We Get New Highs More Frequently After New Highs

This post may fall into the “Dog bites Man” bucket, but I will see if I can’t shed a little more light on the phenomenon. Here’s the question: “When do we see new highs in the stock market most often?” The punchline: “After a recent new high.”

The red squares above show the probability of hitting a new high so many days after a new high. The black line near it is a best fit power curve. The blue diamonds above show the probability of hitting a new high so many days after not hitting a new high. The green triangles above show the ratio of those two probabilities, matching up against the right vertical axis. The black line near it is a best fit power curve.

As time goes to infinity, both probabilities converge to the same number, which is presently estimated to be 6.8%, the odds that we would hit a new high on any day between 1951 and 2015. Here’s the table that corresponds to the above graph:

Probability of a new high after Days after no new high Days after new high Probability Ratio 1st day 3.1% 57.3% 18.29 2nd day 4.2% 43.3% 10.39 3rd day 4.6% 36.7% 7.90 4th day 4.8% 33.8% 6.99 5th day 5.1% 30.0% 5.87 6th day 5.2% 28.2% 5.37 7th day 5.5% 24.2% 4.36 8th day 5.7% 22.5% 3.97 9th day 5.6% 23.4% 4.18 10th day 5.6% 22.6% 4.00 11-15 5.9% 19.0% 3.22 16-20 6.0% 17.2% 2.86 21-30 6.1% 16.4% 2.71 31-40 6.2% 14.5% 2.35 41-50 6.2% 15.2% 2.47 51-60 6.3% 14.2% 2.28 61-75 6.3% 13.9% 2.21 76-90 6.3% 13.6% 2.16 91-105 6.3% 12.8% 2.02 106-120 6.4% 12.5% 1.96 121-140 6.4% 12.0% 1.87 141-160 6.5% 11.3% 1.75 161-180 6.4% 11.5% 1.79 181-200 days 6.4% 11.8% 1.84