If market or individual stock a has a positive predictive correlation with market b, and b had a positive predictive correlation with market a, then there is positive feedback, and an explosive growth when a is up would occur. Similarly, if there is a positive predictive correlation, i.e. the serial correlation of a with b say one day forward is 0.2, then market a goes down. If there is a negative predictive correlation of market a with market b, then when a goes up, b will tend to go down, and vice versa, and there will be a stable equilibrium between the two with each pulling the other in opposite directions.

The situation is very similar to what occurs in all feedback circuits in electronics, including what you seen in any kind of amplifiers where there is negative feedback to maintain stability.

What are the markets that have positive predictive correlation with each other, i.e. when a is up today, b tends to go up tomorrow, and when b is up today, a tends to go up tomorrow? There aren't many. And when such occurs, it is only for a limited time. So you have to be on your toes if you wish to use positive feedback. All this can be quantified with varying degrees of reality and rigor.

Steve Ellison writes:

I evaluated the correlations of the 1-day change (16:00 to 16:00 US Eastern time) in 6 markets with the following 1-day change in each of the 6 markets. The 1-day correlations from September 13, 2010 to September 4, 2012 (498 trading days) were as follows:

      S&P 500 10-year bond  crude oil     gold     silver       euro
S&P 500        -0.08       0.12      -0.05       0.05       0.11      -0.11
10-year bond    0.01      -0.05       0.04       0.05      -0.02       0.04
crude oil      -0.04       0.05      -0.06       0.00       0.04      -0.05
gold            0.01       0.00      -0.01      -0.01      -0.01       0.03
silver         -0.03       0.03      -0.01       0.02       0.05      -0.01
euro           -0.05       0.07      -0.03       0.06       0.06       0.03

By randomly reshuffling the daily changes in each market and running 1000 iterations of a simulation, I identified that a correlation with an absolute value greater than or equal to 0.09 was significant. Hence there were only 3 correlations that were significant, and 2 of them were positive:

10-year bond vs. previous day S&P 500: 0.12
Silver vs. previous day S&P 500: 0.11
Euro vs. previous day S&P 500: -0.11

None of these correlations held up in later data. From September 5, 2012 to May 2, 2013, the correlations of the 10-year bond with the previous day S&P 500 and silver with the previous day S&P 500 were negative. The correlation between the euro and the previous day's S&P 500 was -0.08. However, from May 3 to December 27, 2013, the correlation of the euro with the previous day S&P 500 was positive.

Rocky Humbert writes:

 An apochryphal tale: Rocky was hired to be the operations manager of a local towing company/garage and instructed to optimize his manpower work schedules and resource utilization to improve profitability.

Rocky noticed that tow truck drivers sat around idly drinking coffee at certain times of the day. But then there would be a surge of demand and customers might have to wait many hours to get a jumpstart or tow (and the garage would lose business to competitors).

It was a classic operation research/queueing theory problem. Under pressure to quickly turn the company around, and with a HBA MBA plus a PhD in applied mathematics in tow, Rocky conducted a study looking at six months of trailing data (between November 1st and April 1st) and discovered that the peak demand for service was daily between 7am and 8:45 am. His p-values were low. His T-tests were high. He was highly confident and energized to put his statistics to work concluding that batteries must die sitting unused overnight. So he changed his company's work roster to have more staff at the peak 7:00-8:45 hours and implemented the changes effective May 1st. Lo and behold, starting around May 15th, there were almost no customer calls between 7:00 and 8:45 and instead the demand spiked between 4:00 and 6:00.

So instead of improving things, he screwed them up and by September, Rocky concluded that the prior data must have been faulty and re-jiggered the staff to meet the afternoon demand — and implemented the changes effective November 1st. (Yup, the demand shifted yet again just in time for the chilly autumn air ).

Rocky was fired and became a successful money manager and annoying DailySpec poster. The moral of the story is that all of the cool statistical analyses should produce the QUESTIONS. Not the ANSWERS. What is the underlying process at work????

There will be times when stocks and bonds correlate. There will be times when stocks and bonds negatively correlate. Rocky submits that at some point in the not-too-distant future good news for the economy will be bad news for stocks (which is the opposite of the current regime). This isn't ever changing cycles. It's common sense. Or as Rocky's dad (a pioneer in digital computing) liked to say: GIGO.


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