Fundamentals of Trading/Mathematical Model of a Profitable System

Chapter 8. Mathematical Model of a Profitable System The goal of this chapter is simple: learn to trade by rules, not by feelings. Understand the mathematics behind a trading system and let that math — not emotion — drive your decisions. Three Essential Parameters Every profitable trading system rests on three parameters. All three must be respected on every single trade: Stop-loss — caps your downside on any trade Risk-to-reward ratio — your mathematical edge Win rate — the percentage of trades that close profitably Stop-Loss: Non-Negotiable By cutting losses, you prevent the market from locking you into dead positions that drain your capital and your attention. The worst outcome in trading is not a loss — it's a position you can't exit, sitting there while your account bleeds and you have no capital left to trade with. Stop-Loss Placement Rules Place it beyond a local price extreme Place it beyond the level where your analysis is proven wrong Never move it further away from your entry You may only move it closer — to reduce risk or lock in profit Risk-to-Reward Ratio Minimum acceptable ratio: 1 to 3 Risking 5 points means your potential profit target must be at least 15 points — ideally more: 20, 40, 100. If the ratio isn't there — there is no trade. No matter how perfect the setup looks. Why 1:3 and Not 1:2 At 1:3, you can afford to be wrong more often than you're right and still come out profitable. Each winning trade more than compensates for multiple losers. The Math of Probability Example 1: Random Trading (1:2) Parameters: stop-loss 5 points, take-profit 10 points. 10 trades at 50/50 random outcomes: Trade Type Count Result Losing trades 5 × (−5) −25 points Winning trades 5 × (+10) +50 points Total +25 points Looks promising. But factor in commissions and spreads (~2 points per trade × 10 = −20 points) and the real result is just +5 points — essentially breakeven. Conclusion: Random trading with a 1:2 ratio barely survives transaction costs. Over the long run, it loses. Example 2: Systematic Trading (1:3) Parameters: stop-loss 5 points, take-profit 15 points. 10 trades, 60% winners, 40% losers: Trade Type Count Result Losing trades 4 × (−5) −20 points Winning trades 6 × (+15) +90 points Total +70 points After commissions (~2 points × 10 = −20 points): ~50 points profit. Conclusion: Even with a lower win rate (60% vs 50%), the 1:3 system dramatically outperforms because the math is working for you, not against you. The Expected Value Formula Expected value is the single most important metric for evaluating any trading system: EV = (Win rate × Average profit) − (Loss rate × Average loss) Example calculation: Win rate: 60% Average profit: 15 points Average loss: 5 points EV = (0.6 × 15) − (0.4 × 5) = 9 − 2 = +7 points per trade Positive expected value means the system is profitable over a large sample of trades. Capital Management The Core Principle Your deposit size and risk per trade must be comfortable — they must never threaten your financial security outside of trading. Recommended Risk Per Trade Experience Level Risk Per Trade Beginner 0.5% – 1% Intermediate 1% – 2% Professional Up to 3% Never risk more than 5% of your account on a single trade. The 2% Rule The classic money management framework: Maximum risk per trade — 2% of account Maximum daily loss — 6% (3 losing trades) Maximum weekly loss — 10% Practice and Building Experience Theory without execution is worthless. The Learning Path Open a demo account with a broker of your choice Apply what you've learned under real market conditions Keep a trade journal — log every single trade Review your results — what's working, what isn't Refine the system — let the data guide your improvements Don't trade real money until you've completed at least 100 demo trades. Why 100 Trades Small samples are statistically meaningless 100 trades provide a statistically meaningful result The process builds discipline and genuine skill Trading Is a Marathon The trader who wins is not the one who gets lucky on a single trade. It's the one who executes consistently, manages risk religiously, and compounds results over time. Mistakes at this stage are inevitable — and they shouldn't stop you. Key Takeaways A stop-loss is required on every single trade Minimum risk-to-reward ratio is 1:3 Expected value must be positive Risk per trade — no more than 2% Demo account → 100 trades → real money See Also ← Market Entry Method Main Enemies of a Trader →