Positive drift, coin-flip odds

What this geometric Brownian motion probability question tests

This is a medium-difficulty statistics question that quant trading desks use to assess whether a candidate understands the relationship between drift, volatility, and the distribution of future prices under geometric Brownian motion. It requires translating a continuous financial model into a concrete probability calculation.

To solve problems like this, you need to recognize that the log-return of a GBM-driven asset is normally distributed, and then map the given parameters—drift and volatility—into the mean and standard deviation of that distribution. The key insight is understanding how drift and volatility combine to determine whether future prices are more likely to be above or below the starting point. Success depends on setting up the normal distribution correctly and then evaluating the cumulative probability in a way that yields an exact answer.

• Log-normal distribution of prices under GBM
• Normal distribution of log-returns
• Relationship between drift and probability of positive return