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Does anyone know of any model to estimate the distribution of drawdown length and depth assuming a certain portfolio dynamics? The arcsine law seems to suggest that a portfolio can spend a large portion of time under water if it follows a Brownian motion. I am wondering whether there are research papers that generalize similar concepts under different assumptions of the dynamics. For example, what would be the expected time spent under water if a portfolio follows a GBM with mean mu and variance sigma?

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Here you go,

http://arxiv.org/pdf/cond-mat/9808295.pdf

http://www.cs.rpi.edu/~magdon/talks/mdd_NYU04.pdf

http://www.intelligenthedgefundinvesting.com/pubs/rb-kwcmlr.pdf

However, you mentioned you make an assumption of the portfolio dynamics. That means you either have historical data available about your portfolio returns and standard deviation or you must be able to formulate a model of your specific portfolio under question that allows you to construct portfolio dynamics to be used in a monte carlo simulation. Either case, I strongly recommend you to look as closely as possible at the specific portfolio dynamics assumptions and go from there, because most likely you will never be able to even come close to mimic diversified asset portfolio dynamics with standard distributions.

You mentioned in the end an example. If you assume your portfolio valuations follow a GBM then you can most easily construct a mc simulation. Hope this helps.

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Thanks for the useful comments. Maybe I should clarify a bit. I am more interested in "analytical solutions" that relate drawdown statistics to portfolio assumptions. Even though this is clearly not realistic, I think it can provide insights into the interaction between portfolio parameters and drawdown, whereas simulation probably gives you a better estimate but it's hard to discern insight from the results. –  ezbentley Nov 1 '12 at 15:03

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