I have been looking at the approach for calculating the expected maximum drawdown of a Brownian Motion [1] and the corresponding function maxddStats in the fBasics package in R [2].

I do not understand how for some choices of parameters the value from sampling the maximum drawdown via rmaxdd and the corresponding statistic from maxddStats are so far apart.


maxddStats(mean = 0.01, sd = 0.0427, horizon = 135)
> 0.3142337
mean(rmaxdd(n = 100000, mean = 0.01, sd = 0.0427, horizon = 135))
> 0.2637941

It doesn't seem to be an issue of convergence (increasing small n in rmaxdd), nor of scaling (scaling mean and mu). Am I missing something basic here?

[1] https://www.cs.rpi.edu/~magdon/ps/journal/drawdown_journal.pdf
[2] https://www.rdocumentation.org/packages/fPortfolio/versions/260.72/topics/DrawdownStatistics



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