The Fed Model Is the Misleading, Inaccurate Market-Timing Tool That Refuses to Die

The Fed Model is based on the difference between the stock market’s earnings yield and the

10-year Treasury yield
.

An earnings yield is the inverse of a price/earnings ratio: If the

S&P 500’s

P/E is 20, for example, its earnings yield would be 5%.

In its simplest form, the Fed Model is bullish on equities when this difference is positive and bearish when it is negative, as it is now: The S&P 500’s earnings yield, based on the index’s estimated earnings per share over the next 12 months, is 4.5%. That’s 0.2 percentage point below the current 10-year Treasury yield of 4.7%.

The Fed Model got its name in the mid-1990s, based on a single paragraph in one of the Federal Reserve’s reports to Congress that, more or less in passing, compared the stock market’s earnings yield to the yield on the 10-year Treasury. The Fed didn’t give the model its name, nor has it endorsed it as a worthwhile market-timing indicator. It nevertheless took Wall Street by storm, and around the turn of the century became one of the more-cited reasons why to be in or out of stocks.

The model subsequently fell out of favor. For example, as you can see from the chart below, the Fed Model was bullish in October 2007, at the beginning of the bear market that accompanied the 2008-09 financial crisis. And it was more bullish still in August 2008, immediately before Lehman Brothers collapsed and the bottom fell out of the market.

With those spectacular failures having long since faded from memory, and with the 10-year yield for the first time in more than 20 years higher than the stock market’s earnings yield, the Fed Model is making a reappearance. In some cases it’s implicit, when investors argue that higher bond rates mean that stocks are no longer attractive. But it’s also being resurrected explicitly as well.

If subtracting the 10-year Treasury yield from the earnings yield were a good idea, as the Fed Model assumes, then its track record should be better than using the unadjusted earnings yield alone. But that isn’t the case.

To show this, consider a statistic known as the r-squared, which measures the degree to which one data series (in this case, the Fed Model, or the earnings yield) is able to predict changes in another series (in this case, the stock market’s subsequent return). Based on data since 1871, courtesy of Yale University professor Robert Shiller, the earnings yield has a significantly higher r-squared than the Fed Model.

For example, when predicting the S&P 500’s subsequent 10-year inflation-adjusted total return, the r-squared for the earnings yield by itself is 23%, versus 11% for the Fed Model. In other words, the earnings yield by itself was twice as effective as the Fed Model in predicting the stock market’s subsequent return. Differences of similar magnitude exist for other time horizons as well.

The Fed Model’s failure shouldn’t come as a surprise, according to a well-known article from two decades ago by Cliff Asness, co-founder and chief investment officer at AQR Capital Management. Entitled
“Fight The Fed Model,” it exposed the theoretical confusion at the heart of the Fed Model. Because “over the long term, nominal earnings generally move in tandem with inflation,” the earnings yield is a real, or inflation-adjusted, number. The Treasury’s 10-year yield, by contrast, is not inflation-adjusted. The Fed Model therefore “compares a real number to a nominal number”—apples to oranges, in other words.

A more theoretically sound Fed Model would compare the earnings yield to real yields, according to Antti Ilmanen, a colleague of Asness who is a principal and global co-head of the Portfolio Solutions Group at AQR Capital Management. For real interest rates, he suggested in an email, focus on either the 10-year Treasury inflation-protected securities (yielding 2.2%) or the 30-year TIPS (yielding 2.4%).

To calculate the stock market’s earnings yield, Ilmanen furthermore suggests using the Cyclically Adjusted P/E (CAPE) ratio made famous by Yale’s Shiller. It is similar to the traditional P/E but uses trailing 10-year inflation-adjusted earnings per share for the denominator. The CAPE earnings yield is currently 3.0%.

This more theoretically sound version of the Fed Model is currently positive, therefore, in the range of 0.6 to 0.8 of a percentage point. While it’s good news that it’s positive, unlike the original Fed Model, it’s bad news that it’s lower than its historical average which, Ilmanen says, has averaged in the 3% to 5% range.

As it so often is, the picture is mixed.

Mark Hulbert is a regular contributor to Barron’s. His Hulbert Ratings tracks investment newsletters that pay a flat fee to be audited. He can be reached at mark@hulbertratings.com.

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