Knowledge · Research · Position Sizing: a survey of methods - from Fixed Fractional to Pyramiding

Position Sizing: a survey of methods - from Fixed Fractional to Pyramiding

Strategy analysis 2026-06-11 10 sources
A survey of every sizing family (Fixed Fractional, Risk Units, Kelly, Vol Targeting, Throttles, Pyramiding, Scaling-Out) with academic evidence, the Turtle rules in detail, and the sizing practice of our 20 analyzed traders. Key findings: Vol Targeting adds little on the return side (verified) but provides tail protection; Pyramiding raises the EV of trend following but costs Sharpe; the workable range for us is 1/4-1/2 Kelly ~ 1.75-3.5x exposure.
  • Vol Targeting: Sharpe lift only in equities/credit, negligible in commodities/FX (verified, Harvey et al., 60+ assets); the robust benefit is tail-risk reduction, not return (verified). Confirms our marginal finding (Exp G1: +0.08 Sharpe).
  • Conditional Vol Targeting (intervene only in volatility-extreme quintiles) beats permanent targeting: Sharpe +0.07 in 10/10 markets, +0.23 for momentum strategies - directly testable with our GBM vol forecast.
  • Pyramiding (Turtle-style 1/2N adds) nearly doubles the EV per trade for trend following (26.2 vs 13.0 bps, Concretum, 40 futures markets since 1980) but costs Sharpe and deepens the max DD to ~49% - EV-positive, risk-adjusted negative.
  • Averaging-down is the martingale trap; all serious sources (Davey, Brandt, Paul, Hsaka) rule it out categorically. Scale only in the winning direction.
  • Fractional Kelly: Half-Kelly delivers ~75% of the growth with P=0.89 (instead of 0.67) of doubling capital before halving it; edge estimation errors matter ~20:2:1 more than variance errors -> with 86 trades of history, 1/4-1/2 Kelly (for us: 1.75-3.5x exposure) is the upper bound.
  • The complete Turtle system as a blueprint: 1 Unit = 1% equity per 1N (ATR), max 4 Units, adds every 1/2N above the last fill, -20% trade size per -10% drawdown - vol sizing + pyramiding + equity throttle in one rulebook.
  • Trader consensus from our 20 profiles: risk-based 0.5-2% per trade as the anchor (Brandt 0.6%, Paul 1-2%, Pifagor 1%), vol normalization as the refinement, anti-martingale as an article of faith.
P1 Make the exposure decision: MAX_POSITION_PCT=1.0 (exposure ~1x) as a conservative start, corridor up to max 3x (~ 1/2 Kelly) - the basis for the decision is in sizing_sweep_donchian20 + leverage_mc.
All sources converge on fractional Kelly 1/4-1/2 as the upper bound; our MC confirms it: 3x = P(DD>50%) of 8%, above that the tail risk explodes without a median gain.
P2 Implement an equity-curve throttle as a sizing condition (Turtle rule: -20% notional per -10% DD) and test it in the re-pricing harness of the sizing_sweep.
Mechanical, cheap, lowers risk-of-ruin asymptotically toward zero; exactly testable as re-pricing since it does not change the trade timing.
P3 Vol-target re-test as CONDITIONAL Vol Targeting: apply the GBM forecast (IC 0.83) only in extreme quintiles instead of permanently (Exp-G1 follow-up).
FAJ 2020 evidence: conditional targeting beats permanent targeting clearly, especially for momentum/trend following (+0.23 Sharpe); may explain our marginal G1 finding (permanent + RV proxy).
P4 Backtest price-based pyramiding as a new condition (turtle_pyramiding: adds at +0.5xATR above the last fill, max 3 units, trail the stop) for donchian_breakout - NOT possible via re-pricing, needs sim support.
Concretum evidence: EV doubling for trend following; fits Donchian structurally (same family as Turtle). But DD costs -> only test combined with the throttle.
P5 Do NOT pursue staggered_entry (time-based) as an EV lever - it is pure timing-risk smoothing.
No evidence-based EV effect; the EV-relevant variant is price-based pyramiding in the winning direction (prio 4).

Why sizing is a discipline of its own

Kevin Davey puts it bluntly: the same strategy can ruin you with the wrong sizing and grow with the right one - money management is a separate discipline after strategy validation. And the Concretum study (40 futures markets since 1980) shows it quantitatively: the sizing method shapes the entire return distribution (skewness, hit rate, tail profile), not just the scale. Our own sizing sweep and the leverage Monte Carlo showed the same thing: exposure level and rule family are separate decisions - see Position Sizing and Leverage.

