Earnings Yield vs Bond Yield: The Fed Model Explained

The Fed Model is a widely cited but controversial approach to valuing the broad stock market: compare the earnings yield of the S&P 500 to the yield on 10-year Treasury bonds. If stocks’ earnings yield is higher, stocks are attractively priced; if bonds’ yield is higher, stocks are expensive. It offers a simple, single-number metric for asking whether equities are dear or cheap relative to fixed income.

The Model’s Core Logic

The Fed Model rests on a simple intuition: investors face a choice between two assets—equities (the S&P 500) and risk-free bonds (10-year Treasuries). Each has a “yield” or expected return:

• Stocks offer an earnings yield: the annual earnings of S&P 500 companies divided by their market capitalization. If the index has a price-to-earnings ratio of 20, the earnings yield is 1 ÷ 20 = 5%.
• Bonds offer a current yield: the 10-year Treasury yield, which in recent years has ranged from near-zero to 4% or higher.

The model assumes these yields should be comparable. If stocks’ earnings yield is 5% and bonds yield only 2%, stocks are the better bargain—they offer more annual income per dollar invested. Conversely, if bonds yield 4% and stocks yield only 3%, bonds are more attractive, implying stocks are expensive.

The model’s appeal is simplicity: a single data point (the spread between earnings yield and bond yield) can signal whether the entire market is cheap or dear.

Calculating the Spread: A Concrete Example

Suppose the S&P 500 is trading at 4,500 with trailing 12-month earnings of $220 per share:

Earnings yield = $220 ÷ 4,500 = 4.89%

Simultaneously, the 10-year Treasury yield is 4.0%. The spread is 4.89% − 4.0% = 0.89%, favoring stocks. According to the Fed Model, stocks are undervalued: their earnings yield exceeds the risk-free rate by nearly 1%, so they offer extra compensation (an equity risk premium) for bearing stock market risk.

If the Treasury yield rises to 5.0%, the spread narrows to −0.11%, with bonds now paying more than stocks are earning. The model signals stocks are overpriced.

Historical Application

The Fed Model gained credibility after Federal Reserve researchers highlighted it in the late 1990s as a framework the Fed used informally to assess market valuations. During the 2000s and 2010s, market commentators frequently cited the model as justification for rising equity valuations. When bond yields fell (especially after 2008, as the Fed kept rates near zero), the model showed stocks as “cheap” relative to nearly-free money, seemingly blessing the secular rise in price-to-earnings multiples.

The model became a shorthand in both institutional and retail settings: “See the chart of earnings yield minus bond yield—it says stocks are a bargain” was a common refrain during periods of low rates.

The Fatal Flaws

However, the Fed Model has several well-documented defects that undermine its usefulness as a valuation benchmark.

It ignores the equity risk premium. A core principle of finance is that risky assets must offer higher expected returns than safe assets. An equity risk premium of 3–6% annually is standard: stocks should yield significantly more than Treasury bonds to compensate investors for volatility and drawdown risk. The Fed Model treats earnings yield and bond yield as interchangeable—as if the risk premium simply doesn’t exist. This is backwards. The correct comparison should be: Is stocks’ earnings yield minus expected growth higher than bonds’ yield plus the required equity risk premium? The Fed Model ignores the second part.

It confuses nominal yields with real (inflation-adjusted) returns. Treasury yields fluctuate with inflation expectations. In a high-inflation environment, nominal Treasury yields are high (say, 5%) but real yields (after inflation) are low or negative. The Fed Model compares a nominal bond yield to a nominal earnings yield, but it doesn’t correct for inflation’s effect on real corporate earnings growth. If inflation is eroding real wages and margins, a 5% nominal earnings yield is less valuable than it appears. A more rigorous approach uses real yields and real expected earnings growth.

It assumes earnings are constant, not growing. The earnings yield treats current earnings as if they are the permanent, eternal stream of payouts. But companies typically grow earnings over time. An equity priced at a 3% earnings yield but expected to grow earnings at 5% annually is far cheaper than an equity with a 5% earnings yield and 0% growth. The Fed Model implicitly values all stocks as if they never grow—a huge oversight.

The sample period bias. The model works well for certain historical windows (e.g., 1960–2000) but fails in others. From 2009 to 2021, as bond yields crashed to near-zero while earnings yields remained in the 3–5% range, the model screamed “stocks are cheap!"—yet stocks did rally, but less impressively than the model’s signal suggested. The model’s apparent success in some eras is partly luck.

It ignores credit spreads and bond risk. Treasury bonds are risk-free for U.S. dollar holders, but “risk-free” doesn’t mean “optimal.” If Treasury yields are depressed by central bank purchases or flight-to-safety flows, they may not represent the true opportunity cost of capital. Many investors require returns linked to corporate credit risk, not Treasury yields. A more complete model would compare stocks to investment-grade corporate bonds, not Treasuries—accounting for credit spreads.

A More Rigorous Alternative: The Gordon Model

A better valuation heuristic is the Gordon Model (or Dividend Discount Model), which incorporates growth:

Stock price = Next year’s expected dividend ÷ (Required return − Growth rate)

Rearranging:

Earnings yield = Required return − Growth rate

Or, equivalently:

Earnings yield + Growth rate = Required return

If the S&P 500 has an earnings yield of 4% and long-term earnings are expected to grow at 2%, then the required return is 4% + 2% = 6%. If the 10-year Treasury yield is 3%, the implied equity risk premium is 6% − 3% = 3%. You can then ask: is a 3% equity risk premium reasonable given historical norms (typically 4–6%) and current risk (volatility, drawdown risk, business cycle risk)? This approach at least acknowledges that stocks have growth and that a risk premium is required.

Using the Fed Model Cautiously

The earnings-yield-vs-bond-yield spread is not worthless—it is a useful data point, but not in isolation:

As a coarse screening tool. If the spread is at extreme levels (earnings yield far above Treasury yield, or vice versa), it can flag periods of obvious over- or under-valuation. A 3% or 4% spread favoring stocks might be sustainable; a 1% spread might be tight.

Triangulated with other metrics. Pair it with forward earnings growth estimates, price-to-book ratios, dividend yields, and dividend growth rates. A stock market that is cheap on earnings yield but expensive on forward multiples and capital expenditure efficiency is sending a mixed signal.

Adjusted for growth and inflation. If using the Fed Model in practice, adjust both the earnings yield and the bond yield for expected real growth and inflation. Use 10-year forward earnings growth estimates (from earnings-per-share forecasts), not just trailing earnings, and use TIPS (Treasury Inflation-Protected Securities) yields to isolate real returns.

Contextualized by Federal Reserve policy. The Fed Model is most useful when bond yields are set by economic fundamentals (real growth, inflation expectations, risk premiums). When yields are suppressed by extreme central bank intervention (quantitative easing, negative rates), the model’s signal is unreliable.

See also