When quieter returns lose their survival edge

This archive note reconstructs a paired comparison of quieter and noisier trade-return sequences. Editorial reading: treat the quieter stream as a survival filter that stays dominant only near chance, then locate the indifference hit rate at which a drawdown limit and a risk-of-ruin screen stop preferring the calmer path.

Recovery asymmetry and the loss bound

In the supplied model, return volatility is the scatter of trade results. Wider dispersion is treated as higher volatility. Recovery asymmetry is the extra percentage gain needed to rebuild equity after a loss of the same nominal size as the original target advance.

A move from 100 units to 120 is a 20 percent rise, but a first 20 percent loss leaves 80 units and then requires a 50 percent rise to reach 120. A drawdown limit is a pre-trade bound on loss size so one adverse result does not force that outsized recovery just to regain the prior goal.

Paired sequences near even odds

Monte Carlo simulation, in this workflow, is repeated random draws of paired trade-return sequences used to compare a quieter equity path with a noisier one under a chosen win probability.

Under a 50-50 win assumption, the quieter stream finished ahead in nearly every run. When other conditions were held equal, a stream with half the volatility of its pair finished ahead in about 70 to 80 percent of matched sequences.

Where the quieter stream loses its edge

After the win probability is shifted away from even odds, the half-volatility stream generally beat the noisier stream only while the modeled win rate stayed at 56 percent or below. Near a 56 percent win rate the two streams drew. At 57 percent or higher the noisier stream was more often the one that finished ahead.

That crossing is the indifference hit rate: the modeled winning percentage at which the quieter and noisier streams finish ahead equally often. Setting the quieter stream to 75 percent of the noisier stream's volatility moved the indifference win rate only from 56 percent to 57 percent, so hit rate outweighed volatility in that simulation.

Risk of ruin on the noisier path

Risk of ruin is the chance that a noisier equity path exhausts capital sooner even when it can also produce larger wins. Equity charts of the paired sequences showed the noisier path reaching larger wins while exhausting capital sooner, which is why a bound on loss size is treated as a working control.

How the worksheet rebuilt the comparison

The worksheet builds the comparison by setting win probability away from 0.5, extending period columns, and redrawing both equity lines after each recalculation.