Is the Fed Model a Good Valuation Tool?

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 the 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…

S&P 500 Earnings Yield and Treasury Yield image from 1928 to 2018

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…

S&P 500 Average and Median forward annualized total return chart from 1928 to 2018

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.

Plotted graph of S&P 500 earnings yield and S&P 500 forward total return

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.

Image of S&P 500 data points from 1928 to 2018

So perhaps the strong forward returns in deciles 8-10 were not due to the widespread 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.

Image of S&P 500 earnings yield and S&P 500 forward total retun

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.

S&P 500 average forward annualized total retuns chart from 1928 to 2018

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.


Related Posts:

What is the Relationship Between Interest Rates and Valuations?

Just How Overvalued Are US Equities?

Valuation and Bear Markets?

When Mean Reversion Fails?

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Charlie Bilello is the Director of Research at Pension Partners, LLC, an investment advisor that manages mutual funds and separate accounts. He is the co-author of four award-winning research papers on market anomalies and investing. Charlie is responsible for strategy development, investment research and communicating the firm’s investment themes and portfolio positioning to clients. Prior to joining Pension Partners, he was the Managing Member of Momentum Global Advisors and previously held positions as a Credit, Equity and Hedge Fund Analyst at billion dollar alternative investment firms.

Charlie holds a J.D. and M.B.A. in Finance and Accounting from Fordham University and a B.A. in Economics from Binghamton University. He is a Chartered Market Technician (CMT) and also holds the Certified Public Accountant (CPA) certificate.

In 2017, Charlie was named the StockTwits Person of the Year. He has been named by Business Insider and MarketWatch as one of the top people to follow on Twitter and his work has been featured in Barron’s, Bloomberg, and the Wall Street Journal.

You can follow Charlie on twitter here.


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