Optimal f as a leverage bound for commodity account growth

Risk, exposure, and leverage

Risk is the chance of losing on a trade or a sequence of trades. Exposure is the dollar amount that can be won or lost on a position. Leverage is the control that scales exposure. It is not the futures margin deposit.

Commodity leverage is full contract liability divided by account equity: L equals N times P divided by E. Two S&P 500 contracts at 125000 each against 100000 equity give L of 2.5.

Leverage is also a compound-growth choice

Compound growth of equity with full reinvestment multiplies successive one-plus-return factors. Leverage choice is therefore a growth decision as well as a loss-size decision.

Return on equity equals leverage times the raw price change of the contract. The same 5 percent raw move becomes 12.5 percent with L of 2.5. A loss scales by the same factor.

Use one consistent track-record sample

Leverage analysis needs a consistent sample of at least 30 completed trades from one mechanical system and one market. Mixed markets, pyramiding steps, or mid-sample system tweaks confound the result.

That track-record sample of completed trades is the only input used here for leverage and simulation work.

Treat optimal f as a reference bound

The first worksheet search for a growth-maximizing leverage, shown out to a factor of 9.6 on a 30-trade series, is only a reference bound. Optimal f is the leverage or fraction of equity that maximizes compound growth of a fully reinvested trading record.

The working choice is a lower ideal L. Ideal L is selected at or below that growth-maximizing level to match personal tolerance for exposure, not to chase the single highest growth path.

Monte Carlo tests sequence risk

Monte Carlo simulation reshuffles the same completed trades because the next result is random even when expectation is positive. Serial correlation is treated as already absorbed into the system, so the simulations test sequence risk rather than invent new trades.

Recalculate ideal L only periodically

Ideal L should be recalculated only periodically from a long-run average. Updating after every trade, padding results by marking open positions to market, or mixing paper and live rules will skew the bound.

TradersWeek editorial reading

This paragraph is an editorial reading and is not part of the archive workflow. TradersWeek reads the procedure as a way to treat leverage as a pre-trade exposure bound rather than as a margin setting. First estimate the growth-maximizing fraction from a consistent track-record sample. Then choose a more conservative ideal L. Monte Carlo paths then show how random sequencing can change, or erase, the equity path even when the same average edge is kept.