Same strategy, same trades, four sizing rules - historical backtests of the Wallet-1 strategy (DONCHIAN_20) on Binance 1m data, 2023-01 to 2026-05, start $100. No live-wallet data: "live-sim" only refers to the simulation mode that reproduces the bot's 30s check loop at 1m resolution. The grey legacy curve shows why the absolute $12 cap had to go (+7% in 3.3 years - the cap suffocates compounding); yellow is the Turtle brake running live since June 2026 (same return as 1x with a slightly flatter drawdown), turquoise the regime-gated pyramiding: in a window covering the trend years 2023/2024 it nearly doubles the 1x return (+114% vs. +62%), paid for with a max DD of 17% instead of 13%. Click a row in the legend to toggle curves on/off. Open fullscreen

The sizing families

Family Mechanics Evidence / typical parameters Failure mode
Fixed Fractional Notional = fixed % of equity Our status quo; self-correcting (anti-martingale: automatically smaller after losses) Ignores stop distance -> loss per stop-out varies with volatility
Risk-based / ATR units Size = equity x risk% / stop distance; Turtle original: 1 Unit = 1% equity per 1N (ATR) Brandt 0.6%, David Paul 1-2%, Tharp school 1%, Pifagor 1% conservative; our risk_sizing With very tight stops the notional explodes -> exposure cap needed
Fixed Ratio (Ryan Jones) Scale up per amount of delta earned (contract-based) Designed for small futures accounts; little academic evidence Asymmetric: scales up more slowly than fixed-fractional when growing, harder when shrinking
Kelly / Fractional Kelly / Optimal f Maximizes log growth; Optimal f (Vince) = empirical Kelly on the trade history 2x Kelly = zero growth (Thorp); Half-Kelly ~ 75% of the growth at P=0.89 instead of 0.67 of doubling capital before halving it; estimation errors in the edge weigh ~20:2:1 more than in variance/covariance -> always fractional Full Kelly/Optimal f regularly produces 50%+ drawdowns; reacts extremely to an overestimated edge (overfit x Kelly = ruin)
Vol Targeting Size x (target vol / forecast vol), clipped (verified) Sharpe lift only in risk assets (equities/credit), negligible in commodities/FX/bonds (Harvey et al., 60+ assets from 1926); (verified) the robust benefit is tail-risk reduction, not return; (verified) even the best academic case (Moreira/Muir, US equities) = only ~25% Sharpe lift; OOS critique (Cederburg: 53/103 better, 50 worse, real-time mostly a deterioration) Applied permanently, turnover eats the edge; in 4/10 markets the max DD even rose (FAJ 2020)
Conditional Vol Targeting Intervene only in volatility-extreme quintiles, otherwise 100% FAJ 2020: Sharpe +0.07 in 10/10 equity markets, max DD -6.6%, turnover halved; +0.23 Sharpe for momentum strategies - vol sizing pays off in extremes, not permanently Quintile thresholds are another degree of freedom (overfit surface)
Equity-curve throttle Reduce notional in drawdown; Turtle rule: -20% trade size per -10% DD from the year's start Lowers risk-of-ruin mechanically; anti-martingale family (Davey: the professional approach) Slows the recovery; with a mean-reverting equity curve it costs return
Martingale Scale up after losses Davey: backtested and discarded - works right up to total loss ("Martingale Debacle of 2024") Ruin is built in, only the date is open
Pyramiding / Staggered Entry Add to a winning position; Turtles: start 1 Unit at the breakout, adds every 1/2N above the last fill, max 4 Units Concretum (trend following, 40 markets): EV per trade 26.2 vs. 13.0 bps - scaling-in costs trend following no expected value, it nearly doubles it; IRR ~20% vs. 11.5% p.a.; but max DD 48.7% vs. 25.7%, worse Sharpe, hit rate 42.5->39.3%, monthly skew 3.74 Risk-adjusted worse; the PnL hangs on rare fat-tail trades - statistically hard to validate
Scaling-Out / Partial TP Take partial profits in tranches Our partial_tp (live); Hsaka & Pentoshi: scale out in tranches instead of an all-in exit; mathematically the mirror image of pyramiding: lowers the EV of winners, lowers variance For trend following it cuts off exactly the fat tails the strategy lives on

