Trading the Odds

A statistical approach to profit in the US equity markets, trading the markets like professional card counters are playing Blackjack or expert poker players are playing Poker.

Trading the Odds on Tuesday – March 31, 2009

Trading the Odds on Tuesday – March 31, 2009

After the S&P 500 posted ‘6 Highs‘ on Thursday – March 26, 2009 and 6 Lows on Friday – March 27, 2009 (see my respective posts), it posted another 6 Lows on Monday’s session:

  • posted a lower open,
  • posted a lower low than the previous session’s low,
  • posted a lower high than the previous session’s high,
  • posted a high below the previous session’s close,
  • posted a lower close,
  • and finally closed below the open.

It therefore almost completely complied to the most probable scenario posted in Trading the Odds on Monday – March 30, 2009 and 6 Highs plus 6 Lows = ? (see w/Survey I+II).

The market opened lower on the high of the day and never looked back. Remarkable was the fact that using the SPY (S&P 500 ETF) instead of the S&P 500 not only all of those 6 Lows exceeded the -1.0% bar, but additionally the SPY posted a high today -1.77% below Friday’s low (leaving open an unfilled gap).

Since 01/03/2000, there were 13 occurrences when the SPY posted those 6 Lows exceeding the -1.0% bar, and 57 occurrences when the SPY left an unfilled downside gap (intraday high below the previous session’s low, no minimum percentage wise extent required).

Table I below shows -concerning both setups as well as regarding the at-any-time probabilities and odds- the raw historical number of occurrences (since 01/03/2000) of a higher and lower open, the average change between close and open (close -open), the average daily True Range (Wilder True Range), the number of higher highs and lower lows (than the last session’s high/low) after a higher/lower open, the number of occurrences of the then following higher or lower close as well as the respective sum of all profits and losses going long/short on open, differentiated between

  • 1st column: at-any-time probabilities and odds (taking into account every single trading day),
  • 2nd column: probabilities and odds for the following session after the SPY posted ‘6 Lows‘ all exceeding the -1.0% bar (‘w/Survey I‘),
  • 3rd column: probabilities and odds for the following session after the SPY left an unfilled downside gap (‘w/Survey II‘).

Table I

survey-20090330-4

(click on image to enlarge)

The second one (Table II) shows -percentage wise solely based on the figures of Table I- the historical probabilities (since 01/03/2000) for a higher and lower open, the average change between close and open (close -open), the average daily True Range (Wilder True Range), the historical probabilities for a higher high and lower low (than the last session’s high/low) and a higher or lower close as well as the respective sum of all profits and losses going long/short on open, differentiated identically. But due to the fact that in the 2nd table probabilities significantly above or significantly below their respective at-any-time probabilities (in this case +/-15.00%, but this percentage is up to everyone’s decision what may be regarded as ’significant above’ or ‘below’) are marked by a green (for a probable bullish outcome) and red (for a probable bearish outcome) background color, one may be able to catch on a glimpse if (any), where (e.g. on the open, for a higher/lower close or intraday strength/weakness) and to what extent (historical probabilities) the following session (Tuesday, March 31, 2009) possibly provides a tradable edge concerning both surveys.

Table II

survey-20090330-5

(click on image to enlarge)

Bottom line:

  1. Concerning both surveys historical probabilities favor a higher open on Tuesday’s session (in comparison to the at-any-time probability for a higher open).
  2. Again the market history’s concerning both surveys shows a significantly above random probability for some intraday follow-through of Friday’s and Monday’s weakness during Tuesday’s session. Concerning survey II  (downside gap), in only 14 out of 57 occurrences was the SPY able to post a higher high, but on 38 occurrences it posted a lower low.
  3. At least as the market history tells us concerning both surveys, the direction of the open most probably seems to be a fake, at least with respect to the respective profit factor (theoretically, and for statistical purposes only) going long on a higher open and short on a lower open (the SPY regularly closed below the open in the event the market opened higher, and above the open in the event the market opened lower). This mechanical ‘trading system’ would have always yielded a profit factor below 1 for an overall negative expectancy, so following the direction of the market open would have -on average- been a very unprofitable preposition. At least concerning those setups, shorting a higher open and buying a lower open would have provided a tradable edge.
  4. And last but not least the most interesting question: What are the -historical- chances that the SPY will fill the gap (remember: the SPY posted a high below the previous session’s low) on the then following session ? To make a long story short: chances are slim. Only on 8 out of those 57 occurrences since 03/01/2000 was the SPY able to fill the gap on the then following session.

