4.7.10
Intuition Ek sentence mein badi baatAapki position size ko aapke account ke saath saanS leni chahiye — jab capital grow kar raha ho to aap thoda zyada absolute money risk karo, aur jab drawdown ho to thoda kam , taaki ek losing streak kabhi aapko blow up na kar sake jabki ek winning streak aapko harder compound karne de.
Definition Performance-based position sizingEk rule jisme aap per trade jitna dollar risk karte ho woh aapki current equity ki ek fixed fraction hoti hai , na ki ek fixed dollar figure. Jab equity badhti hai to fraction ek badi position khareedti hai; jab equity girti hai to automatically position shrink ho jaati hai. Isse anti-martingale sizing bhi kehte hain (aap winners ko press karo, losers ko nahi).
Do opposite philosophies:
Style
Loss ke baad behaviourWin ke baad behaviourVerdict
Martingale size up (losses chase karo)
size down
Accounts blow up kar deta hai
Anti-martingale size down
size up
Professional standard
Performance sizing, anti-martingale ka disciplined form hai.
Intuition Losses ke baad kyun shrink karein?Ek drawdown ka matlab hai ya to market regime aapke edge ke against ho gayi, ya variance aapko punish kar raha hai. Dono cases mein aap chahte ho ki jab tak cheezein dobara prove na ho jaayein tab tak kam capital exposed rahe. Smaller size survival time khareedta hai — aur survival hi ek aisi cheez hai jo aapko tab tak zinda rakhti hai jab tak aapka edge wapas nahi aa jaata.
Intuition Wins ke baad kyun grow karein?Winning ka matlab hai woh base jis par aap compound karte ho bada ho gaya. Agar aap ek constant % risk karte rehte ho, toh ek bada base automatically zyada dollars deploy karta hai — yahi compounding hai. Iske bajaay ek constant dollar amount risk karna growth ko waste kar dega.
Iska mathematical heart geometric growth hai. Aapka account N product hai, sum nahi:
E N = E 0 ⋅ ∏ i = 1 N ( 1 + r i )
jahan r i i poore account par. Kyunki yeh ek product hai, ek r i = − 1 E N hamesha ke liye zero par bhej deta hai. Yeh single fact hi wajah hai ki hum fraction risked ko cap karte hain.
Kuch traders f D
f u se d = f ba se ⋅ ( 1 − k D )
Kyun? E accelerate karta hai — ek doosra safety brake.
Worked example Example 1 — Do equity levels par automatic sizingRule: risk f = 2%
Equity $50,000 par:
Dollar risk = 0.02\times 50000 = \ 1000$. Kyun? Current equity ka fixed 2%.
Q = 1000/5 = 200 Kyun? Step 3 formula.
Achhi run ke baad, equity $70,000:
Dollar risk = 0.02\times 70000 = \ 1400$.
Q = 1400/5 = 280 Kyun? Same rule, bada base ⇒ sized up .
$40,000 tak drawdown ke baad:
Dollar risk = \ 800, Kyun? Chhota base ⇒ sized down automatically.
Worked example Example 2 — Drawdown brake in actionf ba se = 2% k = 1 D = 25% = 0.25 f u se d = 0.02 ( 1 − 1 × 0.25 ) = 0.02 × 0.75 = 1.5% =0.015\times40000=\ 600, t o h Yeh step kyun? 25% drawdown ne humein extra cautious bana diya, shares ko 160 (Ex 1) se 120 tak cut kar diya.
Worked example Example 3 — % rule aapko kyun bachata hai (survival math)Maano aap 10 straight losses lete ho fixed 2% risk karte hue.
E 10 = E 0 ( 0.98 ) 10 = E 0 × 0.817 81.7% rakhte ho. Ek shrinking account par fixed $1000 ke saath, 10th loss ek bahut bada percentage hoti, aur zyada gehri khaai khodti.
Yeh step kyun? Geometric buffer dikhata hai: constant % aapko kabhi losing streak se zero nahi kar sakta.
Common mistake "3 losses ke baad mujhe double up karna chahiye taaki wapas win kar sakoon."Kyun sahi lagta hai: "Odds wapas aane chahiye — ek coin hamesha tails nahi land kar sakta." Yeh math jaisi lagti hai.
