Last year, the Signal noticed an eerie correspondence between the highs and lows of the S&P 500 stock market index and the ups and downs of President Barack Obama's odds of winning re-election in the prediction markets. Almost a year later, the two data sets continue to move in remarkable lockstep.

S&P and Obama reelection odds

As thorny correlation issues go, this one is particularly interesting because the phantom hand of causation could move in either direction (or in neither, of course). Consider these various interpretations:

Scenario A: Happy investors lead directly to positive sentiment for the incumbent president. In fact, Matt Lampert, a research fellow at the Socionomics Institute, pointed me to a 1999 study by pioneering market psychologist Robert Prechter (and one-time co-contributor of mine) investigating how soaring markets favor sitting presidents, an observation that Lampert says goes "all the way back to George Washington." Prediction market traders who subscribe to Scenario A will bid up shares for Obama during a bull run in stocks.

Scenario B: Both signals are a factor of the same force: the greater economy. An improving economy simultaneously bolsters both the profits of companies and the prospects for Obama.

Scenario C: Elections don't follow stocks; stocks follow elections. The next president may cut capital gains taxes, reduce tax credits for oil companies or impose tighter regulations on banks. The next president may toss the solar industry money to burn, or choke off support for wind power. From media consolidation to antitrust policies, the party in the White House makes a difference for individual companies and corporate America overall.

The truth is, all three scenarios coexist. Scenario B may be the strongest, but Scenario C is especially intriguing because it would give us clear and direct information about how investors view and react to White House policy.

But can we disentangle all these forces and isolate exactly how much America's choice on Nov. 6 will affect the stock market? Sure, but it would require running an experiment that only an economist could love. To do so, we would need to abolish the election entirely and institute a coin flip instead: Heads, former Gov. Mitt Romney is president, tails, Obama keeps his job.

Under this crazy proposal, the instant reaction of Wall Street after the outcome of the ultimate coin flip (Heads? Buy Exxon Mobil.) could be attributed precisely to the identity of the commander in chief and not any other confounding factor. It's the same principle of randomized trials that we use to evaluate pharmaceutical drugs.

Such an experiment is scientifically valid, but I'm guessing you're not wild about it.