The following table shows the market’s behavior on those 57 sessions after the SPY left an unfilled downside gap (‘w/Survey II‘):

No. Date Open Gap fill Lower
Low
True Range
Close – Open
1 03/03/2009 +1,43% No -1,04% +2,92% -2,15%
2 02/18/2009 +0,72% No -1,12% +2,10% -0,95%
3 01/15/2009 -0,30% No -1,73% +4,18% +0,33%
4 01/08/2009 -0,56% No -0,59% +1,57% +0,98%
5 12/02/2008 +1,66% No +0,22% +4,20% +2,16%
6 10/23/2008 -0,39% No -1,97% +7,33% +1,55%
7 10/07/2008 +2,02% No -0,98% +7,33% -6,37%
8 06/27/2008 +0,04% No -0,82% +1,42% -0,58%
9 06/23/2008 +0,39% No +0,08% +0,69% -0,48%
10 06/03/2008 +0,29% No -0,56% +1,72% -0,87%
11 03/03/2008 -0,51% No -0,41% +1,18% +0,27%
12 02/06/2008 +0,34% No -0,94% +2,12% -1,14%
13 01/07/2008 +0,35% No -0,57% +1,51% -0,44%
14 12/18/2007 +0,71% No -0,62% +1,74% -0,15%
15 09/10/2007 +0,31% No -0,64% +1,64% -0,50%
16 08/29/2007 +0,45% Yes +0,35% +2,10% +1,50%
17 07/11/2007 -0,11% No -0,17% +1,01% +0,82%
18 02/28/2007 +0,64% No +0,58% +1,78% +0,38%
19 09/07/2006 -0,34% No -0,75% +0,93% -0,12%
20 08/02/2006 +0,28% Yes +0,75% +0,97% +0,39%
21 07/14/2006 +0,13% No -0,94% +1,15% -0,52%
22 08/08/2005 +0,24% No -0,24% +0,84% -0,42%
23 01/21/2005 +0,25% No -0,55% +1,15% -0,86%
24 12/20/2004 +0,24% Yes +0,01% +0,94% -0,22%
25 09/23/2004 +0,04% No -0,47% +0,67% -0,58%
26 08/09/2004 +0,16% No +0,23% +0,59% -0,02%
27 07/07/2004 -0,07% No +0,11% +0,73% +0,37%
28 06/15/2004 +0,60% Yes +0,57% +1,08% +0,11%
29 05/11/2004 +0,58% Yes +0,90% +1,12% +0,26%
30 03/23/2004 +0,55% No +0,24% +0,95% -0,72%
31 11/18/2003 +0,30% Yes -0,33% +1,67% -1,33%
32 10/23/2003 -0,63% No -0,34% +1,07% +0,45%
33 09/23/2003 +0,04% No +0,32% +0,91% +0,34%
34 06/10/2003 +0,21% Yes +0,43% +1,09% +0,80%
35 02/05/2003 +0,44% Yes +0,22% +2,40% -1,05%
36 12/19/2002 -0,50% No -0,82% +2,34% -0,21%
37 09/13/2002 -0,84% No -0,83% +1,84% +1,10%
38 09/04/2002 +0,38% No -0,10% +2,48% +1,04%
39 08/29/2002 -0,90% No -1,08% +2,44% +0,95%
40 07/22/2002 -0,71% No -3,38% +5,27% -2,27%
41 06/24/2002 -0,67% No -1,46% +3,46% +1,21%
42 04/23/2002 +0,08% No -0,60% +1,18% -0,51%
43 03/21/2002 +0,03% No -0,93% +1,48% +0,02%
44 02/20/2002 +0,27% No -0,73% +2,55% +1,41%
45 09/18/2001 +0,08% No +3,36% +1,86% -0,32%
46 07/09/2001 +0,37% No +0,13% +1,25% +0,17%
47 06/15/2001 -0,89% No -1,11% +1,64% +0,78%
48 05/24/2001 +0,17% No -0,54% +1,12% +0,12%
49 03/13/2001 +1,12% No -0,19% +2,46% +0,52%
50 03/12/2001 -0,83% No -4,35% +4,55% -3,48%
51 02/20/2001 +0,49% No -0,93% +2,33% -2,02%
52 12/21/2000 +0,12% No -0,45% +2,64% +0,57%
53 12/18/2000 +0,84% No +0,92% +1,91% +0,50%
54 07/19/2000 -0,20% No -0,73% +1,11% -0,61%
55 05/22/2000 +0,09% No -2,43% +3,17% -2,69%
56 05/04/2000 +0,89% No +0,69% +1,14% -0,13%
57 04/17/2000 -0,60% No +0,89% +4,46% +4,11%

(‘open’ and ‘close’: percentage change in comparison to the last session’s close; ‘lower low’: percentage change in comparison to the last session’s high and low respectively; close – open speaks for itself: any positive percentage change means a close above the open and vice versa; ‘gap fill’: Yes/No)

Successful trading,

Frank

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4 Responses

  1. Tom says:

    Frank,

    Thanks for sharing your work. I wish you all possible encouragement to hang in through the days when it might seem few appreciate your generosity.

    tom

  2. Jeremy says:

    On Saturday you posted a video that included analysis where gaps from the past were filled. What is the significance of filling historical, non-intraday gaps? Going back in history, how many gaps for any index have not been filled? This is some wonderful quantitative work you are doing. Thank you.

    • Frank says:

      Jeremy,

      thanks a lot, but I’m quite sure that it was not me who posted a video concerning gap fills. I like to do some further investigations concerning gap fills, but allow for a couple of days to see a respective post.

      Frank

  3. moneyfriend says:

    Thanks for sharing!

    Pretty sure this can be deduced:

    From 2000 to now, downside gaps in the spy have historically taken less than 10 days to fill 75% percent of the time….

    Interestingly, after the 10 days range is surpassed, the other 25% of gaps average 100 days to fill.

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