Position sizing and risk: how much, and how not to blow up

IntermediateDuration ~35 min video + 30 min hands-onTools Python 3 + pandas

Why this lesson

An edge tells you whether to trade. Position sizing tells you how much — and it is the half of the problem that actually kills accounts. You can have a genuine edge and still go broke by betting too large through a normal losing streak; you can have a mediocre edge and survive for years by sizing it sanely. This lesson teaches the two sizing methods worth knowing at this level — fixed-fractional sizing and volatility targeting — frames the Kelly fraction correctly as a ceiling you stay well below, and has you compute your own risk of ruin so the numbers stop being abstract. Robert Carver’s Systematic Trading (Part 3) and Leveraged Trading are the framework’s home; QuantStart’s Kelly articles are the free companion.

Watch

Start with the distinction that everything else rests on: money management (the dollar rules you set) is not the same thing as risk (the probability of a bad outcome, which depends on how often you trade).

Thumbnail for Money Management & The Risk of a Trading Strategy — **Watch for:** Two sub-strategies with identical $40-per-trade risk and the same 5-trade max losing streak, but 10 vs 100 trades a month — the real risk differs, because the streak is far more probable at higher frequency.

Then the measurement itself. This walks the standard Value-at-Risk calculation step by step, then honestly critiques its own assumptions.

Thumbnail for Measuring the Risk of a Trading Strategy — **Watch for:** Why 'max drawdown 25%' is incomplete (25% over a week is not 25% over three months); the VaR recipe — daily returns to standard deviation, scaled by the square root of 21 for the month, times 1.65 for 95% confidence; and where normality breaks down under fat tails. Note: the 95%/1-month choice is a Darwinex platform default, not a universal law.

Why letting risk run high is a one-way door.

Thumbnail for Why High VaR Trading Strategies Don't Survive Long-Term — **Watch for:** A concrete coin-flip sequence where four alternating even-odds trades still leave equity down 29%, then Monte Carlo return distributions across VaR bands showing the hard negative-boundary problem once monthly VaR passes ~30%. (Last ~5 minutes are a product pitch — skip.)

The professional’s own recipe. Carver, ex-AHL, on risk as awareness then measurement then control, and a reusable position-sizing method. Two segments of a long podcast.

Thumbnail for Risk Management with Robert Carver — position sizing recipe — **Watch for:** The three inputs: the point value of the instrument, its expected volatility (ATR or standard deviation), then the percentage of capital you want at risk. This is volatility targeting in plain words.

Thumbnail for Risk Management with Robert Carver — the volatility floor — **Watch for:** Capping how *low* a volatility estimate is allowed to go, illustrated with the January 2015 Swiss-franc peg collapse — otherwise a quiet market talks you into a huge position right before it detonates.

Finally, a lesson in honest testing that doubles as a sizing-adjacent warning: which stop-losses actually help.

Thumbnail for Cesar Alvarez on a quant study of stop-loss types — **Watch for:** A percentage stop and an ATR max-loss stop both roughly quadruple total R; the beloved trailing-ATR stop underperforms or loses money — a surprising result he double-checks before trusting. Caveat stated up front: no commissions or slippage in the study, so read it as relative mechanics, not net profitability.

The explainer

Fixed-fractional sizing is the honest starting point: risk a fixed fraction of your account — say 1% — on each trade, where “risk” means the distance from entry to stop multiplied by position size. If your stop is 40 pips away and 1% of your account is $200, you size the position so 40 pips equals $200. As the account grows, the dollar risk grows with it; as it shrinks, the dollar risk shrinks. This is simple, robust, and hard to blow up with — Carver’s warning is that the common failure is making it too simple (the same fixed contract count across instruments of wildly different volatility) or too complicated (LTCM-style model confidence). One percent is a common, defensible default for a retail system; 2% is aggressive; beyond that you are relying on being lucky about your losing streaks.

Volatility targeting is the upgrade, and it is the core of Carver’s framework. Instead of a fixed stop distance, you size each position so that its expected daily dollar movement is roughly constant across every instrument and every market regime. The recipe from the Carver segment: take the instrument’s point value, estimate its recent volatility (the ATR, average true range, is the standard proxy), and solve for the position size that puts your chosen percentage of capital at risk. The consequence is automatic and important: when volatility doubles, your position roughly halves. You hold less of a wild instrument and more of a calm one, so a quiet EUR/USD and a violent index future contribute the same risk to your book. The one trap is the volatility floor — in an unnaturally calm market the volatility estimate collapses toward zero and the formula tells you to take an enormous position, exactly the setup that detonated accounts in the January 2015 Swiss-franc unpeg. Cap how low the estimate is allowed to go.

