Optimal f contract counts versus equity fractions

Three sizing answers, not one

Kelly criterion belongs to a related growth-oriented sizing family that uses edge and payoff information to decide how large a repeating stake can be before compounding works against the account. Optimal f is a history-dependent fraction that converts account equity and a designated worst-loss amount into a contract count, not a finished cash-bet percentage. Fixed contract sizing is a constant contract-count rule that does not automatically scale with equity, in contrast to fractional formulas that change size as the account moves.

Editorial reading: a growth fraction, a contract translation, and a fixed-contract default can look like the same entry decision, but they are answering different questions and should not be treated as one leverage rule.

The fraction moves with the sample

Optimal f depends on the largest loss seen so far and on the full trade history, so the fraction moves as those inputs fluctuate. The worst-trade loss is the largest losing result in the sample used to compute the fraction.

Using one historical optimal f does not bound the extra drawdowns that appear if later trades imply a different optimal f than the value used to size the position. Editorial reading: a historical worst loss is an unstable leverage input because the designated loss changes as the sample changes.

A contract count is not a cash bet

Optimal f is an input used to compute a contract count from equity and the worst-trade loss, not the percentage of equity to place as a cash bet. In the worked example, equity of 100000, optimal f of one-third, and a worst-trade loss of 500 imply 66 contracts after rounding down, not 3.

The unconstrained reading of that example implies a peak loss of five-thirds of equity, or 220000, in the second series, versus a 7500 figure attached to holding 3 contracts. Editorial reading: the fixed-contract reading and the unconstrained contract-count reading are not describing the same exposure.

Equalized fractions still need a conversion

Equalized optimal f restates the same sizing problem on percentage gains and losses rather than raw currency results; that number becomes an equity fraction only after a further conversion. On an equalized percentage basis, a fraction of one-third and a worst-trade return of 0.05 convert to an equity fraction of 666.7 percent, which means the position is carried on margin.

Secure f is a more conservative fraction proposed to restrain the extra equity swings that appear when a full optimal-f stake is used. The same equalized reading maps a secure-f value of 0.01 to a 20 percent equity fraction.

Proposed ways to stabilize the fraction

A proposed partial stabilizer replaces the largest loss to date with a more conservative larger loss inside the optimal-f calculation. Substituting a larger conservative loss shrinks the implied size. Another proposed stabilizer recomputes optimal f on several windows that contain the same trade count and then averages those estimates.

When cash requirements cap the count

A margin constraint is the cash that must be posted per contract, which can cap the mathematically implied count well below the unconstrained formula. An operational futures version of the contract-count formula uses the larger of the per-contract cash requirement and the worst-trade loss in the denominator, because the unconstrained count may require more cash than the account can post. Editorial reading: a futures cash requirement can make the mathematical size untradable.