# Brownian Motion Path and Maximum Drawdown

Brownian Motion Path and Maximum Drawdown

We illustrate the evolution of a geometric Brownian motion simulating a daily stock return series. The jagged blue line is the cumulative return of the daily return series. The red line is the maximum drawdown to date of the series. Adjusting the mean and standard deviation sliders demonstrates how the cumulative return and maximum drawdown change with respect to these parameters for a given underlying set of random shocks. Adjusting the "new random case" slider allows you to see different random cases to get a sense of how variable a return series can be for a single set of parameters. Note that in general the greater the ratio of mean to standard deviation, the smoother the return evolution is and the smaller the maximum drawdown is.