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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.

require(fBasics)

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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  • $\begingroup$ @noob2 I do not understand the edit, I thought maxddStats is implementing the theoretical expected maximum drawdown as per [1], see the source code: github.com/cran/fBasics/blob/master/R/stats-maxdd.R $\endgroup$
    – Hans-Peter Schrei
    Commented Sep 30, 2020 at 11:47
  • $\begingroup$ Sorry. I will revert. $\endgroup$
    – nbbo2
    Commented Sep 30, 2020 at 12:07

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