I have a model that returns z scores for a mean reversion strategy where z score is the current price minus average and divided by vol.

At the moment, positions are sized inverse linear to the z score as mentioned in many forums and Ernie Chan's book.

I tried to improve by using squared and cubic measures of the z score and realized that there could a mathematical way to optimize this and identify the optimal sizing given z scores. Does something like that exist? Tried searching for research papers on this but did not find any.

  • $\begingroup$ This seems rather odd: as the price moves to the average, you would get arbitrarily large allocations. $\endgroup$ Jan 23, 2019 at 19:46
  • $\begingroup$ Found this paper but seems way over my head for the moment. arxiv.org/pdf/1803.02974.pdf $\endgroup$ Jan 23, 2019 at 23:19
  • $\begingroup$ Might have better luck with Alexander's early paper: papers.ssrn.com/sol3/papers.cfm?abstract_id=315619 $\endgroup$ Jan 23, 2019 at 23:25
  • $\begingroup$ Would it not just help to have a look at conditional distributions (histogram of profit) for a given z? $\endgroup$
    – mojovski
    Aug 2, 2020 at 12:02


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