We Get New Highs More Frequently After New Highs

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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.

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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

 

E.g., as you go down the table the probability 43.3% represents the probability that you get a new high on the second day after a new high.

Here’s an intuitive way to think about it: if you are not at a new high, you are further away from a new high than if you were at a new high recently.  Thus with time the daily probability of hitting a new high gets higher.  If you were at a new high recently, you daily odds of hitting a new high are quite high, but fall over time, because the odds of drifting lower at some point increase.  Valuation is a weak daily force, but a strong ultimate force.

That said, the odds of hitting new highs a long time away from a new high are significantly higher than the odds of hitting a new high where there has been no new high for the same amount of time.

Closing Thoughts

I could segment the data another way, and this could be clearer: If you are x% away from a new high, what is the odds you will hit a new high n days from now?  As x gets bigger, so will the numbers for n.  Be that as it may, when you have had new highs recently, you tend to have more of them.  New highs clump together.

The same is true of periods with no new highs — they tend to clump together and persist even more.

Valuation and momentum are hidden variables here — momentum aids persistence, and valuation is gravity, eventually causing markets that don’t fairly price likely future cash flows to revert to pricing that is more normal.  Valuation is powerful, but takes a long while to act, often waiting for a credit cycle to do its work.  Momentum works in the short-run, propelling markets to heights and depths that we can only reach from human mimickry.

That’s all.

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David J. Merkel, CFA, FSA — 2010-present, I am working on setting up my own equity asset management shop, tentatively called Aleph Investments. It is possible that I might do a joint venture with someone else if we can do more together than separately. From 2008-2010, I was the Chief Economist and Director of Research of Finacorp Securities. I did a many things for Finacorp, mainly research and analysis on a wide variety of fixed income and equity securities, and trading strategies. Until 2007, I was a senior investment analyst at Hovde Capital, responsible for analysis and valuation of investment opportunities for the FIP funds, particularly of companies in the insurance industry. I also managed the internal profit sharing and charitable endowment monies of the firm. From 2003-2007, I was a leading commentator at the investment website RealMoney.com. Back in 2003, after several years of correspondence, James Cramer invited me to write for the site, and I wrote for RealMoney on equity and bond portfolio management, macroeconomics, derivatives, quantitative strategies, insurance issues, corporate governance, etc. My specialty is looking at the interlinkages in the markets in order to understand individual markets better. I no longer contribute to RealMoney; I scaled it back because my work duties have gotten larger, and I began this blog to develop a distinct voice with a wider distribution. After three-plus year of operation, I believe I have achieved that. Prior to joining Hovde in 2003, I managed corporate bonds for Dwight Asset Management. In 1998, I joined the Mount Washington Investment Group as the Mortgage Bond and Asset Liability manager after working with Provident Mutual, AIG and Pacific Standard Life. My background as a life actuary has given me a different perspective on investing. How do you earn money without taking undue risk? How do you convey ideas about investing while showing a proper level of uncertainty on the likelihood of success? How do the various markets fit together, telling us us a broader story than any single piece? These are the themes that I will deal with in this blog. I hold bachelor’s and master’s degrees from Johns Hopkins University. In my spare time, I take care of our eight children with my wonderful wife Ruth.

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