Stock leverage from compounded returns and margin cost

How ending equity is built

With full reinvestment, ending equity is the starting equity multiplied through by one plus each trade's return on equity. Return on equity for a long stock trade can be written from share prices, commissions, dividends, holding days, and margin interest, then restated so a single leverage value can be varied.

Leverage is defined as debt divided by equity, and under a 50 percent initial margin rule the highest debt-to-equity ratio is 1, not 2. Leverage control and margin management keep that bound, and the interest and loss burden, visible before entry and throughout the position.

Completed trades, commission, and interest

A leverage study on one stock needs at least 30 completed trades. Marking unfinished trades to market is treated as an unreliable way to pad the sample.

Commission paid from equity reduces the financed share amount, so the price-to-price-plus-commission factor is always less than 1 and slightly lowers the interest charge.

A fully leveraged one-year long that rises 5 percent while margin interest is 10 percent produces a zero return on equity once interest is deducted. In the worked long-only example, adding commissions and dividends cut the win rate from 68 percent to 49 percent, while the unlevered average trade return stayed positive, which the compounding test requires before leverage is considered.

Resampling one leverage setting

The resampling exercise used a commission-adjusted factor of 0.996, at least 70 simulated rows, and 100 collected outcomes as a practical sample for judging leverage. That check is a Monte Carlo simulation of the same completed-trade sequence.

Across those simulations, leverage was worse than cash only 4 percent of the time, and at a debt-to-equity setting of 0.75 the losing cases stayed within 10 percent of the original stake. An average equity-versus-leverage curve can look favorable while individual paths to that average remain uneven, so a leverage choice is personal rather than universal.