A Puzzle, Plus More on the Market's Back-to-Back Streak
A few people have asked, so here is my data on the longest S&P 500 streaks (since 1950) without back-to-back up days. Considering that there have been 14,565 trading days since January 1950, you can see how we're waaay out in the tail of this particular distribution.
| Ending Date | Streak Length |
| 4/29/1994 | 28 |
| 11/15/1978 | 27 |
| 2/24/1984 | 27 |
| 3/9/1982 | 26 |
| 5/6/1970 | 25 |
| 9/24/2001 | 25 |
| 6/26/1969 | 24 |
| 4/26/1956 | 23 |
| 4/17/1962 | 23 |
| 3/18/1980 | 23 |
| 6/10/1982 | 23 |
| 3/5/2001 | 23 |
| 8/27/1973 | 22 |
| 10/4/2000 | 22 |
| 4/30/2002 | 22 |
| 2/21/1952 | 21 |
| 9/1/1953 | 21 |
| 12/27/1983 | 21 |
| 6/6/1967 | 20 |
| 9/5/1974 | 20 |
| 1/28/1977 | 20 |
| 8/13/1982 | 20 |
| 12/12/1991 | 20 |
| 11/26/2007 | 19* |
| * Ongoing |
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As a math exercise for readers, try the following exercise -- and the first person to post a correct answer here wins a copy of Orrin Pilkey's curmudgeonly book Useless Arithmetic, about why quantitative models of the real world don't work.
First, however, some assumptions.
- Market movements are independent from day to day
- There is a 50% likelihood on any given day the market will be up, and a 50% likelihood it will be down
- Ignore the relatively rare flat-market cases
- There are 14,565 trading days in the period
Now, what is the probability we will see a run length of at least 19 in the period? Of 28? Of 50?
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