What Is the Fed Model?
The Fed model is an investment valuation methodology that suggests a relationship between the earnings yield of the stock market and the nominal yield on long-term government bonds, typically the 10-Year Treasury Bond. It operates on the premise that stocks and bonds are competing investment avenues, and investors will reallocate capital between them based on their relative attractiveness. When the stock market's earnings yield is higher than the bond yield, the stock market is considered more appealing, and vice versa. Despite its name, the Fed model is not officially endorsed or utilized by the Federal Reserve as an official policy tool, nor does it imply a direct endorsement of its predictive power.
History and Origin
The term "Fed model" was coined by Wall Street professionals in the late 1990s, notably by economist Edward Yardeni, then at Deutsche Morgan Grenfell. Yardeni analyzed the relationship between bond yields and stock earnings yields, naming it the "Fed's Stock Valuation Model". This concept gained traction after a graph showing the close relationship between long-term Treasury bond yields and the forward earnings yield of the S&P 500 Index was included in the Federal Reserve's Humphrey-Hawkins Report on July 22, 1997. The report, which covered data from 1982 to 1997, highlighted this observed correlation. While the relationship was noted in the report, and then-Fed Chair Alan Greenspan made further references to it, the Federal Reserve itself never formally endorsed the "Fed model" as a prescriptive tool for equity valuation or policy21. The original use of comparing bond and equity yields in practice, however, predates this specific report and naming.
Key Takeaways
- The Fed model is a stock valuation tool that compares the equity market's forward earnings yield to the nominal yield of long-term government bonds, typically the 10-Year U.S. Treasury Bond.
- It suggests that if the stock market's earnings yield is higher than the 10-year Treasury yield, stocks are relatively more attractive (bullish signal), and if lower, bonds are more attractive (bearish signal).
- The model was not officially endorsed by the Federal Reserve; its name originated from its appearance in a 1997 Humphrey-Hawkins Report and subsequent analysis by Edward Yardeni.
- A primary criticism of the Fed model is its comparison of a "real" earnings yield (adjusted for inflation through expected earnings growth) with a "nominal" bond yield, leading to theoretical inconsistencies, particularly during periods of varying inflation.
- Empirical evidence for the Fed model's long-term predictive power for stock market returns has been mixed, with some studies showing it to be unreliable outside specific historical periods and the U.S. market.
Formula and Calculation
The Fed model's core principle is often expressed as an equality or a comparison between the forward earnings yield of the stock market and the yield of a long-term government bond.
The earnings yield ($E_1/P_S$) is the inverse of the familiar Price-to-Earnings Ratio ($P_S/E_1$).
The formula implies that for the stock market to be "fairly valued," the forward earnings yield should be approximately equal to the 10-year Treasury bond yield.
Where:
- $E_1$ = Expected earnings per share over the next 12 months for a broad market index (e.g., S&P 500).
- $P_S$ = Current price of the broad market index.
- $Y_B$ = Yield to maturity of the 10-year U.S. Treasury bond.
Alternatively, the model considers the spread between the two:
Interpreting the Fed Model
Interpreting the Fed model involves comparing the two yield metrics to gauge the relative attractiveness of stocks versus bonds. If the earnings yield for the stock market (e.g., S&P 500) is significantly higher than the 10-Year Treasury Bond yield, the model suggests that stocks are relatively undervalued compared to bonds. This would indicate a "bullish" market outlook, implying that capital might flow from bonds to stocks to equalize returns. Conversely, if the earnings yield is lower than the bond yield, the model suggests stocks are relatively overvalued, signaling a "bearish" outlook. This would imply that bonds are more attractive, potentially leading to capital flowing from stocks to bonds. It is important to note that the model primarily assesses relative valuation rather than absolute over- or undervaluation of the stock market itself.
Hypothetical Example
Imagine a scenario where the S&P 500's expected earnings per share for the next 12 months ($E_1$) are $200, and the current S&P 500 index price ($P_S$) is 5,000.
The earnings yield for the S&P 500 would be:
Now, let's say the current yield on the 10-year U.S. Treasury bond ($Y_B$) is 3.0%.
According to the Fed model, we compare the 4% earnings yield to the 3.0% bond yield. Since the earnings yield (4%) is higher than the bond yield (3.0%), the Fed model would suggest that stocks are relatively more attractive than bonds. This could imply a "buy" signal for equities relative to fixed income, encouraging investors to shift their asset allocation towards stocks. Conversely, if the bond yield were 5.0% and the earnings yield remained at 4%, the model would suggest stocks are relatively less attractive, indicating a "bearish" signal for equities compared to bonds.
