Do round numbers matter?

Asking for a friend. But seriously, a work colleague is asking - what's the deal with Dow 20K?

I think this is just a psychological thing and mostly a function of media like CNBC acting as cheerleader for the market. It is also a bit like Y2K (for those old enough to remember all the dire computer crash warnings) or turning 30 or 40 or 50 etc, although 20 doesn't seem to be in quite the same league as 16 or 18 or 21. The later three can all be explained in legal freedoms and after that, a lot of people have a thing for the round number decades. But do these matter for stock market prices? Let's look at charts. 

I'm keeping with the Dow here because that is the media circus, even though there is far more volume and trading activity in the S&P 500. In each chart below, 1 bar represents 1 week of price action and the red lines are the round number levels (or close as I could get them to draw).  

Sum
Sometimes round numbers matter, sometimes they don't. Sometimes they are clear resistance, sometimes there is chop. But what seems to be more reliable is that after the Dow clears a level, then later - like 1-3 years later - that level can act as support.

So Dow 20K could be this year's media broken record or maybe it blasts through and holds as support from there. Regardless, I don't think anyone should use this level as part of a decision to buy or sell stocks. There are too many incidences of whipsaw to make any round number in and of itself a reliable strategy.

Weekly chart, 1980-85
Dow 1000 was a thing. Pretty clear resistance and sizeable drop; then once it recovered and acted as support, it was definitive.

Weekly chart, 1985-1990
Dow 2000 didn't matter that much. 2500 was in play somewhat in 1989-90, first as mild resistance then later as clear support.

Weekly chart, 1990-95
Picture perfect tag of Dow 3000 and a drop to near 2500. But what a nightmare in 1991, with media probably going on about Dow 3000 all year - above, below, above, below, ARGH! After all those months of indecision in 1991, Dow 4K was decisive one shot key high in 1994.

Weekly chart 1995-2000
Round number levels are coming much faster now, which makes sense because the percentage move is much less. Dow 5000 support in early 1996; Dow 6000 not really important; Dow 7000 some resistance for several weeks in 1997; thin line Dow 7500 important for all of 3 weeks; Dow 8000 some resistance, kinda, with a few fake-outs above; Dow 9000 same. Then look at that, the level that didn't really work at Dow 7500 became perfect support in 1998; now Dow 10K, almost non event the first time, but that number did act as support later in 1999.

Weekly chart 2000-05
Dow 11000 an exercise in frustration, but decent bounce off Dow 10000 a couple of times. Key lows again at Dow 7500 in 2002-03, and 9000 acting as support for a few weeks. But Dow 10K later in 2004 was non-issue.

Weekly chart 2005-2010
Dow 11K resistance then 10K support in 2005; in 2006 it didn't matter. Dow 12K support in 2007, then 13K not important, but what do you know, 14K very important! 12K support in early 2008, 13K resistance, then crashola all the way down to 7K again. In the recovery in 2009 Dow 9K non event, 10K some support in early 2010.

Weekly chart, 2010-15.
For each 1000 points above 10000, the percentage move is much less and so the market encounters round numbers with much more frequency. Dow 11K resistance, then 10K support. 2011 highs and lows not on round numbers at all. Then in 2012 perfect low on Dow 12000. Dow 15K chopped quite a bit, then 16K clear support in 2004 for several weeks.

Weekly chart 2015+
Again Dow 16000 decent support in 2005 for several weeks in three different clusters. Dow 17K not much. Dow 18000 struggled and after several fake-outs failed. Dow 19,000 was in the middle of a melt up move. And now we are at Dow 20K. What does it mean?