Skip to content
All library documents

Mean Absolute Deviation Portfolio Optimization: Tradeoffs and Evidence

Article Quant Q&A · Author: Richi Wa
Read the original

Summary

The document compares mean absolute deviation portfolio optimization with classical mean-variance optimization. It describes MAD as a linear-risk approach that can be formulated as a linear program, which may reduce calculation time for large portfolios. The answer reports that initial tests and literature suggest broadly similar results, with mean-variance possibly having a slight return advantage, while MAD may yield lower out-of-sample tracking error for index replication.

It also notes that MAD can produce more concentrated portfolios and may be more robust to fat-tailed returns. Under normally distributed returns, the stated relationship between MAD and standard deviation suggests the two optimization approaches can produce the same weights. These claims are qualified: the excerpt supplies no detailed backtest results, and another response cautions that optimizing estimated inputs can create biased portfolio weights. Bayesian approaches are mentioned as an alternative way to address estimation uncertainty.

Key ideas

  • MAD uses a linear risk measure, while mean-variance optimization uses a quadratic one.
  • Both methods are described as having broadly similar performance in the cited initial evidence.
  • MAD may be faster for large portfolios and may reduce out-of-sample tracking error in index replication.
  • MAD may create more concentrated portfolios and respond more conservatively to fat tails.
  • The comparison does not provide detailed backtest results, and estimation error remains a concern.

Tags

Portfolio constructionRisk managementBacktestingStatistics
Full text
# What are pros and cons of mean absolute deviation portfolio optimization?


# What are pros and cons of mean absolute deviation portfolio optimization?












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?

## Answer by purbani (score 1)

https://quant.stackexchange.com/a/16928

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/

## Answer by NBF (score 1)

https://quant.stackexchange.com/a/16930

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.

## Answer by Andrew (score 0)

https://quant.stackexchange.com/a/16925

Think of mean-variance as using a quadratic risk function. MAD uses a linear one.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.