What Is IID Gaussian drawdown?
An IID Gaussian drawdown is a drawdown generated under the simplifying assumption that successive returns are independent and identically distributed (IID) draws from a Gaussian (normal) distribution. It is a model-based benchmark for how deep or long a drawdown could be by chance, given an assumed average return, volatility, observation frequency, and investment horizon. It is not a separate drawdown statistic: the usual maximum drawdown or drawdown duration is measured on a path produced by the model.
One implementation draws log returns from N(mu, sigma²), accumulates them
into a positive equity curve, and measures each path’s decline from
its running peak. Repeating this for many paths gives a distribution of
maximum drawdown depths and time spent below a previous peak. An observed
strategy drawdown can then be compared with that distribution under the IID
Gaussian assumptions. The result depends on the estimated mean and
volatility, the sample interval, the horizon, and whether returns are
modelled as log or simple returns.
Real trading returns may have fat tails, changing volatility, or serial dependence, all of which the IID Gaussian model excludes. Its simulated quantiles are therefore a baseline, not a reliable upper bound on future losses. A drawdown within the model’s expected range does not prove that a strategy is healthy; a drawdown outside it may indicate that the return model or its parameter estimates need revisiting.
Literature and references:
Adam Rej, Philip Seager and Jean-Philippe Bouchaud, You are in a drawdown. When should you start worrying?, 2017.
Malik Magdon-Ismail, Amir F. Atiya, Amrit Pratap and Yaser S. Abu-Mostafa, On the maximum drawdown of a Brownian motion, Journal of Applied Probability, 2004.
See also