- 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.
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
- 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.
- 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_donchian20does exactly that with DD_p95 = 20%). - 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.
- 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.