The randomness of monthly returns and the Lake Wobegon effect

More than 70% of U.S. drivers believe they are better-than-average drivers, an example of the Lake Wobegon effect, https://en.wikipedia.org/wiki/Lake_Wobegon#The_Lake_Wobegon_effect.

Likewise, a higher than expected number of investors probably believe they are better-than-average investors. Essentially, in the stock market, this means they can spot patterns. For instance, they believe they can pick the perfect stock. They believe they know when to buy and when to sell. They believe they know when to exit the market. Most of this is hindsight bias as well -- investors looking at the past and saying they would have bought this or that at the right time and sold this or that at the right time. I am not saying it is not possible but it isn't easy. Some may certainly know how -- but it is likely very few.

The following chart shows the monthly returns (in percent) for the S&P 500, price only, between 2007 and 2015:

I took the returns and simply characterized them as up or down in the following chart:

Perhaps there are patterns here and maybe some say they are obvious. But are they? I used a statistical test called a runs test to check the randomness of the pattern. When I ran the test, I got a result that indicated the pattern was very likely random. In turn, this means monthly returns are very likely random. (In statistical jargon, I get a p-value of 0.8782. Generally, for this test, a p-value below 0.05 suggests a lack of randomness. Here, the p-value is significantly larger than 0.05 -- thus suggesting randomness.) 

If the result of a game is random, it is difficult to play the game many, many times and finish significantly above average -- regardless of what we think of our abilities. Sometimes we get it right. At other times, we get it wrong. Few of us get it consistently right -- and that too is explainable mostly as luck. Think of it this way: You, or I -- or even the residents of Lake Wobegon -- cannot consistently call the next flip of a coin.