With stock markets hitting record highs and the Fed model signaling historically low valuation ranges, investors are faced with a confusing situation. This post examines the intricacies of the equity risk premium, examines traditional valuation models, and presents an updated framework to guide strategic decision-making in today’s volatile environment.
After Donald Trump was re-elected to the White House, US stocks hit recent record highs. The market’s appetite for risk stays high, but equity valuations also appear elevated. The Fed model, which measures the spread between the forward earnings yield of the S&P 500 index and the 10-year U.S. Treasury yield, is currently at -0.1%, a level not seen since 2002 (see Figure 1).
Does the negative Fed model mean the tip of the equity risk premium? Should investors be concerned about current stock valuations? In this paper, we address these questions by evaluating the Fed model through the lens of an intrinsic equity valuation model and decoupling the equity risk premium (ERP) from the equity earnings return.
The Fed model
The FED model has develop into a extremely popular stock valuation indicator since Edward Yardeni introduced the model in 1998. The model as defined within the equation [1]compares the stock forward earnings yield to the risk-free 10-year nominal yield of presidency bonds. A positive value signifies that the stock market is undervalued and vice versa. The valuation range is taken into account similar to the expected ERP.
[1]
The intuition is that stocks and bonds are competing assets; Therefore, buying riskier stocks only is sensible if the stocks can outperform the return of risk-free US government bonds. However, the Fed model has repeatedly been criticized by investors for its lack of theoretical basis.
Intrinsic equity valuation
The Gordon Growth Model (GGM) provides an estimate of a stock’s intrinsic value based on the assumptions of a relentless earnings growth rate, cost of capital, and dividend payout ratio (see equation). [2]). By following the steps described in Equations 3 through 5, we are able to arrive at a modified version of the Fed model shown in Equation 5.
Compared to the Yardeni model, the modified model now not assumes the beta of the risk-free rate of interest, since Equation 1 and the duration of risk-free returns can vary. Meanwhile, the model indicates that ERP is negatively correlated with earnings growth rates when fairly valued, meaning higher earnings growth may result in a lower valuation spread. According to FactSet, S&P 500 corporations are expected to post annual earnings growth of about 14% over the following two years, well above their historical growth trend.
An empirical framework
Many assumptions behind the RCD don’t apply in the actual world. For example, growth rates vary over time; the yield curve just isn’t flat; and so forth. Without going into the extensive mathematical theory, we are able to use a generalized model like in Equation 6 to explain the ERP because the expected stock earnings return above a linear risk of your complete risk-free yield curve.
The long-term beta ratio of stock earnings return to risk-free rate of interest will be estimated using linear regression techniques. For the sake of model parsimony, I selected the yield and yield differential of 3-month Treasury bills (10 years minus 3 months) to approximate your complete yield curve. As shown in Figure 2, the beta coefficients of equity earnings returns in comparison with government bond returns are statistically significant with a t-stat > 7.0.
The historical ERP can then be estimated using the next equation 7. Figure 3 shows the time series of historical ERP. The current model estimate (as of November 30, 2024) is 2.0%, indicating a narrow but still positive ERP.
Source: Bloomberg. Quantitative research on global asset allocation. Data from 1/1962 to 11/2024. Historical trends are not any indication of future results.
Signal effect
Is the modified Fed model a greater valuation signal? To evaluate this, I built two linear models using 10-year equity returns as independent variables and two equity risk premium time series as dependent variables individually. Figure 4 below shows a summary of the regression results. The modified model has higher fitness than the unique model with a better R2 and t-stat of the beta coefficients.
Valuation risk is high because of an unstoppable market rally. The famous FED model shows that stock valuations have slipped into expensive territory. However, I imagine that above-average earnings growth is the principal reason why the valuation range has turned negative. Using a brand new valuation framework based on the intrinsic valuation model, I show that current valuation levels still provide room for positive stock returns, at the very least within the short term.
References
Weigand, R. A., & Irons, R. (2008). Market P/E Compression and Expansion: The Fed Model Explained. The Journal of Investing, 17(1), 55–64. https://doi.org/10.3905/joi.2008.701961
Yardeni, E., 1997. The Fed’s stock market model finds overvaluation. Current Study No. 38. US Equity Research, Deutsche Morgan Grenfell.
Yardeni, E., 1999. New improved stock valuation model. Current Study No. 44. US Equity Research, Deutsche Morgan Grenfell.
