Jan

7

Consider using Mean Absolute Deviation, arithmetic Average of absolute returns, in lieu of standard deviation. This is often done in finance unintentionally. Cant remember which understates variance. Easier to compute.

William Huggins writes:

The problem with MAD in finance is that it is not continuously differentiable, making it hard to include in optimization calculations. Also, variances are additive but MSDs are not (handy for portfolio math). (A student asked me this question last semester and I had to spend some time sorting out the answer for him. As a single stock measure of dispersion, it's fine but its hell in portfolio math.)

Peter Ringel asks:

Isn't MAD or better MAD/median ratio a good non-parametric metric? I use it for range & volatility comparison over different timeframes. I don't trust Stdev in markets. (my ignorance will be exposed very quickly here - Just trying to apply, what I learn from list and it's members.)

William Huggins responds:

it's totally fine for one-to-one comparisons but can't be used to find out what the MAD of a portfolio of two stocks would be without redoing all the math. for stdev, you square it up to variance, add them, then root back to stdev. optimization of portfolios relies on calculus to find the weights that result in minimum variance but you can't differentiate MAD in the same way. so it can be used for a side-by-side comparison, but MADs don't play well when you mix them. (strictly speaking, what I wrote is good for independent stocks - if they are correlated, and they all are - you need to account for their covariance. there is no co-MAD to include in equivalent calculations.)

Bill Egan comments:

One outlier is sufficient to distort the mean and thus the std. Median absolute deviation (MAD) avoids this, being resistant to up to 50% outliers (which ought not happen in price data).

Robust Standard deviation = 1.4826*MAD

Huggins is correct - derivative based optimization methods blow up when you use MAD or similar methods. Simplex or genetic algorithms work for optimization in that case. For estimated covariance, you can try replacing mean with median in the covariance formula.

William Huggins adds:

I last applied MAD, while I was trying to understand better, why markets ( NQ, Spoo) are so absurdly homogeneous with their ranges for different intraday time-frames. And if some time-frames are less efficient than others. And I believe some are. During the last summer market it was very noticeable.


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