I am trying to simulate the distribution of Geometric Brownian Motion drawdowns from realizations of multivariate Normal and Laplace distributions under the same covariance structure. Drawdowns are defined to be the largest peak to trough decline of a cumulative return series where the trough comes after the peak. A cumulative return series is simply the compounded growth of sampled returns (forming something like a geometric brownian motion).
As expected, samples drawn from multivariate Laplace distributions show larger extreme values.
But when I accumulate the returns and take the average of the worst, say 1%, 0.1%, .01% of drawdowns, the normal and laplacian values are quite similar. In fact, the extreme values of the normal drawdowns are not consistently less than those of the laplacian drawdowns. I have been simulating for anywhere between 4 and 30 stocks over 252 days and up to 50,000 drawdowns per simulation (over the 252 days).
There is no portfolio rebalancing. In other words, I allow the weights of the portfolio holdings to drift over the 252 days.
This is not what I expected. Any theoretical insights regarding this finding are appreciated.
