A case study in multiple comparisons and a warning against using cart for market prediction:

"Exercising for 90 Minutes Or More Could Make Mental Health Worse, Study Suggests"
by Sarah Knapton, Science Editor

Steve Ellison writes: 

A statement by Mark Hulbert in Sunday's Wall Street Journal raised my suspicions. He said that the percentage of household financial assets invested in stocks had an R-squared of 61% since 1954 in forecasting the net change of the S&P 500 over the next 10 years.

There have only been 6 non-overlapping 10-year periods since 1954. I have not gotten around to getting the data for household financial assets, but how could any factor possibly have an R-squared of 61% with any significance after 6 observations?

I will grant that the indicator makes some intuitive sense from the perspectives of "copper[ing] the public play" and waiting to buy until the old men are hobbling on canes, but I question the statistics.

Link and relevant excerpt below:

The most accurate of the indicators I studied was created by the anonymous author of the blog Philosophical Economics. It is now as bearish as it was right before the 2008 financial crisis, projecting an inflation-adjusted S&P 500 total return of just 0.8 percentage point above inflation. Ten-year Treasurys can promise you that return with far less risk.
Bubble flashbacks
The only other time it was more bearish (during the period since 1951 for which data are available) was at the top of the internet-stock bubble.
The blog’s indicator is based on the percentage of household financial assets—stocks, bonds and cash—that is allocated to stocks. This proportion tends to be highest at market tops and lowest at market bottoms.
According to data collected by Ned Davis Research from the Federal Reserve, this percentage currently looks to be at 56.3%, more than 10 percentage points higher than its historical average of 45.3%. At the top of the bull market in 2007, it stood at 56.8%.
Ned Davis, the eponymous founder of Ned Davis Research, calls the indicator’s record “remarkable.” I can confirm that its record is superior to seven other well-known valuation indicators analyzed by my firm, Hulbert Ratings.
To figure out how accurate an indicator has been, we calculated a statistic known as the R-squared, which ranges from 0% to 100% and measures the degree to which one data series explains or predicts another.
In this case, zero means that the indicator has no meaningful ability to predict the stock market’s returns after inflation over the next 10 years. On the other hand, a reading of 100% would mean that the indicator is a perfect predictor.
Since 1954, according to our analysis, the Philosophical Economics indicator had an R-squared of 61%. In the messy world of stock-market prognostication, that is statistically significant. Our analysis begins in that year because that is the earliest date for which data are available for all of the other indicators that we studied.

Jared Albert writes: 

As I understand the statement, the R**2 is generated from the correlation between the end of one ten year period and the end of the other.

Is this a fair model:
1) Use the annual returns for the SP500 for the period 1954-2014 broken in the 6 decade buckets.
2) Use the standard deviation of returns for each of those 10 years periods (STD calculated on only 10 yearly values for simplicity).
3) Generate a random return value from a normal distribution for the end year of each period
4) repeat the above for cash and bonds
5) create the portfolio ratio of stocks:bonds:cash
6) calculate the r**2 value between every 10 year period for stocks
7) do this 1000 times and calculate the summary stats for the R**2

Is this the way to build the model? I may do this later, if I can quickly find the cash and bond return. Thank you,





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