Fed model

The Fed model compares the one-year forward-looking I/B/E/S earnings yield ${\displaystyle ({\frac {E}{P}})}$ on the S&P 500 Index to the nominal 10-year US Treasury note yield, ${\displaystyle (Y_{\text{10}})}$.[10][24][25]

${\displaystyle {\frac {E}{P}}=Y_{\text{10}}}$, means the stock market, in aggregate, is fairly valued.[10]

${\displaystyle {\frac {E}{P}}<Y_{\text{10}}}$, means the stock market, in aggregate, is over valued.[10]

${\displaystyle {\frac {E}{P}}>Y_{\text{10}}}$, means the stock market, in aggregate, is undervalued.[10]

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.[24]

While the Fed model was specifically named for the United States stock market, it can be applied to any other stock market.[10]

Original graphic from Humphrey-Hawkins report of 22 July 1997

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 Dr. Ed Yardeni.[5] 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":[24][25]

…changes in this ratio [P/E of the S&P 500 index] have often been inversely related to changes in the long-term Treasury yields, but this year's stock price gains were not matched by a significant net decline in interest rates. As a result, the yield on ten-year Treasury notes now exceeds the ratio of twelve-month-ahead earnings to prices by the largest amount since 1991, when earnings were depressed by the economic slowdown.

— Federal Reserve Humphrey Hawkins report (22 July 1997).[10]

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".[10]

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".[20]

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),[21] 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".[22][26] Yardeni said Powell's actions in 2020, countering the financial effects of the COVID-19 pandemic, could form the greatest financial bubble in history.[27]

The Fed model is often cited by equity strategists and economists to justify lofty equity valuations. It's not too often that a Fed chair engages in that exercise.

— Bloomberg (December 2020)[28]

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.[23]

A number of arguments are listed in favor of the Fed model, the three most important of which are:[10][29][5]

• 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.[7] 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".[11][29] 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).[17] 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".[30] 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":[15]

The Fed Model's attraction to the Wall Street bulls is that it almost always is bullish.

— Mark Hulbert (June 2020)[15]

• 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,[10] 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".[11][2] 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".[31]

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.[14]

• 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.[32] 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.[2] Academics show that outside of the United States, the evidence for a Fed model is weak,[10] 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),[17] or even a mistaken understanding by investors of such Fed actions.[5][11] 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".[33]

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).[10][34]

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.[17] Work by Bekaerk and Engstrom concluded the existence of the relationship could be due to investor habit – i.e. if the relationship holds for a period, then investors will keep following it, and allocating capital that reinforces it until it stops working.[17]

Others have questioned whether the temporary existence of the relationship in the United States is due to the Fed put (also known as the Greenspan put).[18] They argue that from time to time, the Fed has used the Fed model as a guide on the issue of providing "repurchase agreements" (or "repo trades") to Wall Street investment banks; repo trades, as part of the Fed put toolkit, have been used by the Fed to inflate United States asset prices, either to arrest falls in crises or to generate economic growth. Under this theory, it is the Wall Street investment banks who drive the Fed model relationship via the allocation of their repo trades into the markets, which when done on a continuous and steady basis, can also create the investor habit observed by Bekaerk and Engstrom (analysts at the Wall Street investment banks are noted by academics,[10] and financial authors,[15] as some of the strongest supporters of the rationale for the Fed model relationship).[17][19][18] 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,[16] and was the additional use of the Greenspan put to rescue those Wall Street banks after LTCM's collapse.[39]

• Cyclically adjusted price-to-earnings ratio
• Equity risk premium
• Everything bubble
• Greenspan put

• Fed Stock Valuation Model, Monthly Update, Dr. Edward Yardeni
• Investopedia: The Fed Model and Stock Valuation
• Investopedia: Breaking down the Fed model
• Seeking Alpha: Debunking the Fed model
• Relationship between bond and dividend yields has no grounds, Financial Times (2017)
• (Video presentation) Fed Up with the Fed Model | Charts that Count, John Authers, Financial Times (September 2018)