It's over! Stocks and oil may finally break up

If investors want to know what stocks are doing on any given day, all they have had to do is check crude oil. Black gold and equities have begun to maintain a remarkably close relationship, and the correlation has become even tighter in the past week.

Now, the question is whether this volatile couple is finally set to break up.

Out of the past eight sessions, there have been only two when during which crude and the S&P 500 Index moved in different directions, one of them on Friday. And thus far in February, crude oil and the S&P have enjoyed a huge positive correlation of 0.86 (with 1 indicating perfect correlation). Crude and stocks have typically had no real correlation, positive or negative, over long stretches of time.

Read MoreOil is falling, and it's all OPEC's fault: BIS

The recent relationship between stocks and crude have come as oil has turned massively volatile after a steep seven-month plunge. Recently, the critical commodity has vacillated between massive gains and losses, often taking stocks along for the ride.

Yet many market participants say that the close relationship can't last.

"As long as oil doesn't make new lows, the correlation should dissipate," predicted Chicago-based trader Jim Iuorio. "The market has become accustomed to $50 oil. I think that the speed at which it was falling was a bigger deal than the actual price."

For Curtis Holden, senior investment officer at Houston-based Tanglewood Wealth Management, stocks will be able to pay less attention to oil in the week ahead, even if crude stays volatile.

"Volatility will make the market nervous, but I think the bigger issue is just not seeing straight shots down," Holden said. "If oil is down 5 percent one day and up 5 percent the next day, that's not a big a deal as 5 percent down and then 5 percent down... then people say 'Oh my goodness, what's going on?'"

Investors often use correlations as a key to figuring out how to effectively mitigate portfolio risk. However, Holden says investors shouldn't rethink their entire portfolios just because the relationship between stocks and oil has changed of late.

"Just because this is happening in the short-term, doesn't necessarily mean that a we're in a new era where there's going to be a higher correlation," he said. "If anything, in the long-term, falling oil prices should be good for stocks."

The investor points out that falling crude need not take down the market. After all, as oil plummeted back in 1986, stocks soared. Once the jitters abate, then, stocks should do fine with the concept that fuel is much cheaper.

'We ain't seen nothing yet'

A trader works on the floor of the New York Stock Exchange.
Getty Images
A trader works on the floor of the New York Stock Exchange.

For Bill Baruch, senior commodities broker at iiTrader, it's no coincidence that the one day in the past week when oil and stocks moved in opposite directions was the day that the strong January employment report was released.

He says that off of the positive economic news, the prospect of a coming hike in the federal funds rate will begin to obsess stocks (while oil will continue to be driven by trading dynamics).

Still, not everyone believes that oil and stocks will soon resume their traditional "two ships passing in the night" relationship.

Read MoreWhere are oil prices headed from here?

"I expect a continuation and deviation in all markets in 2015, and I think we ain't seen nothing yet," said Andrew Hecht, a former commodities trader and the author of "How to Make Money with Commodities."

"The strength of the dollar and the U.S. economy versus the continuing weakness in the overall global economy will likely cause markets to trade in a manic and bipolar fashion," he said. "So for oil and stocks, expect deviation and reversion on a day-to-day basis."

—By CNBC's Alex Rosenberg.

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