Fractional Kelly Sizer

Kelly's 1956 derivation maximizes the long-run expected log-growth of bankroll. Fixed dollars don't compound efficiently because winning bets aren't pressed and losing streaks don't shrink the bet size. Fractional sizing keeps geometric growth optimal; the cost is that drawdowns can be severe at full Kelly.

No, not when you estimated p and b from data. Full Kelly assumes you know the true win rate and win/loss ratio. With estimation error, full Kelly often turns into over-betting and ruinous drawdowns. Half-Kelly (0.5×) or quarter-Kelly (0.25×) is the standard real-world choice — Thorp and MacLean argue this in print.

It's the fraction of simulated paths where bankroll fell below the threshold you set (typically 50% of starting capital). Ruin rate is sensitive to Kelly fraction, edge size, and number of trades. A non-zero ruin rate at quarter-Kelly is a sign your estimated edge is too thin or your trade count is too high.

Real strategies don't have flat $1 wins and $b losses — there's a distribution around the average. The simulator multiplies outcomes by (1 + 0.1·N(0,1)), floored at 0.1, to inject mild variance. This gives more realistic drawdown distributions than a deterministic model. Heavy-tailed strategies (e.g., option selling) need a smaller Kelly fraction than this Gaussian-noise floor implies.

Kelly was originally formulated for repeated independent bets with known parameters — closer to blackjack than markets. Trading violates several Kelly assumptions: edges drift (regime change), trades correlate (sector exposure), and outcome distributions have fat tails. Treat Kelly as a sizing ceiling, not a target. Most professional traders run far below Kelly-optimal.