Staggered entry/exit - the detail question

Does scaling-in cost expected value? The best available evidence (Concretum, trend following) says: no, on the contrary - adds only in already-confirmed trends concentrate capital in the trades that work. The price is not the EV but the shape of the distribution: deeper drawdowns, lower hit rate, extreme right skew. Three variants that must be kept apart:

  • Pyramiding in the winning direction (Turtle-style, price-based adds at +1/2N) = anti-martingale, evidence-based and defensible for trend following.
  • Averaging-down in the losing direction (buying more into a falling position) = a martingale variant. Brandt, Paul and Hsaka explicitly rule it out ("no averaging down", "no buying more into losses").
  • Time-based staggering (Pifagor: position split into 5 equal parts over consecutive bars; our staggered_entry) is primarily timing-risk reduction, not an EV play - it smooths the entry price, nothing more.

Our staggered_entry is time-based; the Turtle variant (price-based adds with a trailed stop) does not exist in our system yet - that would be a new condition.

Scaling-out is the opposite pole: it makes the equity curve smoother and the psyche calmer, but for trend-following strategies it cuts off the right tails. That our stop-robustness sweep found partial_tp + ATR trailing of all things to be the most robust exit is no contradiction: the first two TP steps finance the trade, the third step + trailing let the tail run - a compromise between both worlds.

What do real-world traders do? (from our 20 trader profiles + sources)

Trader Sizing approach
Turtles (Dennis/Eckhardt) Vol-normalized units (1% equity per 1N), max 4 units/market, 1/2N pyramiding, -20% throttle per -10% DD
Peter Brandt Risk-based, 0.6% per trade; never correlated trades in parallel; aggressive only in trade management
Dr. David Paul Risk-based 1-2%, computed backwards from the stop distance
Larry Williams (account x risk%) / largest historical loss; 5/10/15% conservative/normal/aggressive - ran >50% in 1987, does not recommend it himself
Linda Raschke Vol-weighted: position inverse to the 30-day dollar range - "position sizing is everything"
Kevin Davey Fixed-fractional/anti-martingale; sizing only after validation; Monte Carlo RoR ~ 0 as the live gate
Thomas Skinner MC-optimized sizing against the objective function (prop-firm pass probability) - sizing follows the payoff profile, not a fixed rule
Hsaka Tight stops -> larger nominal size at the same dollar risk; no martingale, no re-entries
Pentoshi Building in tranches + staggered partial profits; rewrote his risk philosophy after the 90% DD in 2018
Benjamin Cowen Risk-metric-scaled DCA: buy volume proportional to (1 - risk score), no leverage
QuantPy VaR/CVaR budgets + portfolio theory instead of a fixed risk %
Mounir (Unbiased) Four-method canon: fixed-% (1-2%), equal-weight, %-volatility, risk-parity

The pattern across almost all of them: risk-based around 0.5-2% per trade as the anchor, vol normalization as the refinement, anti-martingale as an article of faith, and scaling only in the winning direction.

Small accounts with perp leverage: the risk-of-ruin calculation

  1. Fractional Kelly as the upper bound: our own Monte Carlo found the median-growth optimum at ~7x exposure. 1/4-1/2 Kelly = 1.75x-3.5x - exactly the range our drawdown table shows as workable (3x: P(DD>50%) = 8%). The literature justifies this twice over: Half-Kelly sacrifices only ~25% of the growth for drastically better survival odds, and edge estimation errors (for us: 86 trades of history!) demand an additional haircut.
  2. Drawdown budget instead of a return target: first fix the maximum acceptable drawdown, then use a trade-MC to find the exposure whose DD-p95 hits the budget (our sizing_sweep_donchian20 does exactly that with DD_p95 = 20%).
  3. Equity throttle as a ruin brake: the Turtle rule (-20% notional per -10% DD) is mechanical, cheap to implement and makes ruin asymptotically unreachable - the price is a slower recovery.
  4. Leverage is margin mechanics, not sizing: on Hyperliquid the leverage setting only determines the margin requirement; the economically relevant measure is notional/equity. Liquidation is not a binding risk with 1xATR stops (see Leverage) - the cumulative drawdown is.

Verification status

Three core claims on Vol Targeting are adversarially verified (2-0 votes). The remaining findings carry original quotes from primary sources (SSRN papers, the original Turtle rules, Thorp, Concretum), but the verification round failed at the API session limit - one claim was actively refuted (the assertion that monthly c/sigma^2 scaling is the canonical formulation of Vol Targeting). For numerical values from the unverified claims, check the source before using them.