Analysts who track the so-called Fed model, a valuation tool comparing corporate earnings with interest rates, say that now is a good time buy stocks. Should you believe them?

While it's certainly possible that stocks could rise over the next few weeks or months, relying on the Fed model for clues about the market's direction is probably unwise. After all, the model says nothing about absolute expected stock returns, and it has been a poor predictor of the stock market over long periods of time.

"There is no logical basis for the model, nor was there ever a logical basis," said Larry Swedroe, director of research at Buckingham Asset Management in St. Louis and author of

What Wall Street Doesn't Want You to Know

.

The Fed model compares the yield on the 10-year Treasury note with the earnings yield of the

S&P 500

. When the earnings yield, defined as the S&P's expected earnings divided by the price, is higher than the Treasury yield, stocks are considered undervalued relative to bonds. Conversely, when the earnings yield is lower, stocks are considered relatively overvalued. While the

Federal Reserve

has never formally admitted to using the tool, a report to Congress in 1997 suggested that it was something the bank looked at.

Right now, the model is suggesting that stocks are cheap in comparison with Treasuries. The earnings yield on the S&P 500 is sitting at 5.6% compared with a yield of 4.6% for the 10-year note.

Even if the model is right and stocks are cheap relative to bonds, that doesn't mean stocks are cheap on an absolute basis. The model could simply be saying that stocks aren't as wildly overvalued as bonds. This point is often lost on many analysts, who use the Fed model to gauge absolute stock returns.

Of course, there were times when the model seemed to predict turns in the market. In early 2003, for example, it was showing that stocks were more than 40% undervalued relative to bonds. By the end of the year, the S&P 500 had climbed 26%. The Fed model also seemed to foreshadow big losses in August 1997 and in March 2000.

Still, Cliff Asness, managing principal at the hedge fund AQR Capital Management, said the tool has been a poor prognosticator of the market over the long term. "The evidence strongly suggests that the Fed model is fallacious as a tool for long-term investors," he said.

Asness studied the period from 1881 to 2001 and concluded that the model did not have any predictive power in terms of absolute stock returns. A far better indicator of performance was simply the price-earnings ratio. "The bottom line is that for forecasting long-term stock returns, the Fed model is an empirical failure," he said.

Aside from these complaints, experts say, the model is flawed because it compares expected operating earnings with Treasury yields. Analysts' earnings estimates have historically been overly optimistic and often exclude big charges.

The idea that the earnings yield should match the Treasury yield in order for stocks to be fairly valued also seems unfair, given that stocks are a lot riskier than government bonds and deserve a premium.

To combat this problem, some analysts compare the S&P's earnings yield with the yields of corporate bonds, which offer higher interest rates. But this methodology is also flawed, because investors are still comparing a nominal yield with a real one.

Why does this matter? Bond yields are nominal, meaning they are not adjusted for inflation. When you buy a 10-year note, or a corporate bond, you receive a fixed interest payment for the life of the bond. If inflation expectations were to rise to 3% from 2%, the real return on the bond would be negatively affected. In contrast, the real growth in corporate earnings is not affected by inflation. Last year, for example, profits surged, though inflation was very low.

Let's assume that the expected long-term rate of inflation is 2% and the 10-year note is yielding 5%. According to the Fed model, the earnings yield on the S&P 500 also should be 5% for stocks to be fairly valued. But what would happen if inflation expectations rose to 3%? That would send the 10-year note up to 6%, because investors would require more compensation for the added risk.

In order for stocks to be fairly valued, the earnings yield would also have to rise to 6%. Suddenly, stocks could appear overvalued, since the earnings yield would be below the Treasury yield. Yet rising inflation does not affect real earnings and should not affect valuations.

"Because the real return on bonds is impacted by inflation while real earnings growth is not, the Fed model compares a number that is impacted by inflation with a number that is not," said Swedroe.

While there are valid arguments to suggest that earnings and interest rates are connected, the precise correlation suggested in the Fed model is misleading and could cost you money. Over the long term, the best way to predict the market is to look at its price-earnings ratio, and right now that seems high.

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