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10/18/2005
Victor Niederhoffer on Average Absolute Deviation

I have been ruminating briefly about average absolute deviation on some ideas I am fleshing out concerning a fast and simple way to measure momentum versus reversal during a given period. The usual method is the variance ratio. I came across an article suggesting the benefits of diversification have been decreasing lately. Another way of saying this is that it takes more stocks to achieve a given level of diversification.

The article shows, for example, that one stock gave an average of 12% off an equally weighted average in 2001, versus  8% in 1973, and 30 stocks were off by 2.7% average in 2001 versus 1.6% in 1973.

Here is my own update.

I use the dispersion in the  individual companies in the S&P 500 as a benchmark and look at the difference  in % return between the companies ranked in the  20th and 80th percentiles as the measure of how much spread there is per year.

```Year    20th percent    80th percent   Difference

2000       53.3            -22.6          75.9
2001       31.5            -21.5          53.0
2002        5.0            -36.8          41.8
2003       62.0             10.4          51.6
2004       33.9             -3.2          37.1
2005*      20.1            -18.4          38.5*```

* the 2005 table is based on the performance from 12/31/04 to 10/17/05.

The results show that there has been less of a dispersion of the average stock during the most recent years than in the beginning of the period, thereby refuting the tendency that all the academic studies have found and are basing their decisions upon. Of course this is predicted by the law of ever changing cycles.

An interesting byproduct of this study was the preliminary discovery that the dispersion of the ensemble of stocks is greater as of mid October than as of the end of year. This means the difference between 20th and 80th percent performance as of the first 9 1/2 months of 2003 was 66% but the difference at the end of the year was 51.6%. Similar results held for the other years. If this discovery is born out, then one can say that the time  from October 15th to the end of the year is a time for companies to revert to mediocrity. This would not be a candidate for the Minister of non-predictive studies, (a minister with a very dour look recently, due to his inability to play tennis during the last 8 days because of rain, losses and romance).

Such are the unintended consequences, the fruits of very preliminary ruminations on fast and simple methods for determining non-randomness with the average absolute deviation.

Kim Zussman Comments on Average Absolute Deviation:

1. If the distribution of returns in a given period has smaller variance than in another period, and one randomly chooses, (say), 20 points from each distribution to sample,  isn't the mean still the same?  If the purpose of diversification is to reduce the chances of not tracking the mean, I would think the higher variance distribution requires more points to be sure of getting the mean right.
2. Was the interquartile range compression at year end due to losses in prior gainers or gains in prior losers? Lots of papers suggest accelerating year-end losses for YTD losers (and January bounce) as a result of tax-selling, but tax effects might be different in years following down and up markets

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