With stock markets at record highs and Fed models showing historically low valuation spreads, investors face a complex situation. In this post, we explore the intricacies of the equity risk premium, scrutinize traditional valuation models, and introduce a modern framework to guide strategic decision-making in today's volatile environment.
Following Donald Trump's re-election to the White House, U.S. stocks hit record highs. Market risk appetite remains high, but equity valuations also appear to be rising. The Fed model, which measures the spread between the future earnings yield of the S&P 500 index and the 10-year U.S. Treasury yield, is currently -0.1%, a level not seen since 2002 (see Exhibit 1).
Does a negative Fed model signal the end of the equity risk premium? Should investors be concerned about current stock valuations? In this article, we evaluate the FED model through the lens of an essential equity valuation model. We address these questions by disentangling the equity risk premium (ERP) from the equity return yield.
FRB model
The FED model has become a very popular stock valuation metric since Edward Yardeni introduced the model in 1998. The model is defined by equations. [1]which compares the stock futures earnings yield with the nominal yield on the risk-free 10-year Treasury bond. A positive value indicates that the stock market is undervalued and vice versa. The valuation spread is considered equivalent to the expected ERP.
Fed Model = Earnings Yield – US Treasury 10-Year Nominal Yield [1]
Intuitively, stocks and bonds can be thought of as competing assets. Therefore, buying riskier stocks only makes sense if the stocks can earn more than risk-free U.S. Treasuries. However, the Fed model has consistently faced criticism from investors for lacking a theoretical basis.
intrinsic capital assessment
The Gordon Growth Model (GGM) provides an estimate of a stock's intrinsic value based on constant earnings growth, cost of capital, and dividend payout ratio assumptions (see equation) [2]). By following the steps described in Equations 3 to 5, we can arrive at a modified version of the Fed model shown in Equation 5.
Compared to Yardeni's model, the modified model does not assume a beta for the risk-free rate, and the maturity of the risk-free rate can vary. On the other hand, the model shows that when ERP is fairly valued, it is negatively correlated with profit growth, meaning that higher profit growth can lead to narrower valuation spreads. According to FactSet, S&P 500 companies are expected to grow annual profits by about 14% over the next two years, which is well above historical growth trends.
empirical framework
Many of the assumptions behind GGM do not hold true in the real world. For example, growth rates change over time. The yield curve is not flat. and so on. Without going through extensive mathematical theory, we can adopt the generalized model shown in Equation 6 to describe ERP as the forward stock return yield that exceeds the linear exposure across the risk-free yield curve.
The long-term beta exposure of stock earnings yield to the risk-free rate can be estimated using linear regression techniques. In the spirit of model parsimony, we chose the three-month Treasury bill yield and yield slope (10 years minus 3 months) to approximate the entire yield curve. As shown in Exhibit 2, the beta coefficient of stock earnings yield relative to Treasury yield is statistically significant at t-stat > 7.0.
Past ERP can be estimated using Equation 7 below. Figure 3 shows the historical ERP time series. The current model estimate (as of November 30, 2024) is 2.0%, indicating a narrow but still positive ERP.
Source: Bloomberg. Global asset allocation quantitative research. Data from January 1962 to November 2024. Past trends do not predict future results.
Signaling effect
Does the modified FRB model provide a better valuation signal? To assess it, we use the 10-year future stock returns as the independent variable and the two stock risk premium time series as the dependent variables, respectively. I built a linear model. Figure 4 below provides an overview of the regression output. The modified model has a higher R and better fit than the original model.2 and t-stat of beta coefficient.
The constant rise in the market has increased valuation risk. The famous FED model shows that stock valuations have moved into expensive territory. However, I believe that the main reason for the negative valuation difference is the above-normal earnings growth. Through a new valuation framework based on an intrinsic valuation model, we show that current valuation levels still have scope for positive stock returns, at least in the short term.
References
Weigand, R. A., & Irons, R. (2008). Compression and expansion of market P/E: explained using the FRB model. Journal of Investing, 17(1), 55–64. https://doi.org/10.3905/joi.2008.701961
Yardeni, E., 1997. The Fed's stock market model found overvaluation. Topic Research #38. US Equity Research, Deutsche Morgan Grenfell.
Yardeni, E., 1999. New and improved stock valuation model. Topic Research #44. US Equity Research, Deutsche Morgan Grenfell.
