Kelly Criterion
A mathematical formula for calculating the theoretically optimal fraction of capital to risk on each trade, maximising long-run compounded growth while avoiding the catastrophic losses that come from over-betting.
Definition
The Kelly Criterion is a position-sizing formula derived by mathematician John L. Kelly Jr. in 1956 that computes the fraction of capital to deploy on a given trade in order to maximise the expected logarithm of wealth — equivalently, the long-run compounded growth rate — over many repetitions. The formula takes into account both the probability of winning (the strategy's win rate) and the magnitude of wins versus losses (the payoff ratio). Betting more than the Kelly fraction causes the account to grow more slowly in the long run and dramatically increases risk of ruin; betting less is suboptimal but safer, which is why most practitioners use a fraction of Kelly rather than the full amount.
Why it matters
Most retail traders in Indian markets size positions based on intuition, a fixed lot count, or the margin available — none of which are related to the statistical properties of their strategy. The Kelly Criterion provides a principled, data-driven alternative. When applied to an NSE F&O strategy that has been properly backtested, Kelly sizing tells you exactly how large each trade should be relative to your current capital, and it scales down automatically as capital shrinks (protecting against ruin) and scales up as capital grows (compounding gains efficiently).
The formula also reveals how thin a strategy's edge actually is. Many traders discover that their apparent win rate translates to a Kelly fraction of just 2–5%, meaning the mathematically correct position is far smaller than their instinct suggests. This is especially relevant in Bank Nifty weekly options, where the combination of high volatility, wide bid-ask spreads, and erratic event-driven moves can reduce effective edge significantly once realistic transaction costs are included.
Formula
The basic Kelly formula is: f* = (bp − q) / b, where f* is the fraction of capital to risk, b is the net payoff ratio (average win divided by average loss), p is the win probability, and q is the loss probability (1 − p). For example, if a strategy wins 55% of the time (p = 0.55, q = 0.45) and the average winner is twice the average loser (b = 2), then f* = (2 × 0.55 − 0.45) / 2 = (1.10 − 0.45) / 2 = 0.65 / 2 = 0.325, or 32.5% of capital. In practice, most traders use half-Kelly (16.25% in this case) or quarter-Kelly to account for estimation error and to reduce drawdown.
Example
Suppose a trader has backtested a Nifty futures breakout strategy over two years and found a win rate of 48% with an average winner of Rs 6,000 and an average loser of Rs 3,000, giving a payoff ratio b = 2. Applying Kelly: f* = (2 × 0.48 − 0.52) / 2 = (0.96 − 0.52) / 2 = 0.44 / 2 = 0.22 (22% of capital). With a trading capital of Rs 10,00,000, full Kelly would suggest risking Rs 2,20,000 per trade — far too aggressive for most traders. At half-Kelly, the risk per trade is Rs 1,10,000, and at quarter-Kelly it is Rs 55,000. The trader opts for quarter-Kelly to keep drawdown manageable while still capturing most of the strategy's long-run growth potential.
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