Drawing Drawdowns

How position scaling affects drawdown probability in continuous PnL models

This medium-difficulty question tests your understanding of how position scaling interacts with drawdown risk in a continuous stochastic model. It sits at the intersection of portfolio theory and diffusion processes—areas where quant trading desks and asset managers regularly probe candidate intuition during technical interviews.

The core challenge is to reason about what happens to the probability of hitting a fixed absolute loss threshold when you scale both the drift and volatility of the PnL process. You'll need to think carefully about how the signal-to-noise ratio (the Sharpe ratio proxy) and the absolute magnitude of moves both change under scaling. The answer hinges on recognising which parameter—drift, volatility, or their ratio—drives the probability of reaching a given drawdown level.

• Scaling properties of Brownian motion and linear diffusions
• Relationship between Sharpe ratio and drawdown probability
• Hitting times and barrier crossings in continuous models
• Risk–return trade-offs under position sizing