The "Fed model", or "Fed Stock Valuation Model" (FSVM), is a disputed theory of equity valuation that compares the stock market's forward earnings yield to the nominal yield on long-term government bonds, and that the stock market – as a whole – is fairly valued, when the one-year forward-looking I/B/E/S earnings yield equals the 10-year nominal Treasury yield; deviations suggest over-or-under valuation.
The relationship has only held in the United States, and only for two main periods: 1921 to 1928 and from 1987 to 2000. It has been shown to be flawed on a theoretical basis, fails to hold in long-term analysis of data (both in the United States, and international markets), and has poor predictive power for future returns on a 1, 5 and 10-year basis. The relationship can breakdown completely at very low real yields (from natural forces, or where yields are artificially suppressed by quantitative easing); in such circumstances, without additional central bank support for the stock market (e.g. use of the Greenspan put by the Fed in 2020, or the Bank of Japan's purchase of equities post-2013), the relationship collapses.
The Fed model is used by Wall Street sales desks as it almost always gives a "buy signal", and has rarely signaled stocks are overvalued. Some academics say the relationship, when it appears, is driven by the allocation of the Fed's balance sheet to Wall Street banks via repurchase agreements as part of Fed put stimulus (i.e. the relationship reflects the investment strategy these banks follow using borrowed Fed funds when the Fed is stimulating asset prices, e.g. Wall Street banks lending to Long-Term Capital Management-type vehicles being a noted example).
The term was coined in 1997–99 by Deutsche Bank analyst Edward Yardeni commenting on a report on the July 1997 Humphrey-Hawkins testimony by the then-Fed Chair, Alan Greenspan on equity valuations. In 2014, Yardeni noted that the predictive power of the Fed model stopped working almost as soon as he noted the relationship. The term was never formally endorsed by the Fed, however, Greenspan made further references to the relationship. In December 2020, the Fed Chair Jerome Powell, invoked the relationship to justify stock market valuations that were approaching levels not seen since the 1999–2000 Dot-com bubble or the 1929 market bubble, due to exceptional monetary looseness by the Fed.
Formula
The Fed model compares the one-year forward-looking I/B/E/S earnings yield on the S&P 500 Index to the nominal 10-year US Treasury note yield, .
, means the stock market, in aggregate, is fairly valued.
, means the stock market, in aggregate, is over valued.
, means the stock market, in aggregate, is undervalued.
The Fed model only applies to the aggregate stock market valuation (i.e. the total S&P500), and is not applied to individual stock valuation.
While the Fed model was specifically named for the United States stock market, it can be applied to any other stock market.
Origin and use
The term "Fed model", or "Fed Stock Valuation Model" (FSVM), was coined in a series of reports from 1997 to 1999 by Deutsche Morgan Grenfell analyst Ed Yardeni. Yardeni noted that the then-Fed Chair Alan Greenspan, seemed to use the relationship between the forward earnings yield on the S&P 500 Index and the 10-year Treasury yield in assessing levels of equity market over-or-under valuation. Yardeni quoted a paragraph and graphic (see image opposite), from the Fed's July 1997 Monetary Policy Report to the Congress, which implied Greenspan was using the model to express concerns about market overvaluation, with Yardeni saying: "He [Greenspan] probably instructed his staff to devise a stock market valuation model to help him evaluate the extent of this irrational exuberance":
Academics note that I/B/E/S published a similar metric since 1986 called the I/B/E/S Equity Valuation Model, and that the concept was in widespread use by Wall Street with Estrada noting: "Any statement that justifies high P/E ratios with the existence of prevailing low-interest rates is essentially using the Fed model".
The "Fed model" was never officially endorsed as a metric by the Fed, but Greenspan referenced the relationship several times including in his 2007 memoirs, saying: "The decline of real (inflation-adjusted) long-term interest rates that has occurred in the last two decades has been associated with rising price-to-earnings ratios for stocks, real estate, and in fact all income-earnings assets".
In December 2020, Fed Chair Jerome Powell, invoked the "Fed Model" to justify high stock market price-earnings ratios (then approaching levels of the Dot-com bubble, in a period called the everything bubble), saying: "If you look at P/Es they're historically high, but in a world where the risk-free rate is going to be low for a sustained period, the equity premium, which is really the reward you get for taking equity risk, would be what you'd look at". Yardeni said Powell's actions in 2020, countering the financial effects of the COVID-19 pandemic, could form the greatest financial bubble in history.
In February 2021, The Wall Street Journal noted that stock valuations were in a bubble on almost every metric except for that of the Fed Model (i.e. 10-year Treasury yields), which the WSJ felt Powell was using as a guide on how far his policy of extreme stimulus/monetary looseness could be used to push stock prices higher.
