Stocks have surged in the two and a half months since Ben Bernanke started hinting at more monetary stimulus. Betting against the central bank seems unwise: Bernanke says he wants to stimulate the economy by holding down interest rates, an act that tends to push up the prices of assets such as stocks.

Accordingly, indexes such as the S&P 500 are approaching levels last seen just before the meltdown of 2008 — when taxpayers didn’t yet own AIG or GM, and unemployment was 3 percentage points lower.

Yet a wager that quantitative easing will send U.S. stocks steaming higher carries ample risks. Stocks look pricey by several measures, skeptics note, and a surge in commodity prices could spell more trouble for a weak recovery.

Those aren’t the only pitfalls. Japan’s falling stock prices during a long period of low interest rates suggests the benefits of easing could flow to the rest of the world. If that’s not enough, tattered U.S. finances could send foreign investors fleeing for other shores.

“What we have on our hands right now could be a huge sucker’s rally,” writes Gluskin Sheff economist David Rosenberg.

Stock market bears such as Rosenberg have been warning for months that the market looks overvalued, but their caution is worth noting because of its grounding in history.

Stocks in the S&P 500 are trading at around 21 times their cyclically adjusted earnings, using a method devised by Yale professor Robert Shiller. The long-run average is 16 and purchases of stocks at a market multiple of 21 or above “have historically been followed by poor long-term returns,” writes John Hussman, a value investor who runs the Hussman funds in Baltimore.

That isn’t the only measure of stocks’ overvaluation. The dividend yield on the S&P 500 recently dropped to 1.9%, down from 3% at the end of the free fall of 2008 and again below the historical average. Companies could bring that ratio up by boosting their payouts, but there is another way the dividend yield could rise: through falling stock prices.

Other arguments against buying U.S. stocks here stem from the observation that loose monetary policy does tend to pump up asset prices – but not necessarily at home.

That has certainly been the experience of the Bank of Japan, which hasn’t moved its discount rate above 1% for 15 years yet has seen stock and property values plunge.

The culprit there, and likely for coming years of subpar U.S. returns, is the carry trade in which investors borrow cheaply in a low-rate currency such as the yen or dollar and buy assets in higher-rate currencies such as Brazil’s real or the Australian or Canadian dollars.

Stock markets in the United States and Japan, denominated in carry trade currencies thanks to interest rates that have been near or at zero in recent years, have lagged behind the rest of the world lately, notes Bianco Research strategist Howard Simons. Meanwhile those in Europe and the U.K. have outperformed the globe.

“The question of whose stock market returns you enhance with money-printing is a function of whether your currency is fuel for carry trades or not,” Simons writes.

And last but not least, there is the question of whether the decision to pour more liquidity into a world already awash in dollars will, together with dysfunction in Congress, undermine the appeal of the U.S. as an investment destination.

This notion was raised last month by Richard Fisher, the president of the Federal Reserve Bank of Dallas, who raised an eyebrow at companies’ increasing inclination to raise money on the cheap and then “invest it abroad where taxes are lower and governments are more eager to please.”

He then added:

This would not be of concern if foreign direct investment in the U.S. were offsetting this impulse. This year, however, net direct investment in the U.S. has been running at a pace that would exceed minus $200 billion, meaning outflows of foreign direct investment are exceeding inflows by a healthy margin.

Even those who have profitably plied the don’t-fight-the-Fed trade say piling into U.S. stocks now is highly risky given the apparently limited potential rewards.

“The United States is not the center of the investment universe,” says Andrew Barber of investment adviser Waverly Advisors in Corning, N.Y.

He was urging clients three months ago to buy big-cap U.S. stocks at the expense of smaller ones. But he warns now to trim domestic stock exposure, saying, “The forces driving the dollar’s devaluation also undermine the credibility of the U.S. as a place to put money.”