Understand position sizing formulas

Core Concepts

What Is Position Sizing?

WHY it exists: Raw intuition ("buy 100 shares") ignores volatility. A₹50 stock moving₹5 has the same absolute risk as a ₹500 stock moving ₹50, but different position sizes needed.

The Foundation: Risk-Based Position Sizing

DERIVATION FROM FIRST PRINCIPLES:

Start with your risk budget: If you have ₹1,00,000 and risk 2% per trade: $\text{Account Risk} = 1,00,000 \times 0.02 = ₹2,000$ WHY: This is your maximum acceptable loss. You can survive50 consecutive losses before ruin (in theory).
Calculate risk per share: If you buy at ₹100 with stop-loss at ₹95: $\text{Risk Per Share} = 100 - 95 = ₹5$ WHY: Each share you own exposes you to ₹5 of loss if stopped out.
Divide total risk by per-share risk: $\text{Shares} = \frac{2,000}{5} = 400 \text{ shares}$ HOW: If you own 400 shares and get stopped out, loss =400 × ₹5 = ₹2,000 (exactly your budget).

Verification: Total position value = 400 × ₹100 = ₹40,000. If stopped, you lose ₹2,000 (2% of ₹1,00,000 ✓).

Figure — Understand position sizing formulas

Worked example Worked Example 1: Equity Trade

Setup:

Account equity: ₹5,00,000
Risk tolerance: 1.5% per trade
Stock: Reliance at ₹2,400
Technical stop-loss: ₹2,320(support level) Step 1: Calculate account risk $\text{Account Risk} = 500{,}000 \times 0.015 = ₹7,500$ Why this step? Converting percentage to rupees makes it concrete.

Step 2: Calculate risk per share $\text{Risk Per Share} = 2,400 - 2,320 = ₹80$ Why this step? Each share carries ₹80 of downside if hypothesis fails.

Step 3: Calculate position size $\text{Shares} = \frac{7,500}{80} = 93.75 \rightarrow 93 \text{ shares (round down)}$ Why round down? Ensures you never exceed risk budget.

Step 4: Calculate total capital deployed $\text{Position Value} = 93 \times 2,400 = ₹2,23,200$ Verification: If stopped out, loss = 93 × ₹80 = ₹7,440 (≤ ₹7,500 ✓). This is 1.49% of account.

Worked example Worked Example 2: Futures Trade (Leverage)

Setup:

Account equity: ₹2,00,000
Risk: 2% = ₹4,000
Nifty Futures at 21,500 lot size = 50
Stop-loss: 21,350 (150 points below) Step 1: Risk per lot $\text{Risk Per Lot} = 150 \times 50 = ₹7,500$ Why this step? Futures trade in fixed lots; 1 lot = 50 units of Nifty. Step 2: Calculate lots to trade $\text{Lots} = \frac{4,000}{7,500} = 0.53 \rightarrow 0 \text{ lots!}$ CRITICAL INSIGHT: You cannot trade even 1 lot without exceeding risk budget (₹7,500 > ₹4,000). This is why futures are dangerous for small accounts.

Solution: Either (a) increase stop distance to 53 points (₹2,650 per lot), or (b) use options where you can control exposure more granularly.

Active Recall Practice

Recall Explain to a 12-Year-Old

Imagine you have ₹100 pocket money and you're betting on cricket match outcomes with friends. You don't want to lose all your money in one bad bet, right?

Position sizing is like this: You decide "I'll risk only₹2 per bet" (2% of ₹100). Now, if you're betting on India vs. Australia and you think India wins, but you're only 60% sure, you don't bet the full ₹2at once. You might bet ₹1 with your confident friend (who might pay₹1.50 if you win) and save ₹1 for the next bet.

In stocks: You have ₹1,00,000. You find a stock at ₹100 but you're not 100% sure, so you put a "stop loss" at ₹95 (you'll sell if it drops to ₹95). Position sizing formula tells you: "If you're willing to lose ₹2,000 total, and each share risks ₹5, buy 400 shares." That way, if you're wrong, you lose exactly₹2,000, not your entire ₹1,00,000!

