Jun

9

One is always fascinated by a beautiful femme fatale that always keeps you guessing and never does the same thing twice, sort of like Federer's new drop shot or the market mistress.

To test whether there was such a thing as dueness, I had to start somewhere. Do the four urns get filled with balls of different colors to an inordinate degree? Here's a start:

Table I

Number of occasions that a small change failed to occur, by days of failure and probability of continued failure next day

Small rises

#/Observations/Prob. a failure occurred the next day

0 507 0.77
1 388 0.77
2 296 0.82
3 243 0.77
4 187 0.80
5 150 0.83
6 124 0.81
7 100 0.81
8 81 0.91
9 74 0.88
10 65

Table II

Small Declines

0 396 0.83
1 330 0.83
2 275 0.85
3 234 0.83
4 194 0.83
5 161 0.82
6 132 0.82
7 108 0.85
8 92 0.84
9 77 0.80
10 62

there were 2600 days in sample. A small change was defined as less than 0.5% and there have been four such changes in a row.

For example there were 507 days that a small rise occurred; on the next day there were 388 days a small rise did not occur (i.e. 119 where a small rise did occur). Note that 388/507 = 77%.

In conclusion, one will have to reflect on other methods of teasing out this mysterious woman's ability to deceive, possibly with your ideas. 

Steve Ellison submits his study:

After a certain number of whipsaws, is a strong trend due? I tested S&P 500 data from 2005 and 2006. I defined the trend as the direction of the last move greater than or equal to the average true (daily) range. By this definition there is always a trend.

I started with a hypothetical always-in mechanical strategy that one would be long whenever the trend was up and be short whenever the trend was down (I realize real traders don't trade this way). I then categorized the results of each hypothetical trade into the 20% that were most profitable and the other 80%.

I then counted how many of the previous 10 trades would have been in the top 20% and tabulated results by this quantity.

Number of top 20%       Average

trades in previous 10    profit     N

.       0                  -0.1%    20

.       1                   0.0%    44

.       2                   0.0%    57

.       3                   0.0%    55

.       4                  -0.3%    19

.       5                  -0.6%     3

 

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