Fed model

The Fed model compares the one-year forward-looking I/B/E/S earnings yield (\frac{E}{P}) on the S&P 500 Index to the nominal 10-year US Treasury note yield, (Y_{\text{10}}) . :\frac{E}{P}=Y_{\text{10}}, means the stock market, in aggregate, is fairly valued. :\frac{E}{P}, means the stock market, in aggregate, is over valued. :\frac{E}{P}>Y_{\text{10}}, 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". 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: 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". 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": 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. ==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. : P= \frac{D (1 + G)}{R_{\text{f}} + RP - G} P is the price, and D the dividend, G the expected long-term growth rate, R_{\text{f}} the risk-free rate (10-year nominal treasury notes), and RP the equity risk premium; then making the following assumptions: 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. In 2017, Stuart Kirk, head of Deutsche Bank's DWS Global Research Institute and a former editor of the Financial Times Lex column, wrote of DWS's analysis of the long-term data: "In other words no historical relationship between bond yields and dividend yields. By extension, this means that interest rates have nothing to do with share prices either as the former lead bond yields while dividend yields move with earnings yields (the latter being the inverse of the price/earnings ratio). Yes, correlations can be found in the short run, but they are statistically meaningless". Lack of predictive power A test of whether the Fed model is an equity valuation theory with descriptive validity is that it should be able to identify over-valued and under-valued assets. The analysis shows that the Fed model has no power to forecast long term stock returns, and even crude traditional value investing methods that use only the market's P/E have significantly more efficacy than the Fed model. In 2018, Ned Davis Research ran a test of the Fed model's ability to predict subsequent 10-year returns using data from the previous 75 years. Davis found that "it was basically worthless", and that it's r-squared metric of 0.5%, compared poorly that those of other ratios, including P/E (56.3%), P/Sales (67.2%), and Households' equity allocation as a % of Total Financial Assets (88.4%). In June 2020, finance author Mark Hulbert, ran a statistical test from 1871 to 2020 of the Fed Model's ability to forecast the stock market's inflation-adjusted real return over subsequent 1, 5, and 10-year periods, and found that adding long-term Treasury yields, per the Fed model, materially reduced the predictive power of just using the earnings yield (E/P) on its own. Breakdown at very low interest rates It has been shown that the relationship between the forward earnings yield and long-term Government bond yields can more substantially breakdown during periods of very low-interest rates, and particularly very low real rates of interest, either from natural effects or by deliberate central banking actions such as quantitative easing. Similarly, on the bursting of the dot-com bubble in 2002, despite the Fed reducing long-term rates post-2002, the earnings yield of the S&P500 rose consistently for the next decade from 4 percent to 9 percent, while long-term Treasury yields fell from 6 percent to 2 percent. ==Impact of Fed put==

It has long puzzled academics that markets only seem to follow the Fed model in the United States, and only for specific periods (e.g. from 1987 to 2000, but not from 2001 to 2013); evidence for the existence of the relationship outside of the United States is even weaker. The use of the Greenspan put by Wall Street investment banks in the 1990s to fund Long-Term Capital Management (LTCM), is a noted example, and was the additional use of the Greenspan put to rescue those Wall Street banks after LTCM's collapse. ==See also==