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2002issue C031-4

Monte Carlo equity paths from win rate and profit factor

Two published summaries, the share of winning trades and the ratio of gross wins to gross losses, can be redrawn as many randomized equity-growth paths. Each trade is classified against the win rate, booked as a profit-factor payout or a unit loss, and summed so the same rule set can be inspected as a family of paths.

  • A systematic procedure can be evaluated from the share of trades that win and the ratio of gross wins to gross losses.
  • Each trade is classified by a uniform random draw on the unit interval and booked as a profit-factor payout or as negative one, so the running sum is an equity-growth path.
  • Recalculating those draws from the same two statistics produces a different path, which lets the same rule set be inspected as a family of paths.
  • A win rate above one half is not required when winning outcomes are larger than losing outcomes.
Entries in this reading3 entries
Current trackMonte Carlo simulation51 readingsExpected value61 readingsRobustness testing80 readings

Two summary statistics

A systematic procedure can be evaluated from two summary statistics: the share of trades that win and the ratio of gross wins to gross losses. Those two figures are percent profitable and profit factor.

Maximum drawdown, required margin, average result after transaction costs, and runs of consecutive losing trades are listed as additional risk statistics separate from those two summaries. A win rate above one half is not required when winning outcomes are larger than losing outcomes.

Classifying and booking each trade

Profit factor is the ratio of gross winnings to gross losses and is applied as the payout on a trade classified as a win. Each trade is classified by drawing a uniform random number on the unit interval and treating the trade as a win only when that draw falls below the stated win-rate fraction. Percent profitable is that share of trades treated as winners.

A win is booked as the profit-factor payout and a loss is booked as negative one. Expected value is the signed outcome assigned to that classified trade, used to keep each draw's implied gain or loss bounded before the path is summed. The running sum of those signed outcomes is the equity-growth path, plotted so path shape and drawdowns can be compared across reruns.

Several paths from the same statistics

Recalculating the random draws from the same two statistics produces a different equity path, so several paths can be inspected for the same rule set. Robustness testing repeats the same entry, exit, and abstention accounting under new random draws so the procedure itself, not a single backtest order, is what is being evaluated.

Worked illustrations use a 45 percent win rate with a 1.5 profit factor, a 50 percent win rate with a 2.0 profit factor, and a 42 percent win rate with a 1.5 profit factor.

Randomized equity path at 45% wins and 1.5 profit factor

The first twenty-two trades from the article’s default generator wander around break-even instead of compounding. Each point is the running sum read from the Cumulative Profit column, where a uniform random draw below 45 percent books a 1.5-unit win and any other draw books a unit loss of −1.
The first twenty-two trades from the article’s default generator wander around break-even instead of compounding. Each point is the running sum read from the Cumulative Profit column, where a uniform random draw below 45 percent books a 1.5-unit win and any other draw books a unit loss of −1.

The published Excel plot runs through trade 500. Only spreadsheet rows 3–24 are visible, so this series is the exact readable prefix, not the full randomized path.

An alternative shuffle of realized trades

Monte Carlo simulation is the resampling procedure that randomizes either each trade's win-or-loss label or the order of realized trades so a system is judged from a family of equity paths instead of one historical sequence. An alternative Monte Carlo step shuffles the order of realized trades instead of keeping backtest sequence, then reads expected drawdown from the spread of the resulting distribution around its mean.

Maximum drawdown is the largest peak-to-trough decline on an equity path, treated as a capital-planning statistic alongside required margin.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
11 of 26 in the Monte Carlo simulation track
20031-7 pp.Next on Monte Carlo simulationChecking a small system edge with Monte Carlo simulationMonte Carlo simulation can turn a sequence of random win-or-loss draws into a patterned distribution of possible system outcomes.
All readings on this track · 26 readings
  1. 1989Known-bias price streams for system evaluation
  2. 1989Constructing holdout-checked synthetic prices from chaos maps
  3. 1991Closing the feedback loop in auction market simulations
  4. 1994Evaluating eight-year election regimes
  5. 1995Constructing equity versus leverage with resampled trades
  6. 1995Stock leverage from compounded returns and margin cost
  7. 1996Constructing and optimizing volatility position-sizing profiles
  8. 1996Constructing fade rules from an empirical deviation histogram
  9. 1998Return-path volatility and the recovery burden
  10. 1999Monte Carlo checks beyond a single historical path
  11. 2002Monte Carlo equity paths from win rate and profit factor
  12. 2003Checking a small system edge with Monte Carlo simulation
  13. 2003Evaluate a mechanical trading system with a stop-loss order and Monte Carlo simulation
  14. 2005Evaluating momentum rank rotation under portfolio constraints
  15. 2009Bounded risk and rank rotation in portfolio construction
  16. 2010A calendar for walk-forward robustness and Monte Carlo evaluation
  17. 2012Treat the optimize view as an evaluation protocol
  18. 2013Entry, exit and abstention as one testable procedure
  19. 2014Evaluating stop and target bounds before fading large moves
  20. 2014Evaluating system exits when markets get noisier
  21. 2015Memory-bearing synthetics for dominant-cycle spectra
  22. 2015Constructing next-session implied-volatility forecasts by reordering closes
  23. 2016Mechanical systems as a gated factory
  24. 2017Four-sleeve Monte Carlo annual-loss bounds
  25. 2018When to retire a mechanical system with Monte Carlo drawdown limits
  26. 2020Treat mechanical system design as a revalidation lifecycle
By fieldSystem design203 readingsBy year2002145 readings
All 51 readings tagged Monte Carlo simulation
Also on Monte Carlo simulation5 readings
2002Trade-count horizon for equity-curve survival2007Expected-equity sizing and geometric drag2009Bounded risk and rank rotation in portfolio construction2010Risk of ruin with fractional and reserve betting2014Evaluating stop and target bounds before fading large moves