From a trading goal to the conditions it would require

What would trading have to deliver to support a particular goal, and what could prevent an apparently profitable account from supporting that goal along the way?

This is a modelling note. It grows from a discussion about accuracy, earnings, compounding, and drawdown. It is separate from the seven historical studies. Its examples explain relationships; they do not report an achieved trading record.

For a simplified trade with win probability p, a win of bR, a loss of aR, and an additive cost cR, expected net R is p × b − (1 − p) × a − c. This calculation requires a full outcome definition. It does not establish the inputs or guarantee the sum over a particular sequence.

With fixed fractional sizing, account changes multiply. A profitable arithmetic average can coexist with weak or negative typical compounded growth when exposure is large. A changing risk ladder requires its own path calculation.

An uninterrupted sequence of k full losses at fixed fraction f leaves a proportion (1 − f)^k of the preceding equity, before additional cash flows. Maximum drawdown can be deeper than the largest uninterrupted losing run because partial recoveries can separate further losses.

Withdrawals add another dependency. Two sequences containing the same percentage returns can support different cash payments when those returns arrive in a different order. A terminal balance alone does not measure whether income was available when needed.

A simulation needs to specify the distribution of outcomes, their dependence, costs, sizing, cash-flow timing, and any stopping condition. An average win rate and a range of possible monthly values do not fully specify a model.

Probabilities of losing runs under independent trades assume a fixed true win probability. Conditioning on an exact number of wins and losses is a different model. Neither calculation alone estimates the drawdown risk of a real strategy with uncertain skill or clustered losses.

Likewise, the original discussion's fixed percentage reduction from directional accuracy to trade win rate is an illustration. General conversion includes both correct calls that win and incorrect calls that win.

The discussion's large compounded balances are outcomes of assumed sustained performance and aggressive exposure, not empirical career evidence. Its unspecified stress-scenario quantiles and incorrectly labelled compounded-return Sharpe figures are not public findings.

William Sharpe's explanation distinguishes simple summed-return relationships from compounded multiperiod returns and notes the complications introduced by serial dependence. The relevant return series and time period must be stated before comparing ratios.

We compare what a goal requires with what a record supports. Capital, time, desired income, and the acceptable path can change that gap. A required win rate or opportunity count remains a requirement, not a setting the market must supply.

Open questions concern the reader's actual after-cost record, independent opportunity supply, performance uncertainty, and ability to withstand income shortfalls.

Source discussion: Calculate Trade Win Rate, supplied by ContextChart. Public interactions use separately specified illustrations rather than treating the conversation as validated performance research.