Practical Applications
The Fed model has been primarily used by financial professionals and market commentators as a quick "market timing" tool and for broad equity valuation insights20. It offers a simplistic way to compare the relative attractiveness of the stock market to the bond market. For investors, it can inform asset allocation decisions by suggesting whether equities offer a higher potential return per unit of risk than bonds. Some practitioners use the yield gap to identify periods when stocks are significantly cheaper or more expensive relative to bonds, guiding tactical investment decisions19. For example, a large positive spread (earnings yield much higher than bond yield) might encourage increased equity exposure, while a negative spread might suggest reducing it. Historical 10-year U.S. Treasury yields are publicly available from sources like the Federal Reserve Bank of St. Louis's FRED database, allowing for historical analysis of this relationship.18 Research suggests that the Fed model may perform better at predicting relative returns between stocks and bonds over short to medium-term horizons (12-36 months) rather than absolute stock returns over longer periods16, 17.
Limitations and Criticisms
Despite its simplicity and historical appeal, the Fed model faces significant theoretical and empirical criticisms. One of the most prominent theoretical flaws is its comparison of a "real" quantity (the earnings yield, which implicitly grows with nominal earnings in an inflationary environment) with a "nominal yield" (Treasury Bond yield, which includes an inflation component)14, 15. Critics argue that inflation affects stocks and bonds differently. If inflation rises, nominal bond yields increase, while corporate earnings are also expected to rise with inflation, ideally maintaining the real value of stocks. This disparity means the model might incorrectly signal overvaluation during periods of low inflation and undervaluation during high inflation, due to an "inflation illusion"13.
Empirically, the Fed model's predictive power for future real returns has been shown to be weak, especially outside specific periods (e.g., 1987-2000) and the U.S. market12. For instance, it failed to predict significant market downturns, such as the 2008 financial crisis, often remaining bullish even on the cusp of collapses. Ned Davis Research, among others, has found the Fed model to be among the least accurate in predicting bull and bear markets compared to other valuation metrics. Research Affiliates, a prominent investment management firm, has published extensive critiques, emphasizing the model's theoretical unsoundness and poor forecasting ability for long-term returns11. They note that the empirical fit observed historically does not necessarily imply a causal or robust long-term relationship10.
Fed Model vs. Equity Risk Premium
While both the Fed model and the equity risk premium (ERP) relate stock and bond returns, they are distinct concepts. The Fed model posits a direct relationship or equality between the stock market's earnings yield and a long-term nominal bond yield. It suggests that these two yields should converge, implying a state of equilibrium where stocks and bonds offer comparable current returns9.
The equity risk premium, on the other hand, is the expected excess return that stocks are anticipated to provide over a risk-free rate, typically represented by government bonds7, 8. It explicitly accounts for the fact that equities are inherently riskier than government bonds, and investors demand additional compensation (the premium) for bearing that risk6. Unlike the Fed model's implied equilibrium, the ERP measures the additional return investors expect for holding stocks, acknowledging their higher risk profile. The ERP is a forward-looking concept that can be estimated using various models, including the Capital Asset Pricing Model (CAPM) or by examining historical spreads and expected growth rates, and it does not necessarily assume a direct equality of yields, but rather a justified differential5. Confusion often arises because both metrics compare stock and bond market returns, but the Fed model seeks parity in yield, while the ERP seeks to quantify the compensation for equity risk.
FAQs
Is the Fed model officially used by the Federal Reserve?
No, despite its name, the Fed model is not an official tool or endorsed policy of the Federal Reserve. The name originated from a chart in a 1997 Humphrey-Hawkins Report and was popularized by market analysts.
What is a "bullish" or "bearish" signal according to the Fed model?
A "bullish" signal occurs when the stock market's earnings yield is higher than the 10-Year Treasury Bond yield, suggesting stocks are relatively more attractive. A "bearish" signal indicates the opposite, with the bond yield being higher, making bonds more appealing.
Why is the Fed model criticized?
The primary criticism of the Fed model stems from its comparison of a real earnings yield (which accounts for expected inflation in corporate earnings) with a nominal bond yield (which includes an inflation component, but whose coupon payments are fixed). This can lead to misleading signals, especially during periods of changing inflation3, 4.
Does the Fed model predict future stock returns accurately?
The empirical evidence for the Fed model's ability to accurately forecast long-term stock returns is mixed and often challenged. While some studies suggest it may have some predictive power for relative returns over shorter horizons, its overall track record as a reliable long-term predictor of absolute stock market direction is not consistently supported1, 2.
Are there alternatives to the Fed model for market valuation?
Yes, many other investment valuation methods exist, such as analyzing Price-to-Earnings Ratio (P/E) directly, the Dividend Discount Model, price-to-sales ratios, and various forms of discounted cash flow analysis. These models often consider additional factors beyond just current yields to assess market attractiveness.