The Workshop · The Math · trading in probabilities · lesson 7 of 10
The same rules at half size and at double size are three different products.
These are the desk's own rules: the Bernoulli generation, replayed month by month since 2019 after average trading costs (2 bps a side on a stock, 1 on a fund, included for fairness; yours vary by broker), against the S&P 500 over the same months. The same replay, with the first generation beside it, is drawn on the engine page. The slider scales the book, half size, full size, double. Nothing else changes: same trades, same exits.
| book at 1.0× | S&P 500 |
|---|
At 1× the book returns less than the index with far less swing. Around 1.6× it matches the index's volatility and beats its return with a worst drawdown less than half the size. Push to 2.5× and the return keeps rising, and so does the drawdown, and so does the interest bill, and the summer of 2026 becomes a fall you would have felt in your sleep.
Fact. This is how professional desks pursue return: a proven ratio, scaled. A 1.0-Sharpe book at 12% volatility is an asset; a 0.5-Sharpe book at 20% is the index with extra steps. Leverage does not create edge, it multiplies whatever is there, including the bad months. Every number here is a replay; the live record on the engine page is the one that counts.
Three places. Borrow costs and margin calls are real above 1×. The replay assumes fills at the close; size adds slippage. And the worst drawdown in a replay is the worst so far, not the worst possible, every strategy's true worst drawdown is still ahead of it. Size to the drawdown you can hold, then halve it.
Your account size and per-position percentage in Account are this dial for your own book: a full line is account × percentage, so 5% is twenty slots, the same shape as the house. Raise the percentage and every line sizes up together; the closed view shows your worst drawdown beside your return so you can see what the dial cost.
Keep this: seek return by scaling a stable engine, never by loosening its rules, and size to the fall, not to the gain.
The Workshop is education, not advice. Replayed numbers are averages over many trades, after average trading costs (2 bps a side on a stock, 1 on a fund, included for fairness; yours vary by broker and liquidity) unless stated, and are not forecasts; the live record is on the engine page. Analytical tools and historical measurements for educational and informational purposes only; not investment advice or a recommendation. Replayed figures are hypothetical: today's rules applied to past prices, after modelled costs, and no account was traded on them. Hypothetical results have inherent limitations and do not represent actual trading. Past performance, including backtested results, does not guarantee future outcomes. Trading stocks involves substantial risk of loss. About · Support · Terms · Privacy · Refunds Open the deskManualThe EngineChangelog