How to obtain the probability distribution of Maximum Drawdown, starting from the probability distribution of Daily Returns? Here the details:
Suppose I have a time serie of N=1000 daily returns.
Each daily return is normally distributed, like 𝒩[μ=1\$,σ=10\$]
Suppose I run 100 simulations of that time series. At every simulation I create a new realisation of the time series, by I pulling 1000 random values from that normal distribution 𝒩[μ=1\$,σ=10\$].
At every simulation I calculate the Maximum Drawdown (MDD).
Obviously, I get a different MDD every time, because each of the 100 realisations of the time series is different, although they all originate from the same normal distribution.
I want to generalise these results and understand how MDD varies as a function on μ, σ, N days. How can I do that?