The Kelly criterion

The mathematically optimal position size for a repeating bet with known edge and known payoff.

Kelly formula

Kelly fraction = (bp − q) / b

Where: b = payoff ratio (win amount / loss amount) p = probability of winning q = probability of losing = 1 − p

Example

Kelly for an iron condor

Your iron condor:

  • Wins 85% of the time (p = 0.85, q = 0.15)
  • When it wins: makes ₹2,250 (max profit)
  • When it loses: loses ₹2,750 (max loss)
  • Payoff ratio b = 2,250 / 2,750 = 0.818

Kelly fraction = (0.818 × 0.85 − 0.15) / 0.818 = (0.695 − 0.15) / 0.818 = 0.545 / 0.818 = 0.666

Kelly says: risk ~67% of your account per trade.

This is way too aggressive for real trading.

Why full Kelly is dangerous

Kelly assumes:

Overestimate your win rate by 10%, and Kelly recommends 2-3× the correct amount. Result: blow-up.

Fractional Kelly (the realistic version)

Most professionals use quarter Kelly or half Kelly:

For the iron condor above:

Compare to the 2% rule: quarter Kelly is 8× larger. That’s the trade-off — higher returns but bigger swings.

The reality check

Kelly-based sizing only works if your edge estimates are accurate. For 95%+ of retail traders, edge estimates are optimistic. Backtest results include survivorship bias, hindsight bias, and small samples.

Realistic recommendation:

Volatility-based sizing

Instead of fixed % per trade, scale size inversely to volatility:

Volatility-target sizing

Position size = (Target volatility × Account value) / (Position’s standard deviation)

Or, expressed as: Position size = Target risk in ₹ / Expected daily standard deviation of position

Example

Vol-scaling an iron condor

Account: ₹5,00,000. Target: 1% daily portfolio vol.

Iron condor’s expected daily P&L standard deviation (from backtest): ₹1,200 per lot.

Target position: (0.01 × 5,00,000) / 1,200 = 5,000 / 1,200 = ~4 lots

Compare to fixed 2% rule (2 lots max). Vol-scaling doubles size when the strategy is quiet.

Now say Nifty vol spikes and iron condor daily P&L std doubles to ₹2,400/lot: Target = 5,000 / 2,400 = ~2 lots

Automatic reduction when environment gets riskier.

Vol-scaling in practice

Rule: as market volatility (VIX) rises, reduce position count. As it falls, increase.

Simple version:

This ensures your account never faces catastrophic vol at maximum leverage.

Position sizing across multiple strategies

If you run 3 strategies simultaneously (iron condors, calendar spreads, cash-secured puts):

Rule: treat total portfolio exposure as one budget.

Correlations matter — all three strategies may go bad simultaneously if there’s a big Nifty move.

Portfolio-level Greeks

Beyond simple sizing, monitor:

Rebalance when any exposure exceeds your set limit.

The anti-Kelly principle

Some professional traders deliberately size BELOW Kelly to maximize compounding rate:

“Safety-first Kelly” — never bet so much that a bad streak forces you out. Even if it means lower short-term returns.

Warren Buffett’s essential insight: “Never lose money” isn’t literal — it means “never lose so much that you can’t recover.”

Practical hierarchy of sizing methods

Use in this order as sophistication grows:

  1. Fixed rupee amount — beginner (₹500 per trade regardless)
  2. Fixed % of account — early intermediate (2% per trade)
  3. Vol-scaled fixed % — intermediate (2% adjusted by market vol)
  4. Quarter Kelly — proven systematic trader
  5. Portfolio Greeks limits — advanced multi-strategy

Skip levels only when you have data to justify it. Most retail should stay at levels 2-3 forever.

⚠️ The universal rule

No matter how sophisticated your sizing math, keep an absolute cap: never risk more than 20% of your account across ALL open positions at any time. This protects against correlated blow-ups.

Common sizing mistakes

The sizing playbook for the average Indian retail trader

Start with:

After 12 months of tracked results: