A lot of investors rely on intuition to estimate the odds of the market going up or down, and this influences their trading decisions. The Dow Jones Industrials has been going up five years in a row, so now we are overdue for a down year, isn’t it? There hasn’t been a 10% correction for over a year, so in 2014 we should get a big correction, right? It appears logical, but can we rely on this kind of “gut feelings”? It turns out that human intuition is generally very poor at estimating odds, with the birthday paradox as a classic example. In the markets our intuition can be an equally poor guide. For example, what do you think to be more likely:
1) the DJIA going up 7 years in a row.
2) the DJIA going down 3 years in a row.
Or, what do you think about this idea: “When the market has had a very strong up year, it is more likely to be followed by a down year.”? The truth about these questions may surprise you, as we will prove with some simple math. More on this “intuition trap” below.
Last week the markets tried to build on recent gains, as expected. The Nasdaq has broken out to new multi-year highs, but the S&P 500 is still hesitating near its recent highs (click for larger image):
Technically we see the S&P has bounced back to its January highs, but the Earl indicator is turning down from overbought level, indicating the possible start of a pullback here. The slower Earl2 has formed a major bottom and shows more room to rise. We remain in lunar green period for the next week, which also favors a further push higher.
I see two scenarios going forward. Most likely is a push to marginally higher highs in the next week or two ( say ~1870 on the S&P), followed by another leg downwards that would probably go on to test the major support zone around 1700. Alternatively, we may get a surge towards the magical 2000 level by April. These big round numbers tend to become an attractor. If the S&P manages to reach 1900 then the media hype about the 2000 barrier will start. If this comes to pass, then I would look for it to be followed by a dip back to 1700 as well.
To invest successfully we are supposed to turn the odds in our favor. Doesn’t that imply that we should know what the odds are? The best way to know the odds is by calculating them rather than rely on our intuition. So, let’s have a look. (note: I have used the yearly return of the Dow Jones Industrials, which goes back to 1896. That’s enough for some quick estimate.)
Q1: Is the Dow more likely to have a down year after a strong up year?
A: Well, if we look at the DJIA over the last 116 year, it has gone up in 76 years, or 65.5%. It was down in 40 years (34.5%). This is normal. Long term we get more up years in the stock market because of long term inflation, GDP growth and increasing population. Now, if we look for years when the Dow was up more than 15%, then we find 40 cases. The ensuing year was a down year in 14 cases. That’s 35%. This suggests that the odds of getting a down year after a strong up year are just the same as for any other year, ~35%.
Q2: What is more likely? Dow down for 3 years in a row or Dow up for 7 years in row.
A: Most people would intuitively think that 3 down years is much more likely, but that’s false. Here is the math based on 65% chance for an up year:
0.65 ^ 7 = 0.049 (= 4.9% chance)
0.35 ^ 3 = 0.043 (= 4.3% chance)
Seven up years in a row has slightly higher odds if we assume that the yearly performance is completely independent of the previous year’s return. Further study of the data actually finds little or no dependence on the previous year. This is counterintuitive, but it is what it is.
Some basic math can go a long way towards avoiding this kind of intuition traps. Intuition has its place, but shouldn’t be used wherever math can do the job much better.
Referring to Adverse move ratio, I am interested on how to determine the formula for AMR.
Could you please give me any suggestions on how to calculate it?
Thank you very much for any suggestions :>
The formula was posted in the comments section of the given blog post.
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