# Is the Fed Model a Good Valuation Tool?

By Charlie Bilello

Should investors use bond yields as a baseline to determine if stocks are over-or-under valued?

If you believe in the “Fed Model,” your answer is “yes.” The model instructs investors to compare the S&P 500’s earnings yield (Earnings/Price, the inverse of the P/E ratio) to the 10-Year Treasury yield:

• If the Earnings Yield is above the Treasury Yield, stocks are said to be “undervalued.”
• If the Earnings Yield is below the Treasury Yield, stocks are said to be “overvalued.”

With the Earnings Yield (“EY”) today currently above the 10-Year Treasury Yield (“TY”), many pundits are arguing that stocks are still undervalued (and therefore attractive), despite other metrics indicating otherwise (click here for recent post on this). Are these pundits correct? Is comparing the Earnings Yield to Treasury Yields an effective way to value stocks and forecast future equity returns? Let’s take a look…

Data Sources for all charts/tables herein: Robert Shiller, Bloomberg, YCharts.

Going back to 1928, we can separate EY minus TY into deciles, from lowest (-4.4% to -2.1%) to highest (7.0% to 14.9%). We can then calculate average and median forward returns over the next 1 to 10 years within each decile…

If you’re struggling to find a strong relationship in the above tables, that’s because there isn’t one. While the highest EY-TY decile is indeed followed by the strongest returns, the lowest EY-TY decile has above-average returns from 4 years through 10 years forward. The weakest returns reside in the middle deciles (4-7), with a slight bias to higher forward returns with higher EY-TY starting levels.

We can observe this bias in the upward slope of the trendline line in the scatter chart below, which compares the starting EY-TY levels to forward 10-Year Total Returns. The R Squared in this case is .11, meaning that knowledge of EY-TY accounts for only 11% of the variation in future 10-year returns.

Why is there a correlation between EY-TY and forward returns at all?

Digging into the data, we find our answer. In the highest EY-TY decile 10 which showed the strongest forward returns, the median P/E ratio of 9 was by far the lowest of any decile, and the median earnings yield of 11.1% the highest. Many of the data points were from the late 1940s and early 1950s when stocks were exceptionally cheap and bond yields were exceptionally low.

Deciles 8 and 9 also showed below-average P/E ratios.

So perhaps the strong forward returns in deciles 8-10 were not due to the wide spread between EY and TY after all, but simply because of the lower starting P/E ratios (or higher EY).

If this is indeed the case, we should observe a stronger relationship between EY and forward returns than EY-TY. That is exactly what we find. The R Squared between EY and forward returns moves up to .45, meaning 45% of the variation in forward 10-year returns can be explained by the starting Earnings Yield. This is significantly higher than the R Squared of 0.11 for EY-TY.

The conclusion: cheap stocks tend to be followed by above-average forward returns – and expensive stocks below-average forward returns – regardless of where bond yields are.

This makes intuitive sense, particularly when viewed in the extreme. Let’s say the 10-year Treasury Yield went negative, as was the case in recent years in both Japan and Germany, and still is the case in Switzerland. Under the “Fed Model,” that would imply that the P/E ratio could literally go to infinity and still deliver a higher Earnings Yield (E/P) than the yield on bonds. If the P/E ratio on Swiss stocks went to 1000, the Earnings Yield would be 0.10% (=1/1000), still higher than the yield on 10-Year Swiss Bonds (-0.10%).

Would you call Swiss stocks undervalued today at a P/E ratio of 1000? I rest my case.