Of the five people considered in the running for the Fed chair position, only one really strikes any fear into the market's heart. The rest either are considered more likely to adhere to the central bank's current collective philosophy or have little real chance of getting President Donald Trump's nomination — or a little of both. John Taylor, a Stanford economist and proponent of a rule bearing his name, might push the Fed into a considerably different direction than investors have been used to for the past 12 years. "I suspect the markets would be most pleased with some form of continuity. Things have gone so well for markets the last few years," said Ed Keon, managing director and portfolio manager at QMA. Worry over what Taylor might do "is a legitimate concern. The most famous rule for a mechanical approach to monetary policy bears his name." Three of the other candidates — current Chair Janet Yellen, Fed Governor Jerome "Jay" Powell and Trump economic advisor Gary Cohn — are distinct without being terribly different. Also, by this point Cohn, who would take a more deregulatory approach than the others, has been all but completely dismissed as a legitimate contender. Finally, there's Kevin Warsh, a former Fed governor who would provide a break from the monetary philosophy of the Yellen-Ben Bernanke Fed. However, his chances seemed to have diminished in recent weeks, as public pronouncements from Trump have not mentioned Warsh. Markets for now figure that Powell is the leading contender. A source told CNBC on Friday that Trump remains undecided but is leaning toward Powell. However, market participants are keeping an eye on Taylor for his potential to be a transformative central bank leader. Taylor is thought to be the preferred pick of Vice President Mike Pence, while Treasury Secretary Steve Mnuchin reportedly favors Powell.

Impact on a variety of fronts

"We do not think that monetary policy would change notably in the near term if Taylor were to replace Yellen in February 2018," Nomura economist Lewis Alexander said in a note. "However, in the longer run, his chairmanship would likely have important implications to the policy rate path, the Federal Reserve's optimal balance sheet, and responses to economic downturns." That's because the Taylor rule, a gauge of where the Fed's benchmark funds rate should be in regard to economic conditions, has long argued that policy should be considerably less accommodative than it's been since the financial crisis.

John Taylor Andrew Harrer | Bloomberg | Getty Images

Assuming a 2 percent inflation target, the rule would put the funds rate at 3.7 percent, or more than triple the current level of 1.15 percent. "Taylor has written a number of papers arguing that economic performance would have been better, or the economic damage from the global financial crisis would have been smaller, had the Fed followed the Taylor rule from 2003 through 2005," Alexander said. "Thus, he thinks that a rule-based policy is helpful in mitigating risks of a recession." Taylor is considered a longshot at this point, but he's not out of the mix for a Fed position. One scenario has him getting the vice chair's position to Powell's chair, a move that would serve "as an elegant solution to win plaudits from the multiple camps within Trump's orbit," Beacon Policy Advisors said in a note Friday. PredictIt, an online marketplace for wagering on outcomes of varying events that has become a popular outpost for Fed watchers, is now taking bets on vice chair. Warsh is currently the leader while Taylor is second; Powell has a wide lead for the chair position. Indeed, Trump has multiple positions to fill at the Fed, and Wall Street is watching closely for the direction he takes not only with Yellen's job but also the other three openings. "There is some movement towards selecting individuals who are focused in on rules, who are focused in on very specific models, and I believe that's a mistake," Abby Joseph Cohen, a semiretired high-profile strategist at Goldman Sachs, said at a Yahoo Finance conference earlier this week. "The next people who go onto the board really have to be people who are flexible in their thought processes and willing to take in a lot of new information."

Controlling growth