NEW YORK (CNN/Money) - Remember when people thought the Fed model broke?

In early 1999 the popular valuation tool said that stocks were getting too expensive. By the beginning of 2000 it said that the market was 60 percent higher than it should be. Bearish strategists, who used similar models, were considered fools -- when they were given a consideration at all.

Well, it looks like the model, which was working great until that 1999 experience, is broken again. But now it's broken in the other direction. Starting in May, it began to indicate that stocks were undervalued and now it says they're more than 40 percent below where they should be. Only in the depths of the selloff this past fall did it show a lower reading.

"Nobody believed in the model when it said that stocks were 60 percent overvalued and nobody believes in it now," said Prudential Securities chief investment strategist Ed Yardeni. "Valuation is like beauty -- it's in the eye of the beholder."

It's Yardeni who coined the term Fed model after a Federal Reserve report to Congress in July 1997 suggested the bank was following it -- the Fed itself has never endorsed it or any other stock market valuation method -- but the idea behind the model has been around for a lot longer than the term. Both Morgan Stanley's Byron Wien and J.P. Morgan's Doug Cliggott developed similar models that predated the 1997 Fed report, for instance.

In its simplest form, the model compares the 10-year Treasury note and the S&P 500, with the idea that the expected return of the two competing investments should be more or less the same.

The Treasury's return is easy -- it's the yield, the annual return investors get if they hang on until the note's maturity. The equivalent for stocks is the "earnings yield," or expected earnings divided by price. It's just the inverse of the more common price/earnings (P/E) ratio, and tells you how much in earnings you can expect to get for each dollar you pay.

Based on the current Treasury yield of about 3.90 percent -- which should, according to the model, be roughly equal to the "earnings yield" on stocks -- the S&P 500 could trade at about 25.6 times expected earnings. Instead, according to First Call, it trades at 15. So how come people aren't buying the pretty picture the Fed model is painting?

Probably the biggest issue that investors have with the model right now is that they put so little faith in analysts' estimated earnings. The problem isn't analysts' endemic optimism (although there is that) so much as that they're estimating "operating earnings," which don't include many of the big charges that companies have been taking lately.

"Today's earnings quality is less than in the past," said Brett Gallagher, head of U.S. equities for Julius Baer.

In 1997, for example, S&P 500 earnings under generally accepted accounting principles, or GAAP, were about 85 percent of what they were if you looked at the operating earnings companies put out in press releases. Last year, estimates suggest, GAAP earnings came in at about 60 percent of operating earnings.

In fact, Doug Cliggott, who now works for a hedge fund, has told CNN/Money that he puts considerably less faith in expected earnings now than when he was at J.P. Morgan, with the implication that if he still maintained his old valuation model now, he would rework it substantially. By Cliggott's reckoning, GAAP earnings have historically been about 85 percent of operating earnings, suggesting that operating earnings still need to come down by a lot.

But complaints about the Fed model go deeper than just grousing over how it's been skewed by companies' recent penchant for inflating earnings -- some critics contend that it wasn't of much use from the get go.

Fed model forecasts Date  Fed model says stocks are...  S&P 500, 3 months later  Aug. 1987  34% overvalued  down 30%  Oct. 1998  10% undervalued after Russian debt crisis  up 16%  May 1999  37% overvalued, more than 1987  up 1%  Mar. 2000  52% overvalued  down 4%  Sept. 2001  10% undervalued  up 10%  Now  42% undervalued  ?

For Cliff Asness, managing principal at the hedge fund AQR Capital Management, one of the most basic problems with the model is that bond yields and earnings have, or should have, a lot do with each other. Bonds price on inflation expectations -- when investors are worried that inflation is heating up, they sell bonds, sending rates higher. But over the long run earnings and inflation move up and down with each other. The current low-rate environment suggests there won't be much inflation at all, with the implication that there won't be much earnings growth. Why would investors want to pay a high price for low earnings growth?

For an extreme example, take a look at Japan, where as a result of deflationary forces the 10-year government bond yields about 0.8 percent. Apply the Fed model, and that means the Japanese stock market should have a forward P/E multiple of 125. That would bring the Nikkei index from the present 8,600 to around 23,400.

But going back to 1979, which is as far as the data on estimated earnings goes back, the Fed model appears to have performed well in the U.S. market. Why is that?

"The Fed model shows that when interest rates are high, people buy a high P/E," said Asness. "It explains that behavior; what it doesn't do is justify it. The Fed model is theoretically flawed -- it's the liquor that accidentally gets investors to buy high P/Es occasionally, and I think the people pushing it are liquor salesmen."

Look back over history, notes Asness, and you'll see that buying high P/Es is almost always a recipe for lousy returns, regardless of where interest rates are. (For what it's worth, Asness looks at how the market trades compared to its GAAP earnings over the past 10 years. The market has come down to the point where he thinks valuations may be reasonable.)

Still, the basic notion that investors are comparison shopping between stocks and bonds continues to hold some sway over Wall Streeters, and they have worked up valuation tools that avoid some of the pitfalls of the Fed model. One of the things Yardeni has done, for instance, is compare earnings yields on stocks with corporate bond yields, rather than the lower Treasury yields. Do this and stocks appear modestly, rather than grossly, undervalued.

The model that Morgan Stanley U.S. market strategist Steve Galbraith and quantitative strategist Qi Zeng have developed uses historical GAAP earnings rather than estimated forward operating earnings. It also includes what Zeng calls a "penalty function" for environments where rates have come low enough that deflation is a concern, since deflation will cut into earnings power.

"The penalty becomes more severe as deflation becomes more apparent," she said. Rates are low enough in the current environment that the penalty has kicked in. As in the late 1950s -- the last time serious deflation worries hit the U.S. -- the model suggests that higher, rather than lower rates are what investors should hope for now.

Still, some people think the boring old version of the Fed model, warts and all, has its merits.

"I've thrown the Fed model into statistical backtesters and gotten good results," said Trilogy Advisors chief investment strategist Bill Sterling. "But the thing is, if you find a model that works 60 or 70 percent of the time, it's going to make you feel like the village idiot 30 or 40 percent of the time."

And although the arguments against the model seem sound, it may be useful to remember some of the criticism it was getting in early 2000.

Lehman Brothers strategist Jeff Applegate (he left the firm this past fall), for instance, used to say that the Fed model was "intellectually ridiculous" because the U.S. companies' growth was so much more than what their earnings for the next year implied.

It seemed like a convincing argument at the time.