Supporting arguments
A number of arguments are listed in favor of the Fed model, the three most important of which are:
Competing assets argument. Stocks and bonds are competing asset classes for investors. When stocks yield more than bonds, investors are better off investing in stocks. When funds flow from bonds into stocks on a large scale, the yield on bonds should increase and the yield on stocks decreases until the Fed model equilibrium is reached. In a 2003 paper, Cliff Asness argued that investors do set stock market P/Es (inverse of E/P) based on nominal interest rates, but that they do so in error. By confusing real and nominal, investors suffer from "money illusion". Other academic research indicates some support for the competing assets argument, but that the driver is due to "habit-based risk aversion", which could be linked to the use of the Fed put (see below). The Wall Street Journal noted that the model's use of 1-year forward earnings makes it a favourite of Wall Street analysts whose earnings estimates are "... permanently bullish, thus always making stocks look cheap versus [Treasury] yields". In 2020, finance author Mark Hulbert, in demonstrating the poor statistical performance of the model, also emphasized that the competing assets argument is really a "Wall Street sales line":
Present value argument. The value of stocks should be equal to the sum of its discounted future cash flows, being the present value. The government bond rate can be seen as a proxy for the risk-free rate. Thus, when the government bond rate falls, the discount rate falls, and the present value rises. And this implies that when interest rates fall, E/P also falls. Academics consider this a flawed argument as it doesn't take into account why the bond yields fell, with Asness adding: "It is absolutely true that, all else being equal, a falling discount rate raises the current price. All else is not equal, though. If when inflation declines, future nominal cash flow from equities also falls, this can offset the effect of lower discount rates. Lower discount rates are applied to lower expected cash flows". In 2020, when then-Fed Chair Jerome Powell used the present value argument to justify high P/E multiples, The Wall Street Journal described Powell's comparison as an attempt to "rewrite the laws of investing".
A larger example of Asness' point was post-1990 Japan when the collapse of the Japanese asset bubble saw the earnings yield of the Nikkei rise materially for several decades while Japanese Government bond yields collapsed to almost zero; only when the Bank of Japan started directly buying large of equities from 2013 onwards (i.e. forcing the earnings yield down), did the Fed model begin to reapply.
Historical data argument. For a specific period in the United States from 1995 to 2000, the correlation between the forward earnings yield and the 10-year Treasury yield was estimated at 75 percent. However, over the 1881–2002 period the correlation was only 19 percent, and post 2002, the correlation has been weaker, with long periods of complete divergence. Academics show that outside of the United States, the evidence for a Fed model is weak, with academics wondering if the existence of periods when the Fed model does apply in the United States, is really due to specific unseen or misunderstood actions by the Fed via Wall Street investment banks on asset prices (i.e. the Greenspan put), or even a mistaken understanding by investors of such Fed actions. After the Fed model's relationship broke down post-2000, Bloomberg wrote in 2017 of the connection between the relationship and the understanding of the Fed's stimulus of the markets that, "Wall Street likes to play up the Federal Reserve's role in boosting the market, but by one popular gauge at least the Fed's influence on stocks seems to be diminished".
Academic analysis
Academics conclude that the model is inconsistent with a rational valuation of the stock market, or past long-term observations, and has little predictive forecasting power. In addition, the Fed model only seems to apply for specific periods in the United States, while international markets have shown weak evidence with long period of dramatic divergences (e.g. Japan post-1990, US post dot-com burst).
Lack of theoretical support
The competing asset argument listed above argues that only when stocks have the same earnings yield as nominal government bonds, that both asset classes are equally attractive to investors. But the earnings yield (E/P) of a stock does not describe what an investor actually receives as not all earnings are paid out to the investor (either via dividends or share buybacks). In addition, corporate bonds (with a yield above the government bond yield as a risk premium), do not fit into the Fed model of valuation, which therefore implicitly assumes that equities have the same risk profile as government bonds.
For example, a number of unrealistic assumptions need to be made to go from the academically robust constant growth dividend discount model of equity valuation, to the Fed model of market valuation, which Estrada broke down, starting with the Gordon growth model:
P is the price, and D the dividend, G the expected long-term growth rate, the risk-free rate (10-year nominal treasury notes), and RP the equity risk premium; then making the following assumptions: That all earnings are paid as a dividend (i.e. D=E); and That the dividend growth rate is equal to zero; and That the equity risk premium is also equal to zero. one gets the Fed model: E/P=. Estrada finds these assumptions seem unrealistic at best, and theoretically unsound as a form of valuation.
In addition to the above basic flaws, it is also noted out that the Fed model compares a real metric (E/P, which moves with inflation), with a nominal interest rate metric.
Data selection and international markets The Fed model equilibrium was only observed in the United States, and for specific time periods, namely 1921 to 1928 and 1987 to 2000; outside of this time window, or in various other international markets, equities and Treasury yields do not show the relationship outlined in the Fed model.