This has been bugging me for while. Say I want to use real world measure to produce stochastic scenarios to project equity return, and for simplicity sake, I am going to use Geometric Brownian Motion as my distribution for return. I know that under risk free measure the scenarios would be based off normal distribution with ln (return (t)/(return (t-1)) ~ N (risk free rate - 0.5 x sigma ^2, sigma^2) as per Girsanov Theorem. But for real world projection, what is wrong with projecting the equity return using ln (return (t)/(return (t-1)) ~ N (drift, sigma^2) to produce the scenarios? Thanks very much
