A trader with Rs 50 lakh of risk capital stakes 5% of current capital per trade at a 52% win rate with even payoffs; the desk stops her at a 30% drawdown. How likely is the stop, and what changes at 2%?

At 5% staking the stop is hit on about 100% of simulated 500-trade paths; at 2% it falls to about 60%. Each trade adds only about 0.08% of expected log growth against a 5.0% swing, so the account is nearly a driftless random walk and 30% is a short distance to wander. At 2% the barrier is 18 swings away; at 1% the chance is about 6%. She should run 2% or less: the edge is the same at every stake, and only a small stake gives it time to show.

Picture a coin that lands heads 52 times in a hundred. Betting a twentieth of your money on every toss, you expect to be ahead by 4% of the stake per toss, which is 0.2% of your money, while the money swings by 5% on every single toss. The expected growth per trade in log terms is 0.52 x ln(1.05) + 0.48 x ln(0.95), about 0.075%, against a per-trade standard deviation of 5.0%: the signal is about 1.5% of the noise. Over 500 trades the expected log gain is 38%, which sounds fine, but the standard deviation of the log over the same 500 trades is 112%. The trader's two years are a bet on the path far more than a bet on the edge.

There is a clean formula for a random walk with drift g and standard deviation sigma starting at zero: the chance of ever falling by a log distance a is exp(-2ga / sigma squared). A 30% fall is a log distance of 0.357. At 5% staking that gives exp(-2 x 0.00075 x 0.357 / 0.0025), about 81%; at 2% staking it gives about 34%. That formula measures a fall from the starting capital with no time limit. The desk's rule is harsher, a fall from the running peak, and the horizon is 500 trades, so simulate it: 20,000 paths of 500 trades each. The 5% staker hits the stop on 100% of paths, typically around trade 51; the 2% staker on 60%. The two methods agree on the shape; the peak-to-trough rule pushes the simulated figure up, and the 500-trade horizon pulls it down, which is why the 1% case comes out a little under its formula.

Because the stake enters the formula twice, once in the drift and once, squared, in the variance. Halving f roughly halves g and roughly quarters sigma squared, so the exponent 2ga over sigma squared roughly doubles. The 2% staker's barrier is 18 per-trade swings away against 7 for the 5% staker, and the formula's answer falls from 81% to 34%; measured from the peak within 500 trades it falls from near certain to about 60%, and at 1% staking to about 6%. The price is a slower expected climb: median capital after 500 trades is about Rs 67.5 lakh at 2% against Rs 72.8 lakh at 5%. But the 5% figure is the median of the survivors and the stopped; a trader who is closed down at trade 51 does not collect the median.

Give the desk head a view. Run 2%, and argue for 1% until the hit rate is proven, because the edge is the same at every stake and the point of a desk stop is to let a real edge survive long enough to show. The full Kelly stake for a 52% even-money bet is 2p minus 1, which is 4% of capital; 5% is more than full Kelly, where growth is already falling and variance is enormous, while 2% is half Kelly, the usual working size. A trader who insists on 5% is saying her edge is larger than 52%, and the right answer to that is to prove it on the smaller size first.

State the limits. The 52% is itself an estimate; with 500 trades its standard error is about 2.2 points, so the true rate could be 50% and the whole edge imaginary, which the small stake also protects against. Trades are assumed independent with fixed odds; a strategy whose losses cluster will hit the stop sooner than either calculation says.