Kyun galat hai: Markets ki koi memory nahi hoti ; past losses next-trade odds nahi badhate. Martingale sizing ek normal losing streak ko ruin mein badal deti hai kyunki required bet exponentially badhti hai jabki capital shrink hoti hai.
Fix: Ulta karo — losses ke baad shrink karo (anti-martingale). % rule ko yeh aapke liye karne do.
Current equity ki jagah starting balance se sizing karna.
Kyun sahi lagta hai: Compute karna simpler hai; "Maine ek baar set kar diya."
Kyun galat hai: Drawdown ke baad aap chhote account ki ek badi fraction risk kar rahe hoge (over-risk), aur gains ke baad aap under-compound karoge.
Fix: Hamesha aaj ki equity use karke f ⋅ E
Common mistake Risk-% aur position-% ko confuse karna.Kyun sahi lagta hai: "Maine apna 20% account mein lagaya, toh main 20% risk kar raha hoon."
Kyun galat hai: Aap sirf entry se stop tak risk karte ho. 5% stop ke saath ek 20% position sirf 0.20 × 0.05 = 1% Fix: Risk = position size × stop distance. Risk size karo, notional ko nahi.
Recall Feynman: ek 12-saal ke bachche ko explain karoSocho tum ek game mein marbles bet kar rahe ho. Smart rule: har round, sirf unhi marbles ka ek chhota hissa bet karo jo abhi tumhare paas hain. Agar tum jeedte rehte ho, tumhara dher badh jaata hai, toh wahi slice zyada marbles hoti hai — tum bade bet karo aur faster grow karo. Agar tum haarte rehte ho, tumhara dher shrink ho jaata hai, toh slice kam marbles hoti hai — tum chhota bet karo aur diwaaliya nahi ho sakte. Baewakoofi ki rule hai ki haarne ke baad zyada bet karo "taaki wapas le sako" — aise hi bachche ek buri streak mein saari marbles kho dete hain.
"Winners ki bet badhao, losers ki bet bhookha rakho."
Aur formula ke liye: REP — R isk = E (equity) × P ercent, phir stop distance se divide karo.
Fixed-fractional (anti-martingale) sizing kya hai? Current equity ki ek constant fraction ko per trade risk karna, taaki size wins ke baad badhta rahe aur losses ke baad shrink hota rahe.
Losses ke baad size DOWN kyun karo? Survival time khareedne ke liye — jab aapka edge/regime uncertain ho tab kam exposure; account ek streak se blow up nahi ho sakta.
Wins ke baad size UP kyun karo? Badi equity base ka matlab hai ki ek constant % zyada dollars deploy karta hai, jo gains compound karne deta hai.
Quantity formula batao. Q = ∣ P e n t r y − P s t o p ∣ f ⋅ E
Equity growth geometric kyun hai, arithmetic kyun nahi? Account ek product E 0 ∏ ( 1 + r i )
5% stop ke saath ek 20% position account ka kitna % risk karti hai? 0.20 × 0.05 = 1%
10 straight 2% losses ke baad capital ka kitna fraction bachta hai? ( 0.98 ) 10 ≈ 0.817
Drawdown brake f u se d = f ba se ( 1 − k D ) Drawdown D
Martingale sizing dangerous kyun hai? Markets ki koi memory nahi hoti; losses ke baad doubling karne se bet exponentially badhta hai jabki capital shrink hoti hai → ruin.
Kya starting balance ya current equity se size karna chahiye? Current equity — har trade mein f ⋅ E
Position Sizing — woh parent skill jise yeh note refine karta hai.Fixed-Fractional vs Fixed-Dollar Sizing Kelly Criterion — max geometric growth ke liye mathematically optimal f Maximum Drawdown — woh metric jise down-scaling protect karta hai.Compounding & Geometric Returns — kyun product-of-returns caution force karta hai.Stop-Loss Placement — sizing formula ka denominator set karta hai.Risk of Ruin — probability model jo anti-martingale ko justify karta hai.
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
