Position Sizing · learning TA

The question everyone skips

Most traders spend 95% of their energy on entries and exits and 5% on position size. Professional money managers invert the ratio. Kaufman's position on this is uncompromising:

More fortunes have been lost through poor position sizing than through poor system design.

An entry is a direction; an exit is a timing; position size is the bet. A great system sized too aggressively will blow up during an ordinary drawdown. A mediocre system sized correctly will produce an acceptable equity curve for years. Kelly, the Turtles, and every serious institutional framework treat sizing as the primary risk-management lever.

This lesson covers the three frameworks you'll actually use.

Framework 1 — Fixed-fractional

The oldest and simplest rule: risk a constant fraction of current equity on every trade.

\text{shares} = \frac{\text{account} \times r}{\text{stop distance in price}}

Where $r$ is your per-trade risk fraction (typically 0.5% to 2%). This is the formula running in the calculator below — the same one Turtle System 1 uses with $r = 0.01$ and stop distance = 2 × ATR.

ATR position sizing calculator

Account size ($)Risk per trade (% of account)1.0%ATR value (points)Stop multiplier (×ATR)2.00×Entry price ($)

Risk ($)$250

Stop distance5.00 pts

Shares50

Capital deployed$5000

Formula: shares = (account × risk%) / (ATR × multiplier). Capital deployed: $5000 (0.20× of account). Notice the risk per trade stays constant at $250regardless of instrument — that's the whole point. A volatile stock gets fewer shares with a wider stop; a calm stock gets more shares with a tighter stop. Same dollar risk either way.

Why the constant-risk framing is useful

Notice what's constant and what varies as you change the inputs:

Risk in dollars stays constant at $r \times$ account (e.g., $500 on a $50k account at 1%)
Shares adjusts inversely to volatility — a choppier stock with 2× ATR of $5 gets half the shares of a stock with $2.50 ATR
Capital deployed can vary dramatically

This is the correct framing for diverse instruments. A small-cap biotech with 8% daily swings and a mega-cap with 1% daily swings should not get equal dollar allocations; they should get equal dollar risk. Fixed-fractional enforces that naturally.

Compounding and deleveraging

The fixed-fractional rule compounds automatically: after a winning trade, account grows, next trade's dollar risk grows proportionally. After a losing trade, the reverse. This is anti-martingale behavior — bet more when winning, less when losing — which Kaufman explicitly contrasts with dangerous martingale systems (kaufman.txt:40087):

Martingale systems, which double the bet after each loss, promise mathematical certainty under infinite bankroll and infinite patience. Real traders have neither.

The Turtles added a drawdown multiplier on top of fixed-fractional (covered in the Turtle lesson): every 10% equity drawdown reduces position size by an additional 20%. This deleverages faster than natural compounding during losing streaks — a critical survival mechanism.

Framework 2 — ATR / volatility-based (Turtle style)

A refinement of fixed-fractional: instead of a fixed price stop, use a multiple of current volatility (ATR) as the stop. This is what the calculator above implements.

\text{stop distance} = k \cdot \text{ATR}

\text{shares} = \frac{\text{account} \times r}{k \cdot \text{ATR}}

Benefits:

Volatility-neutral position sizing. A trade in a calm market and a trade in a choppy market both risk the same dollar amount
Dynamic stops that adapt to regime shifts — as volatility expands, your stops widen, but your position shrinks to compensate
Kaufman's Table 23.4 (kaufman.txt:42602, 42631) applies identical math to stock and futures positions with different $/point values

Kaufman's worked example: an account of $100,000 targeting 1% risk per trade with a 2×ATR stop on a stock with ATR of $2.50 → shares = ($100,000 × 0.01) / ($2.50 × 2) = 200 shares. That's exactly the Turtle "1 unit" calculation.

Why ATR and not a fixed percent stop?

Two reasons:

Market-adaptive: ATR reflects current volatility, not historical average. A low-vol regime stock's 2×ATR stop might be 3%; a high-vol regime's might be 12%. Fixed-percent stops would over-risk one and under-risk the other.
Regime-tolerant: when volatility expands (a market stress), your 2×ATR stop automatically widens too — so you're not stopped out on normal noise in a high-vol regime.

ATR stops adapt to volatility

14-bar ATR$1.01

2×ATR stop2.0%

Shares (1 % risk)247

$ at risk$500

Tight ATR stop — narrow candles, small swings. Same $50k account, same 1 % risk per trade — but the ATR stop adapts. In the low-vol regime the stop is tight and you take bigger share count; in the high-vol regime the stop widens and you take fewer shares. Dollar risk is identical either way: $500.

