By now, most investors have at least a passing familiarity with the so-called

Fed

model, a valuation metric used to determine stocks' relative attractiveness to Treasuries. But does it work? What is its history as a market prognosticator? And is comparing stocks to Treasuries really a fair measure?

To recap, the Fed model compares the earnings yield (the inverse of the price-to-earnings ratio) of the

S&P 500

to the yield of the benchmark 10-year Treasury note. The key to the model, as described in a

1997 monetary policy report to Congress prepared by the Fed, is its reliance on "consensus estimates of earnings over the coming 12 months." Forward earnings estimates, in other words.

Based on forecast 2003 operating earnings of $53.04 and Monday's closing price of 932.88, the S&P's earnings yield is 5.68% vs. the 10-year's yield of 4.18%. When the S&P's earnings yield exceeds the 10-year Treasury yield, shares are said to be undervalued, by about 27% at present, according to the Fed model. Yes, that's even after the market's big rally since Oct. 9.

Of course, one of the big criticisms of the Fed model is its reliance on analysts' projected earnings, which have proven to be notoriously overly optimistic, in some cases laughably so.

Furthermore, the value of operating earnings has been severely diminished by widespread abuses in the recent past, where companies were excluding as "extraordinary" any number of real expenses from their profit calculations, as detailed

here.

On a GAAP, or reported, earnings basis, S&P 500 profits are forecast to be $39.50 next year, resulting in an earnings yield of 4.23%, meaning stocks are essentially fairly valued at current levels. Reported earnings sharply limit what "one-time" items companies are allowed to exclude from their bottom line. (Currently, there are no forecasts for so-called core earnings, an even stricter measure of profitability; still, the more stringent model means it likely would show shares to be sharply overvalued at current levels.)

Setting aside, for now, the debate over the worth of earnings projections and the value of operating earnings, fans of the Fed model say, quite simply: It works.

Reeling in the Years
A history of the Fed model shows relative under- and overvaluation of stocks vs. the 10-year Treasury note

*Ratio of S&P 500 index to its fair value (12-month forward consensus expected operating earnings per share divided by the 10-year U.S. Treasury bond yield) minus 100. Monthly through March 1994, weekly after.
Source: Prudential Securities, Thomson Financial

'Extremely' Valuable

"The Fed stock valuation model worked quite well in the past," wrote Edward Yardeni, chief investment strategist at Prudential Securities, in a report on the subject in August. "It identified when stock prices were excessively overvalued or undervalued, and likely to fall or rise," including:

Showing, with back-testing, the market was "extremely undervalued" from 1979 through 1982, a precursor to a major rally that lasted until the 1987 crash;

Reaching a then-record overvaluation peak in late summer of 1987, before the crash;

Indicating stocks were undervalued in the mid-1990s, at the cusp of the biggest rally in history;

Hitting overvaluation in the summers of 1997 and 1998, prior to sharp drops in share prices, and a steep undervaluation in the fall of 1998, at the cusp of the blowoff phase of the biggest rally in history. In January 2000, the Fed model said stocks were overvalued by a record, and extraordinary, 70%.

More recently, and famously thanks to a

Barron's

cover story, the Fed model showed shares were significantly undervalued in late September 2001, then swung to overvalued early this year. In late July 2002, the Fed model said stocks were undervalued again, right around the July 22 bottom. However, they stayed undervalued prior to the September 2002 swoon, reaching more extreme levels of undervaluation in early October.

"The Fed model is not a perfect market-timing tool," as an over- or undervalued market can become even more so, wrote Yardeni, who is widely credited (including by Yardeni himself) with coining the term "Fed model" to describe something the central bank has never formally endorsed. "However, the Fed model does have a good track record of showing whether stocks are cheap or expensive."

Critics, naturally, contend otherwise.

Unsafe at Any Level

"I hate the Fed model for a couple of reasons," said Thomas McManus, equity portfolio strategist at Banc of America Securities.

First and foremost, earnings yield of the S&P 500 is "not representative of the market," McManus said, recalling that so-called average stocks were dramatically

undervalued

in March 2000, even as major averages such as the S&P 500 were vastly overvalued.

Late 1999 and early 2000 was a point of "crisis valuation" for stocks, he said, noting the Chinese characters for crisis is a combination of danger and opportunity. "The Fed model failed to tell you there was danger in

Cisco

(CSCO) - Get Report

at $82 and opportunity in

Conagra

(CAG) - Get Report

at $15."

Second, "the math used in the Fed model is w-r-o-n-g," McManus argued. Rather than as a ratio, stocks' earnings yield should be compared with Treasuries on a spread basis, he said, similar to how corporate bond yields are discussed vs. Treasuries.

Third, and finally, McManus prefers a model which valuesnominal yields -- inflation expectations plus real interest rates -- to determine the expected return on common stocks. (Even Yardeni concedes the Fed model is a "very simple stock valuation model" and "should be only one of several inputs investors use.")

Having said all that, McManus believes the average stock remains attractive at current levels based on his proprietary valuation model, which he declined to specify further.

Bill Gross, managing director at Pimco, which has over $300 billion under management, takes an even harsher view of the Fed model.

"Should the Street really be using 10-year Treasuries as the convenient bogey to beat?," Gross mused in a report on Pimco's Web site earlier this month. "After all, Treasuries are risk-free and stocks anything but." (The idea that the S&P's earnings yield should be equal to the 10-year's is controversial, although the average spread between the two is only 25 basis points since 1979, according to Yardeni.)

Instead of comparing shares to the 10-year's yield, Gross suggested using Baa-rated corporate bond yields, "a pretty fair measure of the composite debt of S&P 500 companies."

Using this "apples-to-apples" metric, stocks are about 30% overvalued compared with the near-7% yields on Baa corporates, he wrote. "In the end analysis, it is fair to ask who is the true fool -- the eternal 'glass more than half full' stock optimists or the bond guy with a supposed axe to grind."

As always, investors are encouraged to draw their own conclusions about that statement, as well as the value of the Fed model. My conclusion is the Fed model is a decent guide for the relative attractiveness of the S&P 500, but is far from an infallible indicator.

Aaron L. Task writes daily for TheStreet.com. In keeping with TSC's editorial policy, he doesn't own or short individual stocks, although he owns stock in TheStreet.com. He also doesn't invest in hedge funds or other private investment partnerships. He invites you to send your feedback to

Aaron L. Task.