The Market's Back-to-Back Streak

Includes: DIA, QQQ, SPY
by: Paul Kedrosky

Assuming the current red ink on the major stock markets hold until end of day, the mixed-market streak is in intact. We will have hit 19 straight days on the S&P 500 without back-to-back up days. That's not a record, admittedly, but it has now put us into pretty rarefied stock market space.

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.

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?