Earnings Yield vs Bond Yield
Every investment competes with every other investment for capital. When a 10-year Treasury bond yields 5%, stocks must offer a compelling return premium to justify their additional risk. When that same bond yields 1.5%, stocks become relatively more attractive even at higher valuations. The comparison between earnings yield and bond yield is one of the oldest and most fundamental frameworks in investing, connecting the stock market to the bond market in a single calculation that reveals whether equities are cheap, expensive, or fairly valued relative to fixed income.
Earnings yield is the inverse of the P/E ratio:
Earnings Yield = Earnings Per Share / Stock Price = 1 / P/E
A stock with a P/E of 20 has an earnings yield of 5%. A stock with a P/E of 15 has an earnings yield of 6.67%. The metric expresses the return an investor earns on each dollar invested if the company paid out 100% of its earnings. By expressing stock valuation in yield terms, it becomes directly comparable to bond yields, real estate cap rates, and other investment returns.
The Equity Risk Premium
The difference between the earnings yield on stocks and the yield on risk-free government bonds is called the equity risk premium (ERP). This premium compensates investors for the additional risk of owning stocks, which can decline in value, cut dividends, and go bankrupt, none of which apply to Treasury bonds.
Equity Risk Premium = Earnings Yield on Stocks - 10-Year Treasury Yield
Historically, the equity risk premium has averaged approximately 3-4 percentage points in the United States. When the S&P 500 earnings yield is 5.5% and the 10-year Treasury yields 2.5%, the equity risk premium is 3.0%, roughly in line with historical norms. When the earnings yield is 8% and Treasuries yield 3%, the equity risk premium is 5%, suggesting stocks are relatively cheap. When the earnings yield is 4% and Treasuries yield 5%, the equity risk premium is negative, suggesting stocks are relatively expensive compared to bonds.
The equity risk premium is not a market timing tool in the short-term sense. A negative equity risk premium does not mean stocks will decline tomorrow. It means that the compensation for owning stocks over bonds is thin, and the long-term expected return on stocks relative to bonds is below average. Investors who maintain awareness of the equity risk premium are better positioned to adjust portfolio allocations between stocks and bonds as relative attractiveness shifts.
The Fed Model
The Fed Model, named not because the Federal Reserve endorses it but because it was referenced in a 1997 Fed report, formalized the comparison between earnings yield and bond yield. The model suggests that stocks are fairly valued when the S&P 500 forward earnings yield equals the 10-year Treasury yield. When the earnings yield exceeds the bond yield, stocks are undervalued. When the bond yield exceeds the earnings yield, stocks are overvalued.
The model has an intuitive appeal. Both stocks and bonds represent claims on future cash flows. If a risk-free bond offers 5%, an investor should demand at least 5% from stocks (after adjusting for risk) to justify owning the riskier asset. When stocks offer a lower yield than bonds, the risk-return trade-off favors bonds.
The Fed Model correctly identified stocks as cheap relative to bonds during much of the 2010s. With Treasury yields below 2% and S&P 500 earnings yields around 5-6%, the equity risk premium was well above average, suggesting that stocks were attractively priced relative to fixed income. This was consistent with the strong equity returns that followed.
The model also flagged the late 1990s as a period of extreme stock overvaluation. The S&P 500 earnings yield fell below 3% in early 2000 while 10-year Treasuries yielded over 6%. The equity risk premium was deeply negative, suggesting that bonds offered a far better risk-adjusted return than stocks. The subsequent dot-com crash vindicated this signal.
Criticisms of the Fed Model
The Fed Model has significant theoretical problems that limit its usefulness as a standalone tool.
Inflation treatment asymmetry. The most serious criticism, articulated by Cliff Asness of AQR and others, is that the model compares a real quantity (earnings yield, which benefits from inflation because companies can raise prices) with a nominal quantity (bond yield, which is fixed and eroded by inflation). In a high-inflation environment, bond yields rise to compensate for expected inflation, but earnings also rise. Comparing the two without adjusting for inflation creates a bias that makes stocks look cheap during inflationary periods and expensive during deflationary periods.
Adjusted for inflation, the comparison should use real earnings yield versus real bond yield (TIPS yield). This adjustment significantly changes the signal in many periods. During the early 1980s, when nominal Treasury yields exceeded 15%, the Fed Model suggested stocks were cheap because earnings yields were below bond yields. But much of the bond yield reflected expected inflation, and the real bond yield was not as high as the nominal yield suggested.
Growth is not captured. Earnings yield measures the current return on a stock investment if earnings do not grow. But earnings do grow. The total return on a stock investment is approximately equal to the earnings yield plus the earnings growth rate. A stock with a 4% earnings yield and 6% expected growth offers a 10% expected return. A bond with a 5% yield and zero growth offers exactly 5%. The Fed Model, by comparing yields without growth, systematically undervalues stocks relative to bonds during periods when earnings growth expectations are high. This concept ties directly to Enterprise Value vs Market Cap.
Regimes change. The historical average equity risk premium of 3-4% may not be stable across all environments. During periods of high uncertainty (wars, financial crises, pandemics), investors may demand a higher equity risk premium. During periods of stability and optimism, they may accept a lower premium. The "right" level of the equity risk premium is not fixed, and models that assume a constant fair value produce misleading signals when the regime shifts.