The Kelly fraction is where beginners hurt themselves. Kelly gives the bet size that maximizes the long-run growth rate of your capital, and it is real mathematics — but it is a ceiling, not a target. Full Kelly assumes you know your edge and your win distribution exactly, which you never do; it produces gut-churning drawdowns; and it punishes any overestimate of your edge brutally, because being wrong about your edge on the high side pushes you past the growth-optimal point into the region where growth turns negative. The practitioner’s rule is to trade at half-Kelly or less. Treat full Kelly as the “do not cross” line, not the destination.

Why all this care? Because of risk of ruin and the arithmetic of recovery. A 25% drawdown needs a 33% gain to get back to even; a 50% drawdown needs 100%. The high-VaR video makes it concrete: once your Value-at-Risk climbs past roughly 30% monthly at 95% confidence, the losing sequences that a fifty-fifty process throws off routinely are deep enough that recovery becomes statistically improbable — the negative boundary (zero) is absorbing, and you can only fall through it once. And crucially, as the first video showed, real risk is not just per-trade dollar loss — it scales with frequency, because more trades per month means a bad streak of any given length is more likely to happen. Two systems with the same per-trade risk are not equally risky if one trades ten times as often. (Correlated positions do the same thing to a portfolio — five trades that all move together are really one big bet. We name that correlation clustering here and take it seriously in Level 3.)

You will now compute these numbers yourself, so “1% versus 2% versus 5%” stops being a slogan and becomes a table you can read.

Do it

Part A — volatility-targeted sizing in ~20 lines. Size positions so each targets the same daily dollar risk regardless of the instrument’s volatility.

import numpy as np
import pandas as pd

def atr(high, low, close, n=14):
    prev_close = close.shift(1)
    tr = pd.concat([high - low,
                    (high - prev_close).abs(),
                    (low - prev_close).abs()], axis=1).max(axis=1)
    return tr.rolling(n).mean()

def vol_target_size(capital, target_risk_pct, atr_value, point_value,
                    atr_floor):
    # Don't let a quiet market inflate size without limit.
    atr_used = max(atr_value, atr_floor)
    dollar_risk = capital * target_risk_pct
    # Units such that one ATR of move is about the dollar risk budget.
    return dollar_risk / (atr_used * point_value)

# Example: $10,000 account, target 1% daily risk, point value $10/point.
for atr_now in [5, 10, 20, 40]:
    size = vol_target_size(10_000, 0.01, atr_now, 10, atr_floor=6)
    print(f"ATR={atr_now:>3}  ->  size = {size:6.1f} units")

Run it and confirm the behavior: as ATR rises, size falls; and the floor (atr_floor=6) stops the calm-market blow-up by refusing to size up past that volatility.

Part B — a risk-of-ruin table for 1% / 2% / 5% per trade. Simulate many trade sequences and count how often the account falls into a ruinous drawdown.

rng = np.random.default_rng(7)

def risk_of_ruin(risk_per_trade, win_rate=0.45, payoff=1.6,
                 ruin_level=0.40, n_trades=500, sims=20_000):
    ruined = 0
    for _ in range(sims):
        equity = 1.0
        peak = 1.0
        wins = rng.random(n_trades) < win_rate
        for w in wins:
            equity *= (1 + risk_per_trade * payoff) if w else (1 - risk_per_trade)
            peak = max(peak, equity)
            if equity <= (1 - ruin_level) * peak:   # drawdown from peak
                ruined += 1
                break
    return ruined / sims

print(f"{'risk/trade':>10} {'P(ruin)':>10}")
for r in [0.01, 0.02, 0.05]:
    print(f"{r:>10.0%} {risk_of_ruin(r):>10.1%}")

Read the table. With this modest positive edge (45% win rate, 1.6:1 payoff), 1% risk-per-trade should show a small probability of a 40% drawdown, 2% noticeably higher, and 5% alarming — the same edge, sized three ways, with wildly different survival odds.

Part C — one experiment. Set win_rate=0.50, payoff=1.0 (zero edge) and rerun Part B. Notice that even with no edge, ruin probability rises steeply with bet size — proof that sizing alone can bankrupt you, edge or no edge.

Terms introduced

Check

You can move on when you can… size a position by both fixed-fractional and volatility-targeting methods and explain what each does when volatility doubles, state in one sentence why Kelly is a ceiling and not a target, and read your own risk-of-ruin table well enough to justify a specific risk-per-trade choice out loud.

Go deeper

Robert Carver, Systematic Trading (Part 3) and Leveraged Trading — the volatility-targeting framework in full; the arithmetic is arithmetic, not calculus.
QuantStart, “Money Management via the Kelly Criterion” — the free derivation and the case for fractional Kelly: https://www.quantstart.com/articles/
Better System Trader ep.70 (Carver) and ep.37 (Cesar Alvarez on stops) — the full versions of the interviews excerpted above: https://bettersystemtrader.com