The Market's Back-to-Back Streak

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?

Comments

[Woodshedder:]

.00000190734 of 19 days

.000000001862 of 28 days

2007 Nov 27 01:14 PM

[David44:]

Please post the answer and calculation method when you have a chance. Thank you. David

2007 Nov 27 07:55 PM

[Woodshedder:]

Whoops. Did calcs at work by hand on calculator.

Try these:

19 days = 0.0000953674%
28 days = 0.0000001863%
50 days = 0.0000000000%

2007 Nov 28 12:03 AM