If one micro contract is $200 of risk, you cannot run four strategies at $100 each. There is no such thing as a third of a contract. Every strategy you add puts another $200 on the account whether you intended it or not.

Simulated — same setup, but each added strategy keeps its full size:

99.5% → 99.8% → 100% for one, two and four strategies.

Adding is not diversifying. On a $2,000 allowance, “diversify” and “size down” are in direct conflict.

2. The correlation you assumed is not the correlation you get

The 0.5% figure assumes genuine independence. Push the correlation to 0.7 and four strategies breach 62.8% of the time instead of 0.5%. Push it to 1.0 and the benefit is gone entirely.

Strategies on related instruments drift toward moving together under stress — which is precisely the day the limit gets tested. Correlation measured on a calm backtest systematically overstates the protection you will actually have.

What it looked like on our own engines

We ran a block bootstrap on five of our engines against a $2,000 trailing limit, each at its normal size, which is the way people really combine them.

Probability of breaching a $2,000 trailing limit

1.3% – 30.1% — each strategy, alone in its own account
74.7% — the same five, sharing one account

Worse than the worst of them individually, because nothing was re-sized. That is the experiment almost everyone actually runs.

So we did not throw diversification away. We moved it.

It belongs across accounts, where each strategy gets its own allowance, its own limit, and its bad hour cannot reach the others — and where adding one does not silently enlarge the position the others have to share.

One strategy per account is not naivety about portfolio theory. It is what portfolio theory gives you once the constraint is a hard floor you cannot fall through and a contract size you cannot subdivide.

There is a real exception, and it is worth stating because it cuts against our own product: on your own capital, none of this applies. No trailing threshold, no evaluation, no firm. Several engines in one account genuinely do net against each other there, and the diversification benefit is the real one.

Simulations: one account, $2,000 trailing limit, 250 trading days, correlated daily outcomes, intraday paths modeled so the account experiences the sum of open positions moment to moment. Ruin figures from exact lattice computation, costs excluded — commissions and slippage make every number worse. The formal treatment of shrinking size as a drawdown floor approaches is Grossman & Zhou (1993), Optimal Investment Strategies for Controlling Drawdowns.