Intuition The big idea in one sentenceYour position size should breathe with your account — when your capital is growing you risk slightly more absolute money , and when you draw down you risk slightly less , so a losing streak can never blow you up while a winning streak lets you compound harder.
Definition Performance-based position sizingA rule where the dollar amount you risk per trade is a fixed fraction of your current equity , not a fixed dollar figure. As equity rises the fraction buys a bigger position; as equity falls it automatically shrinks the position. This is also called anti-martingale sizing (you press winners, not losers).
Two opposite philosophies:
Style
Behaviour after a loss
Behaviour after a win
Verdict
Martingale size up (chase losses)
size down
Blows accounts up
Anti-martingale size down
size up
Professional standard
Performance sizing is the disciplined form of anti-martingale.
Intuition Why shrink after losses?A drawdown means either the market regime turned against your edge, or variance is punishing you. In both cases you want less capital exposed until things prove out again. Smaller size buys survival time — and survival is the only thing that lets you be around when your edge returns.
Intuition Why grow after wins?Winning means the base you compound on got bigger. If you keep risking a constant % , a bigger base automatically deploys more dollars — this is compounding. Risking a constant dollar amount instead would waste the growth.
The mathematical heart of this is geometric growth . Your account after N N N product , not a sum:
E N = E 0 ⋅ ∏ i = 1 N ( 1 + r i ) E_N = E_0 \cdot \prod_{i=1}^{N} (1 + r_i) E N = E 0 ⋅ ∏ i = 1 N ( 1 + r i )
where r i r_i r i i i i whole account . Because it is a product, one r i = − 1 r_i = -1 r i = − 1 E N E_N E N forever . This single fact is why we cap the fraction risked.
Some traders make f f f D D D
f u s e d = f b a s e ⋅ ( 1 − k D ) f_{used} = f_{base}\cdot(1 - k\,D) f u se d = f ba se ⋅ ( 1 − k D )
Why? Beyond the automatic scaling from E E E accelerates the shrink during ugly streaks — a second safety brake.
Worked example Example 1 — Automatic sizing at two equity levelsRule: risk f = 2 % f = 2\% f = 2%
At equity $50,000:
Dollar risk = 0.02\times 50000 = \ 1000$. Why? fixed 2% of current equity.
Q = 1000 / 5 = 200 Q = 1000/5 = 200 Q = 1000/5 = 200 Why? Step 3 formula.
After a good run, equity $70,000:
Dollar risk = 0.02\times 70000 = \ 1400$.
Q = 1400 / 5 = 280 Q = 1400/5 = 280 Q = 1400/5 = 280 Why? Same rule, bigger base ⇒ sized up .
After a drawdown to $40,000:
Dollar risk = \ 800, , , Why? Smaller base ⇒ sized down automatically.
Worked example Example 2 — Drawdown brake in actionf b a s e = 2 % f_{base}=2\% f ba se = 2% k = 1 k=1 k = 1 D = 25 % = 0.25 D=25\%=0.25 D = 25% = 0.25 f u s e d = 0.02 ( 1 − 1 × 0.25 ) = 0.02 × 0.75 = 1.5 % f_{used} = 0.02(1-1\times0.25)=0.02\times0.75 = 1.5\% f u se d = 0.02 ( 1 − 1 × 0.25 ) = 0.02 × 0.75 = 1.5% =0.015\times40000=\ 600, s o , so , so Why this step? The 25% drawdown made us extra cautious, cutting shares from 160 (Ex 1) down to 120.
Worked example Example 3 — Why the % rule saves you (survival math)Suppose you take 10 straight losses risking a fixed 2% each.
E 10 = E 0 ( 0.98 ) 10 = E 0 × 0.817 E_{10}=E_0(0.98)^{10}=E_0\times0.817 E 10 = E 0 ( 0.98 ) 10 = E 0 × 0.817 81.7% of capital. With a fixed $1000 on a shrinking account, the 10th loss would be a far larger percentage , digging a deeper hole.
Why this step? Shows the geometric buffer: constant % can never zero you out from a losing streak.
Common mistake "After 3 losses I should double up to win it back."Why it feels right: "The odds must swing back — a coin can't land tails forever." It feels like math .
Why it's wrong: Markets have no memory ; past losses don't raise next-trade odds. Martingale sizing turns a normal losing streak into ruin because the required bet grows exponentially while your capital shrinks.
Fix: Do the opposite — shrink after losses (anti-martingale). Let the % rule do it for you.
Common mistake Sizing off thestarting balance, not current equity.
Why it feels right: Simpler to compute; "I set it once."
Why it's wrong: After a drawdown you'd be risking a bigger fraction of the smaller account (over-risk), and after gains you'd under-compound.
Fix: Always recompute f ⋅ E f\cdot E f ⋅ E today's equity.
Common mistake Confusing risk-% with position-%.Why it feels right: "I put 20% of my account in, so I risk 20%."
