The Federal Reserve's monetary policy is guided by a dual mandate: to achieve maximum employment and stable prices.

So, it can be a bit conspiratorial to suggest that the Fed will react to swings in the stock market.

But according to new research from UBS, the stock market is a bigger driver of the path of monetary policy than changes in payrolls or expectations for prices. They came to this conclusion by observing how various economic and market variables moved with the Fed dots, which represent the Fed's expectation for future interest rates.

"We find that the most significant driver of changes in the Fed dots from one meeting to the next is changes in equity prices," UBS's Daniel Waldman said. "The second half of 2015 is helpful in thinking about the equity-Fed feedback loop. October’s 8% S&P 500 rally was an important driver of the Fed's December hike, though the domestic data wasn't overall better in December than it had been in September."

The correlations UBS found are summarized in the chart below.

To be fair, the stock market does not exist in a vacuum. Indeed, it is a major part of the financial system, and favorable financial conditions are critical for a healthy growing economy. In fact, when Janet Yellen was nominated to be Fed Chair, she pledge to "promote maximum employment, stable prices, and a strong and stable financial system."

So, what's next?

Waldman isn't suggesting you bet the house on this relationship.

"Will the recovery in the S&P 500 from the February lows compel the FOMC to become more hawkish and eventually raise its dots, pushing risky assets lower? In all likelihood, the Fed’s reaction function to equity prices is probably different now, with larger rallies required to trigger a hawkish response," he said.

Waldman considered recent comments yellen made in March during a post-FOMC meeting press conference.

"Chair Yellen emphasized that the Fed should 'proceed cautiously' on the basis of risks, especially those from global financial conditions," he said. "That said, it is important not to get too complacent. At some level of equity prices, the Fed may turn more hawkish."

–

Sam Ro is managing editor at Yahoo Finance

Read more:

The biggest issue facing the stock market right now

Obama uttered a single word that explains so much about the economy

Merrill Lynch chief economist nails the truth about risk in a perfect 3-word sentence

Gutsy Wall Street analyst dares to debunk a sacred truism about the stock market