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In this question a paper about mean absolute deviation portfolio optimization is mentioned and in the answer a spreadsheet with an implementation is attached.

What is the use of this procedure? Does it produce sparse portfolios (it says something about the number of zeros)? Does it give better results than mean-variance optimization? Can we see a back-test? Reference to a back test?

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Reviewing the available literature and doing my own initial tests seems to confirm that the results of the MAD method versus those of the classical MVO are a statistical dead heat with MVO perhaps having a slight return edge - possibly due to MAD, which is more sensitive to fat tails, producing slightly more conservative portfolios*. However for moderate to large size portfolios of 300 or more assets the difference in cacluation time is markedly in favour of MAD and other LP methods. ( Mean Gini and Mean CVaR can be similarly formulated with the common link being through the Absolute Lorenz curve and SSD ). There is also some evidence of MAD methods producing better (lower) out-of-sample tracking errors making it well suited for index tracking and replication purposes

The Mean Absolute Deviation (MAD) is related to the Standard Deviation by the formula MAD:SD=SQRT (2/Pi) or 0.7979 for the strictly normal or Gaussian case. The closer the ratio of your MAD to Std Deviation is to 0.7979 the more 'normal' the data is. This means that in the case where your underlying data is actually normal the optimal weights generated by the LP MAD portfolio optimization model will be the same as those generated using the Quadratic Mean Variance model.

The method does tend to produce more concentrated or sparse portfolios due to the upper bound on nonzero assets being T + 2 see Feinstein and Thapa (1993).

Some R code (not mine) for backtesting and comparison available here https://systematicinvestor.wordpress.com/2011/11/01/minimizing-downside-risk/

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It's supposedly more robust.

But they all fail as do any plugin estimator version of things. The estimators are typically optimized and unbiased, but the optimized portfolio weights are absolutely biased.

Bayesian methods have gone much further. It's better to smear out your estimators before you optimize.

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  • $\begingroup$ An application of Bayesian statistics sounds interesting. Do you mean anything beyond shrinkage (which could be seen as Bayesian)? Do you know a shrinkage estimator in the context of MAD? $\endgroup$ – Richard Mar 11 '15 at 8:02
  • $\begingroup$ There are quite a number of papers on it. I don't mean to say these two are absolutely the best but I really liked both: D Avromov and G Zhou, Bayesian Portfolio Analysis Ann Rev Fin Econ (2010). Very good overview of pros and cons of all the different approaches. T L Lai, H Xing, and Z Chen, Mean-Variance Portfolio Optimization when means and covariances are unknown, Ann Appl Stats, 2011. This compares and contrasts plugs with bootstrap with bayesian(-ish) approaches like Black-Litterman, and their own empirical bayes estimator. One thing to note: dynamic pbms have their own challenges. $\endgroup$ – Nick Firoozye Mar 12 '15 at 8:11
  • $\begingroup$ Thanks for the comment, could you provide links to the papers too? Thanks! $\endgroup$ – Richard Mar 12 '15 at 9:36
  • $\begingroup$ scholar.google.co.uk this finds everything. Look at different versions, you can find a PDF lying around somewhere. $\endgroup$ – Nick Firoozye Mar 12 '15 at 22:43
  • $\begingroup$ scholar.google.co.uk/… for instance! BTW, advanced use of Google Scholar--read "cited by" for more recent articles on similar topics. $\endgroup$ – Nick Firoozye Mar 12 '15 at 22:44
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Think of mean-variance as using a quadratic risk function. MAD uses a linear one.

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    $\begingroup$ It's a short answer, but it's particularly useful for modelling. Something about OP's background tells me it's not what he's looking for, because it's so obvious and probably one of the first things that occurred to him. $\endgroup$ – Nathan S. Mar 10 '15 at 16:42
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    $\begingroup$ Hehe.. That's right :) $\endgroup$ – Richard Mar 11 '15 at 7:02

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