Connections

Risk Management Fundamentals - Position sizing is the execution layer of risk management
Stop Loss Strategies - Your stop placement directly determines position size
Kelly Criterion - Optimal sizing for maximum long-term growth
Leverage and Margin - How borrowed capital amplifies position sizing calculations
Portfolio Allocation - Position sizing for individual trades fits into broader portfolio limits
Average True Range (ATR) - Volatility measure for adaptive position sizing
Expectancy and Win Rate - Your system's statistics inform Kelly-based sizing
Drawdown Management - Position sizing prevents catastrophic drawdowns

Flashcards

#flashcards/stock-market

What is the basic position sizing formula? :: Position Size (shares) = Account Risk (₹) ÷ Risk Per Share (₹)

What is Account Risk in position sizing?

Account Equity × Risk % per trade (e.g., ₹1,00,000 × 2% = ₹2,000)

What is Risk Per Share?

Entry Price - Stop Loss Price (the amount you lose per share if stopped out)

If you have ₹5,00,000, risk1.5%, buy at ₹2,400 with stop at ₹2,320, how many shares?

Account Risk = ₹7,500; Risk/share = ₹80; Shares = 7,500 ÷ 80 = 93 shares

Why round down position size instead of up?

To ensure you never exceed your risk budget; rounding up could risk more than planned

What is the Kelly Criterion formula?

f* = [p(b+1) - 1] / b, where p = win probability, b = win/loss ratio

Why is full Kelly considered too aggressive?

It maximizes growth but causes high volatility; Half-Kelly reduces equity swings while still growing capital

What is the ATR-based position sizing formula?

Shares = Account Risk ÷ (ATR × Multiplier), where ATR adapts to stock's volatility

Why is "always buy 100 shares" a mistake?

Ignores different risk per share across stocks; a ₹50 stock with ₹5 stop has different total risk than ₹500 stock with ₹50 stop

What secondary check prevents over-concentration?

Position Value ≤ Portfolio Limit % × Account Equity (typically 20-30% per stock)

Why should stops be set at technical levels, not arbitrary percentages?

Arbitrary stops may be too tight (stopped by noise) or too wide (wasting capital); technical levels reflect actual support/resistance

In a futures trade, why might you be unable to trade even 1 lot?

If Risk Per Lot exceds your Account Risk budget (e.g., ₹7,500 risk per lot but only ₹4,000 risk budget)

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Position sizing matlab tumhe yeh bata hai ki kitne shares kharidne chahiye jab tum koi tradelete ho. Yeh bahut simple formula hai: tumhara total risk (jo tum haar sakte hoek trade mein) ko divide karo tumhare per-share risk se (entry price minus stop loss). Samjho agar tumhare pas 1 lakh rupaye hain aur tum 2% risk lena chahte ho, toh ₹2,000 risk ho gaya. Ab agar tumhari stock₹100 pe hai aur tum ₹95 pe stop loss rakhoge, toh har share pe ₹5 ka risk hai. Toh shares =2000 ÷ 5 = 400 shares kharidne chahiye.

Yeh formula kyun zaroori hai? Kyunki agar tum hamesha "100 shares kharidta hun" sochoge, toh galat ho jayega. Ek ₹50 wali stock ka100 shares aur ₹500 wali stock ka 100 shares — dono ka risk bilkul alag hai! Proper position sizing se tumhara risk consistent rahega, chahe stock ka price kuch bhi ho. Yeh tumhe bachata hai bade losses se aur tumhara account lambe time tak survive karta hai.

Ek aur common mistake: log stop loss ko randomly5% ya 10% rakh dete hain bina chart dekhe. Galat approach! Pehle chart pe technical levels dekho (support, resistance), wahan stop rakho, phir formula se calculate karo kitne shares lene hain. Agar tum pehle shares decide karoge aur phir stop rakhoge, toh tum risk manage nahi kar rahe, bas luck pe chal rahe ho. Position sizing tumhara armor hai market ke surprises ke against!

Core Concepts

What Is Position Sizing?

The Foundation: Risk-Based Position Sizing

Advanced Formulas

Common Mistakes

Active Recall Practice

Connections

Flashcards

Concept Map

Hinglish (regional understanding)

Test yourself — How to Trade — Execution & Platforms

Connections