Adding Up the Fed Model's Flawed Math

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.