The Math Behind Profitable Trading

Summary

The video explains that trading profitability depends on positive expectancy, risk management, and executing a system over enough trades—not simply on having a high win rate.

Key concepts and examples

• Expectancy is calculated as: (Win rate × average gain) − (Loss rate × average loss)

For example, a system that wins 80% of the time, with an average gain of $10 and an average loss of $100, has an expectancy of −$12 per trade. Across 100 trades, that would imply an average loss of about $1,200.

The takeaway is that neither win rate nor risk-to-reward, considered alone, establishes whether a strategy has an edge.

• Strategy trade-offs:
  • Mean reversion often has a higher win rate—typically 60% or more, sometimes around 70%—but smaller average wins than losses. The speaker’s backtested example reportedly had a 66% win rate, 4.1% average profit, and 4.7–4.8% average loss. Its equity curve was described as rising from 2000 to the present, with drawdowns along the way.
  • Trend following often has a lower win rate, typically 35–45%, but larger winners can outweigh losses. The speaker’s backtested example reportedly had a 45% win rate, 188% average profit, and 99% average loss. These are system-test figures, not necessarily the amount risked on each trade; position sizing matters.
  • The speaker argues that traders should expect a trade-off rather than assume they can combine a very high win rate with a consistently favorable risk-to-reward ratio.

Risk management and position sizing

The video emphasizes that even a positive-expectancy strategy can fail if losses are too large. The speaker recommends usually defining risk as 1–2% of trading capital per trade.

For shares, the position-sizing formula is:

Dollar amount at risk ÷ (entry price − stop-loss price)

Examples:

• With $100,000 of capital and 1% risk ($1,000), buying at $100 with a $90 stop gives a position size of 100 shares.
• With the same risk and entry price but an $80 stop, the position size is 50 shares.

A wider stop means fewer shares; a tighter stop means more shares, while the intended dollar risk stays constant. The speaker cautions against using the same share count for stocks with different volatility, citing McDonald’s and Nvidia as examples.

A separate illustration compares two traders with $10,000 accounts using a system with a 50% win rate and 1:3 risk-to-reward:

• One risks $5,000 per trade and is wiped out after two consecutive losses.
• The other risks $100 per trade. After five losses and five wins, this trader is $1,000 ahead, or up 10%.

Variance and execution

The speaker uses coin tosses to explain the law of large numbers: short sequences can differ substantially from the expected probability, while results tend to move closer to the underlying probability over many trials.

Applied to trading, a system can have losing streaks and short-term results that diverge from its expected performance. The speaker cautions against abandoning a system after a few losses, provided it has been validated with data and is being followed consistently.

Assets, instruments, and trading approaches

• Stocks, including McDonald’s and Nvidia; no ticker symbols are stated.
• Mean-reversion, trend-following, and breakout trading systems.
• Chart-pattern trading and algorithmic trading are mentioned in the introduction.
• No specific ETFs, bonds, commodities, or cryptocurrencies are discussed.

Promotional content and disclaimer

The presenter promotes the book Trading Systems That Work, described as covering three systems—mean reversion, trend following, and breakout—with rules and backtested data. The promotion also mentions bonuses and a 180-day full-refund offer.

No explicit “not financial advice” disclaimer appears in the subtitles.

Presenter and sources mentioned: Rayner Teo (presenter); Dan Zanger, Andrea Unger, and Ed Seykota (traders cited in the introduction); Trading Systems That Work (promoted book).