## Tuesday, December 4, 2012

### `tis the season(ality) part 4

now let's take a look an equity with some strong seasonality:

the mathematical measure of the spread of data is the standard deviation. it was developed to help scientists describe how variable is the repeated measurement of the same thing. in the math literature it is provable that 68% percent of the data points can be shown to fall within one standard deviation from the average. when applying this to seasonality for traders it quickly became apparent to me that what is of interest is when the lower standard deviation line tracks above the flat line in a bullish season or when the upper standard deviation line tracks below the flat line in a bearish season. however, for traders the important thing is how much of the data lies above the lower line and if one uses a 1x standard deviation then 84% of the seasons will track above the lower line. however, if one uses the 1x multiple then one will find that hardly any equity has a season that is so predictable. hardly any of the 1x std lines cross the flat line within a reasonable holding period for traders, say 3 months or so.  the rigorous standard for scientific publication is too rigorous for trading.

in jeffery ma's book, the house advantage,  jeffery claims that his mit blackjack team held only about a 5% advantage over the house when the card count was right. say 52.5% to 47.5%. so i applied this principle to the multiple i apply to the standard deviation of the seasonality. i discovered that 0.3 standard deviations provides a fair but selective number of short term seasonality plays. mathematically it can be shown that 24% of the data falls within 0.3 standard deviations of the mean, or that 62% of the data tracks higher than the lower 0.3x band. if that 62% translates well into the probability of success in a trade then that is a reasonable sort of edge.  to my eye this multiple produces a band that tracks closer to the projection average and provides a much better feel for the seasonality. look at how long the splash hugs the projection average for xrt in the spring before spreading out. to me that's a really good indication that xrt has a tradable season.

however, with this loose a standard, it would not be surprising at all to see that maybe xrt is not on track to repeat this seasonality this time around the wheel. how can we evaluate if xrt is on track with the season? that will be the subject of the next blog ...