A More Complete Framework
A more sophisticated comparison incorporates expected earnings growth and adjusts for inflation.
Expected Stock Return = Earnings Yield + Expected Earnings Growth
This can be compared to the expected return on bonds:
Expected Bond Return = Current Yield to Maturity (nominal) or TIPS Yield (real)
For example, in early 2024, the S&P 500 traded at approximately 20 times forward earnings, implying an earnings yield of 5%. Expected earnings growth for the S&P 500 was approximately 8-10% per year. The implied expected return on stocks was roughly 13-15% nominal. The 10-year Treasury yielded approximately 4.2%. The spread between expected stock returns and bond returns was approximately 9-11 percentage points, a wide premium that suggested stocks were reasonably priced relative to bonds even at elevated P/E ratios.
Compare this to late 1999. The S&P 500's forward earnings yield was approximately 3%. Expected earnings growth was optimistically estimated at 15-20% (the dot-com era). Even using the most generous growth estimates, the expected stock return was 18-23%, versus roughly 6% on 10-year Treasuries. The spread was 12-17 percentage points on paper. But the growth estimates proved wildly optimistic. Actual S&P 500 earnings grew at approximately 5-6% annually over the following decade, making the true expected stock return closer to 8-9%. The actual realized equity risk premium was only 2-3 percentage points, inadequate given the risk, and stocks delivered poor returns for the following decade.
The lesson is that the comparison is only as good as the earnings growth estimate. Earnings yield is observable. Bond yield is observable. Growth is estimated. The quality of the growth estimate determines the quality of the comparison.
Practical Applications
Asset allocation between stocks and bonds. The earnings yield versus bond yield framework provides a rational basis for shifting portfolio weights between asset classes. When the equity risk premium is wide (stocks are cheap relative to bonds), tilting toward higher equity allocations is justified. When the premium is narrow or negative, reducing equity exposure and increasing bond holdings is prudent.
This does not mean mechanically shifting 100% into stocks when the premium is wide or 100% into bonds when it is narrow. It means adjusting allocations at the margin: 70/30 stocks-to-bonds when stocks are relatively cheap, 50/50 when valuations are neutral, and 40/60 or 30/70 when stocks are relatively expensive. These shifts are gradual and probabilistic, not binary.
Individual stock analysis. Earnings yield on individual stocks can be compared to bond yields as a sanity check on valuation. If a stable, predictable company like Johnson & Johnson offers an earnings yield of 6.5% and 10-year Treasuries yield 4%, the equity risk premium on that individual stock is 2.5%. Given J&J's modest growth rate (3-5%), the expected total return is approximately 9.5-11.5%, which is reasonable for a low-risk equity. If the same stock's earnings yield falls to 3%, the expected return is only 6-8%, barely exceeding the risk-free rate, and the stock is likely overvalued.
For high-growth companies, the comparison requires more nuance because the earnings yield alone dramatically understates the expected return. Amazon's earnings yield at various points in its history was 1-2%, well below bond yields. But the expected earnings growth was 20-30%, making the total expected return 22-32%. The low current yield was compensated by extraordinary growth.
Comparing across international markets. Earnings yield versus bond yield can also be applied across countries to identify markets where equities are relatively attractive. If the Brazilian stock market offers an earnings yield of 10% versus domestic government bond yields of 12%, the equity risk premium is negative 2%, suggesting bonds are more attractive. If the German stock market offers an earnings yield of 7% versus Bund yields of 2%, the equity risk premium is 5%, suggesting stocks are attractively priced.
The Historical Record
Several historical periods illustrate the power and limitations of the earnings yield versus bond yield comparison.
1982: The S&P 500 earnings yield was approximately 12-13% (P/E of 7-8). The 10-year Treasury yielded roughly 14%. Stocks appeared expensive relative to bonds on a simple yield comparison. But inflation was declining rapidly, bond yields were about to fall dramatically, and corporate earnings were poised to recover from recession. Stocks turned out to be extraordinarily cheap, and the subsequent 18-year bull market produced the best equity returns in history. The yield comparison was misleading because it did not anticipate the inflation decline.
2000: The S&P 500 earnings yield was approximately 3% (P/E of 33). The 10-year Treasury yielded about 6.5%. The equity risk premium was deeply negative. Stocks were expensive relative to bonds, and the subsequent decade produced dismal equity returns. The yield comparison was accurate.
2012: The S&P 500 earnings yield was approximately 7% (P/E of 14). The 10-year Treasury yielded about 1.8%. The equity risk premium was over 5%, the widest in decades. Stocks were cheap relative to bonds, and the subsequent decade produced strong equity returns. The yield comparison was accurate.
2023-2024: The S&P 500 earnings yield was approximately 5% (P/E of 20). The 10-year Treasury yielded about 4-4.5%. The equity risk premium was 0.5-1.0%, below the historical average. Stocks were not obviously cheap relative to bonds, though the comparison depended heavily on growth expectations.
The framework does not predict short-term market movements. It assesses relative attractiveness over multi-year periods, which is exactly the time horizon over which investment decisions should be made. Investors who paid attention to the equity risk premium were better positioned to overweight stocks when they were cheap relative to bonds and underweight them when they were expensive. That positioning, applied consistently over decades, is worth significantly more than any short-term trading signal.
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