Many investors are obsessed with the Federal Reserve's efforts to boost the economy, but perhaps they're looking in the wrong direction.

"There seems to be a perception that central bankers are gods (or at the very least minor deities in some twisted economic pantheon)," James Montier, a portfolio manager at money management firm GMO, writes in a commentary.

"Coupled with this deification of central bankers is a faith that interest rates are a panacea. Whatever the problem, interest rates can solve it. Inflation too high, simply raise interest rates. Economy too weak, then lower interest rates."

You might be getting the idea that Montier holds some doubts. Indeed, he does. "This obsession with interest rates as a cure-all rests on some dubious views about the way the world works," he writes.

"It would appear that monetary policy isn't the most effective tool for managing the economy."

The government should turn to fiscal policy instead, Montier argues.

As for the Fed, it has kept short-term interest rates at record lows since December 2008 and isn't expected to raise rates until September at the earliest.

Meanwhile, with the Vanguard Total Bond Market Index Fund now the world's biggest mutual fund in the fixed-income space, its manager Greg Davis reigns as the new king of the bond market.

So what does he think of the economy and Fed policy? Economic growth is "relatively muted," he tells CNBC. GDP expanded just 0.2 percent in the first quarter, and the Atlanta Fed's forecasting model puts second-quarter growth at only 0.7 percent.

"One in nine Americans are still underemployed. You don't see a ton of strength in the labor market," Davis explains. The unemployment rate was 5.4 percent in April. Meanwhile, inflation remains low, he notes. Consumer prices slid 0.2 percent in the 12 months through April.

Davis sees growth of about 2.5 percent for the year as a whole. And what does that mean for the Fed?

"Our best estimate is for them to start the rate hike cycle sometime in September or December," he said, matching the forecast of many other experts.

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