Toggle between the two regimes. Same account, same 1% risk fraction — but the stop distance and share count adapt automatically. In the low-vol chart the candles are tight and the stop is close; in the high-vol chart the candles are wide and the stop moves out to match. Dollar risk stays constant at $500 either way.

Framework 3 — Kelly criterion

The math-derived optimal betting fraction — originally from John Kelly's 1956 paper on signal/noise ratios at Bell Labs, adapted to trading in the 1980s.

f^* = \frac{bp - q}{b}

Where $b$ = win/loss payoff ratio (avg_win / avg_loss), $p$ = win probability, $q = 1 - p$ .

Worked example

You have a system with 55% win rate, average winner $300, average loser $200.

b = \frac{300}{200} = 1.5, \quad p = 0.55, \quad q = 0.45

f^* = \frac{1.5 \times 0.55 - 0.45}{1.5} = \frac{0.825 - 0.45}{1.5} = \frac{0.375}{1.5} = 0.25

Kelly says bet 25% of bankroll on this trade. For a $100k account, that's risking $25k per trade.

Why nobody actually bets full Kelly

Full Kelly maximizes long-run growth rate in theory. In practice it produces drawdowns that no human can tolerate. A 25% bet size means losing 25% of the account on a single losing trade. Ten losses in a row (which happens in a 55% win-rate system) brings you to $100k × (0.75)^10 ≈ $5,600 — a 94% drawdown.

Two practical adjustments:

Half-Kelly — multiply the result by 0.5. In the example above, 12.5% per trade. Gives up ~25% of growth in exchange for ~75% less volatility
Quarter-Kelly — multiply by 0.25. The common institutional heuristic. For the example, 6.25% per trade — still aggressive by retail standards

Kaufman on why (kaufman.txt:44600):

The Kelly formula assumes known and stationary win rate and payoff — conditions that live markets never actually meet. Using half or quarter Kelly is insurance against estimation error in those inputs.

Kelly fails when inputs are wrong

If you estimate your win rate as 55% but it's actually 50%, full Kelly gives you:

f^* = \frac{1.5 \times 0.50 - 0.50}{1.5} = \frac{0.25}{1.5} = 0.167

And you're betting 25% thinking it's optimal when optimal is 16.7%. That 50% over-bet is enough to turn growth into ruin over a long series. Kelly's inputs have to be right for the output to be right. Most retail traders massively over-estimate their win rate and payoff, which is why Kelly-sized bets blow up in practice.

Comparing the three frameworks

	Fixed-fractional	ATR-based	Kelly
Simplicity	Very simple	Simple	Requires stats
Volatility adaptive	No	Yes	No (implicit)
Max per trade	0.5–2% typical	0.5–2% typical	6–25% (raw); half-Kelly ~3–12%
Growth rate	Conservative	Conservative	Optimal (if inputs correct)
Robust to bad estimates	Yes	Yes	No — blows up

Practical defaults for retail traders:

Beginners: 0.5% fixed-fractional. Slower growth, survives drawdowns that look catastrophic.
Systematic traders with meaningful backtest history: 1% ATR-based. Turtle-compatible.
Traders with multi-year verified live stats: quarter-Kelly. The full math, heavily de-risked for estimation error.

Martingale — why to avoid it

The opposite of anti-martingale. After a loss, double the bet to recover plus earn the original target. Mathematically, if your bankroll is infinite, this always wins eventually.

Kaufman (kaufman.txt:40087):

Every martingale system is a promise to lose your entire account. The only question is when.

With a finite bankroll, a long enough losing streak (which is guaranteed in any probabilistic system) forces a bet larger than your remaining capital. Account goes to zero. The reason retail casinos happily accept martingale players: table limits enforce truncation at the far end of the distribution, and the house edge is permanent.

For trading: never double down on losing trades. Never average down into a short below a stop level. Losing streaks happen to every system; the only protection is sizing that shrinks (not grows) during the streak.

Quick check

Question 1 / 20 correct

Your system has 60% win rate, average winner $250, average loser $100. What's the full Kelly fraction?

What you now know

Fixed-fractional risks constant $%$ of equity per trade — the foundation of every sizing system
ATR-based sizing (Turtle style) adapts stop distance to current volatility → constant dollar risk across diverse instruments
Kelly criterion gives the mathematically optimal bet size — but requires accurate inputs, so use half-Kelly or quarter-Kelly in practice
Anti-martingale (bet more after wins, less after losses) is the only sustainable pattern; martingale is guaranteed ruin
The Turtle drawdown rule (10% drawdown → 20% size reduction) is a concrete example of manual deleveraging on top of natural compounding

Next: Risk/Reward & Expectancy — turning win rate, win/loss size, and frequency into a single number that decides whether your system is worth trading.