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25-Jun-2006
Cyclicality, Students, Seasonality

It is always good to hear from former students, especially if they have advanced to prominent and successful careers, even if they sometimes try to grab me by the beard. Such a pull came recently from one of the best of my 1970-ish class at Berkeley, Mr. William Rafter, now a math investment personage, as follows:

In response to Rod Fitzsimmons Frey's June 7, 2006 post on seasonality; On Fourier Analysis
The 21-day cyclicality you found is caused by options expiration, there being on average 21 trading days in a month. For an illustration, look at the open interest:
One of the best ways to create a surrogate or smoothed data set is to analyze the data series for cyclic behavior, find the best fitting cycles and put them together. The magenta line below is a composite of the 10 most dominant cycles that can be obtained from the dataset using Fourier Analysis.
This cyclic behavior is an excellent way to fit past data. Furthermore, since one has the formulae for their construction, those formulae can be used to produce a cyclic prediction. But just because you can do something, does not mean that you should do it. Although FA can be used to generate a prediction, that prediction has no reliability. Many other smoothers are not good predictors either; it's just that most people believe that the past cycles will be repetitive. The Chair might have a horse racing parallel. Chiefly, the cyclic values are not stable/constant over time. That is, if you cyclically analyze N days through the most recent Monday, and then analyze an identical number of N days through Tuesday, the entire fit of Tuesday values will be different from the entire fit of Monday values. Thoroughly revisionist history. Contrast that with what happens if you smooth with other tools like (perish the thought) moving averages. -- Bill Rafter

Now Bill knows as well as anyone that I am one of the world's most ardent deflators of seasonality and cyclicality and I don't believe them predictive, but merely descriptive and so beset by multiple comparisons and changing cycles to be completely destructive of value. Indeed, I have found that almost all who use seasonality as a descriptive tool have stopped trading and if they haven't they have special interests in using a descriptive factoid to help their already ingrained position along, in perhaps the hope that poor followers will further their thinking along.

Such is the case for example with some ardent exponents of the January barometer. When January is down, like it was in 2000 and the market drops another 70 points the rest of the year, they're bearish as a thousand devils, but in 2001 when it 's up 40 in January, why that's bearish, also thus justifying the 218-point drop that followed.

Moving to 2003.well ha ha, it's down again 25 points in January, and the 260-point rise the rest of the year was an anomaly. In 2004, it did work , up 20 points, with another 80 points the rest of the year, but it wasn't bearish so forget it the rest of the year.

In 2005, it's down 20 in January, and that's bearish again, let's shout it from the rooftops. But indeed the market rises 37 points, an anomaly. In 2006, the market's up 32 points, in January, there must be something wrong with it's bullish position as it's  the second  year of an election and 2002 and 1990 were down years. And if it happens to be up  in 2007, why everyone know that the third year of presidential election cycles are bearish. That's typical of seasonal indicators to me. They explain everything , are good for all eventualities in helping a previously engrained prediction and are changeable as the tides and are about as accurate, 50% correct in real life as the January barometer, which is widely trumpeted as one of the best.

 Year    Jan Move    Rest of Year Move
 2000       -75           -74
 2001        46          -218
 2002       -18          -250
 2003       -25           256
 2004        20            80
 2005       -30            67
 2006        32

Thus, when a friend of mine recently sent me some seasonal stuff showing that if you look at quarterly expirations only and stop well before 2001(when the week after the September expirations, the market rose some 75 points from 966 adjusted to 1040 to 1071 the week after), you can come up with some pretty good numbers showing the market has a tendency to go down in the week after quarterly expiration of options (always the third Friday of the month). It would be amazing indeed if one weren't able to come up with something of that nature, considering you are varying the week (before, during or after), the quarterly or monthly, and the starting point, and if not the options expirations, perhaps the Open Market meetings. With as many degrees of freedom or multiple comparisons as this, it's well over 99% that you'll be able to pick and choose and find a week that like the week following the quarterly expirations in the last three years has gone down an average of 1% with a 80% chance of a decline.

Such is guaranteed to happen, as Jimmy Cannon and the Specs liked to say. But in honor of my former student and my friend, I thought it would be worthwhile to look at the moves in the second week after quarterly expirations. For example if the current quarterly expiration was June 16, we would look at the move from the close of Friday, June 23, to the close on Friday June 30 ( if a four-day week followed without a Friday close, I looked one day forward to the fifth day, a Monday). Here are results:

 Moves in the Second Week Following Expiration
                  Yearend 2002 to present
                  
  Date of           Level first week       Level Second week     Change
  Friday after            close                  close
  Exiration
   12 27 02              868                   906              38
   03 28 03              905                   922              17
   06 27 03              968                   997              29
   09 26 03              991                   1025             34
   12 26 03              1091                  1118             27
   03 26 04              1105                  1141             36
   06 25 04              1183                  1173            -10
   09 24 04              1113                  1135             22
   12 23 04              1256                  1259             03
   03 20 05              1216                  1218             02
   06 24 05              1231                  1236             05
   09 23 05              1249                  1263             14
   12 23 05              1286                  1285            -01
   03 24 06              1313                  1303            -10
   06 23 06              1264
  totals                                                       206

One has the same degree of confidence for such a seasonal study as one does for the January Barometer , but as they say in Fiddler,

It doesn't matter at all,
But all the same, it's nice to know.

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