Why it's wrong: You only risk from entry to stop . A 20% position with a 5% stop risks just 0.20 × 0.05 = 1 % 0.20\times0.05=1\% 0.20 × 0.05 = 1% Fix: Risk = position size × stop distance. Size the risk , not the notional.
Recall Feynman: explain to a 12-year-oldImagine you're betting marbles in a game. The smart rule: each round, only bet a small slice of the marbles you have right now. If you keep winning, your pile grows, so that same slice is more marbles — you bet bigger and grow faster. If you keep losing, your pile shrinks, so the slice is fewer marbles — you bet smaller and can't go broke. The dumb rule is to bet more after losing to "get it back" — that's how kids lose all their marbles in one bad streak.
"Grow the winners' bet, starve the losers' bet."
And for the formula: REP — R isk = E (equity) × P ercent, then divide by stop distance.
What is fixed-fractional (anti-martingale) sizing? Risking a constant fraction of current equity per trade, so size grows after wins and shrinks after losses.
Why do you size DOWN after losses? To buy survival time — smaller exposure while your edge/regime is uncertain; account can't be blown up by a streak.
Why do you size UP after wins? A bigger equity base means a constant % deploys more dollars, letting you compound gains.
State the quantity formula. Q = f ⋅ E ∣ P e n t r y − P s t o p ∣ Q = \dfrac{f\cdot E}{|P_{entry}-P_{stop}|} Q = ∣ P e n t r y − P s t o p ∣ f ⋅ E .
Why is equity growth geometric, not arithmetic? Account is a
product E 0 ∏ ( 1 + r i ) E_0\prod(1+r_i) E 0 ∏ ( 1 + r i ) ; one −100% return zeroes it permanently, so we cap the fraction risked.
A 20% position with a 5% stop risks what % of account? 0.20 × 0.05 = 1 % 0.20\times0.05 = 1\% 0.20 × 0.05 = 1% — position-% ≠ risk-%.
After 10 straight 2% losses, what fraction of capital remains? ( 0.98 ) 10 ≈ 0.817 (0.98)^{10}\approx 0.817 ( 0.98 ) 10 ≈ 0.817 , i.e. ~81.7%.
What does the drawdown brake f u s e d = f b a s e ( 1 − k D ) f_{used}=f_{base}(1-kD) f u se d = f ba se ( 1 − k D ) Extra-shrinks the risk fraction as drawdown
D D D grows, a second safety brake beyond automatic equity scaling.
Why is martingale sizing dangerous? Markets have no memory; doubling after losses grows the bet exponentially while capital shrinks → ruin.
Should you size off starting balance or current equity? Current equity — recompute
f ⋅ E f\cdot E f ⋅ E every trade.
Position Sizing — the parent skill this note refines.Fixed-Fractional vs Fixed-Dollar Sizing Kelly Criterion — mathematically optimal f f f Maximum Drawdown — the metric the down-scaling protects.Compounding & Geometric Returns — why product-of-returns forces caution.Stop-Loss Placement — sets the denominator of the sizing formula.Risk of Ruin — probability model that justifies anti-martingale.
equity is product not sum
one r_i = -1 ruins forever
Martingale blows up account
E_N = E_0 times product of 1+r_i
Q = f times E over stop distance
Intuition Hinglish mein samjhoBhai, position sizing ka asli funda yeh hai: har trade mein tum apne current account ka ek fixed percentage (jaise 2%) risk karo, fixed rupaye nahi. Iska seedha matlab — jab account badh raha hai to same 2% zyada paise ban jaata hai, to tumhari position automatically badi ho jaati hai (sizing up). Aur jab loss ho raha hai, account chhota, to 2% kam paise, position choti ho jaati hai (sizing down). Yeh apne aap ho jaata hai, formula ke andar hi baitha hai: Q = f ⋅ E / ( entry − stop ) Q = f\cdot E / (\text{entry} - \text{stop}) Q = f ⋅ E / ( entry − stop )
Yeh kyun important hai? Kyunki account geometric tarike se badhta hai — matlab returns multiply hote hain, add nahi. Ek baar agar tumne 100% blow kar diya to game khatam, permanently zero. Isliye har trade pe sirf chhota slice risk karke tum apni survival pakki karte ho. Losing streak aaye to bhi ( 0.98 ) 10 (0.98)^{10} ( 0.98 ) 10
Sabse bada trap: martingale — loss ke baad size double karke "wapas jeetne" ki koshish. Dimaag kehta hai "coin ab head aayega hi", par market ka koi memory nahi hota. Yeh soch tumhe ek hi bure streak mein zero pe le aayegi. Ulta karo — anti-martingale : loss ke baad choti bet, win ke baad badi bet. Aur ek aur galti se bacho: position-% aur risk-% alag cheez hain. 20% position with 5% stop ka matlab sirf 1% risk hai. Hamesha stop distance se risk calculate karo, aur equity aaj ki lo, purani nahi.
