Jun

13

 The S&P index was at exactly 1500 yesterday at 10:00 a.m., with the futures at exactly 1515 at the same time. The total ground covered in the S&P futures yesterday, using two point up and down swings as a measure, had to be one of highest in history. From a 1525 close the previous day to a 1517 open, to 1522 at 9:40, 1513 at 10:30, 1521 at 11:40, 1516 at 1:00 p.m., to 15:26 at 2:00 p.m. (at which time I tried to book tennis court), to 1506 at the close. That is 65 points of movement to make a mistake in — truly disruptive and encouraging Fechnerian decision making.

Today, (Wednesday), the cast bond has moved up from a low of .90 to .9126 at its high, (it was at .9116, as of 10:10 a.m., time of writing), after moving from .9216 to .9016 yesterday, mostly between 2:00 - 5:30 p.m..

The omniscient market of Israel has moved from its low of 1078 to 1094 this morning, up slightly on day, and the VIX has moved from its 14.7 Monday close to 16.7 by yesterday's close, near its high of 17.1, but dropped back to 15.7 today. Many markets seem to be trading about half way between their recent highs and lows.

The move on retail sails in the S&P and the Bonds, down three quarters of a percent and then up one percent from there, was completely disruptive. It reminded me of the play by play of a sumo match, which also takes place in 25 seconds and is the only thing in the world that goes through so many gyrations in that short amount of time. 

We calculated Kendall Tau for S&P prices for 5, 10, 15, and 20 day non-overlapping intervals since 1996.

We then compared these empirical estimates to estimates calculated from synthetic price series created using bootstrapped daily changes.

In general, the observed Kendall Taus were higher than you'd expect from the simulated distributions, significant at about a ten percent level.

Method (using the 5-day as an example):
1) First I generated 1000 bootstrapped price series.
2) Split each series into non-overlapping 5-day intervals
3) calculated Kendall Tau for all 1000. now we have a distribution of taus:

The average of Tau was 0.0482, and the standard deviation of Tau was 0.0243

4) Calculate the Tau from the actual observed price series = 0.0778
5) Figure out where 0.0778 falls within the simulated distribution: in this case it turns out that the Empirical Tau (0.0482) was greater than 88.39% of the Taus from the simulated distribution.

Results: Simulated Distribution of Kendall Tau (based on 1,000 simulated price series for each interval):

Interv.                                                     5-day   10-day   15-day   20-day
mean                                                       0.0482  0.0455   0.0446   0.0460
stdev.                                                      0.0243  0.0317   0.0374   0.0418

Empirical Distribution mean                         0.0778  0.0900   0.0898   0.1120
%le of Emp. mean in Simulated Dist. %le      0.8839  0.9189   0.8911   0.8541


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