View source for Fed model

{{short description|Disputed equity valuation model}}
[[Image:S and P 500 pe ratio to mid2012.png|320px|right|thumb|[[Robert Shiller]]'s plot of the [[S&P 500 Index|S&P 500]] [[price–earnings]] ratio (P/E) versus long-term Treasury yields (1871–2012), from ''[[Irrational Exuberance (book)|Irrational Exuberance]]''.<ref name="IE2">{{cite book |last=Shiller |first=Robert |title=Irrational Exuberance (2d ed.)|year=2005 |publisher=[[Princeton University Press]] |isbn= 0-691-12335-7 |title-link=Irrational Exuberance (book) }}</ref><br>The P/E ratio is the inverse of the E/P ratio, and from 1921 to 1928 and 1987 to 2000, supports the Fed model (i.e. P/E ratio moves inversely to the treasury yield), however, for all other periods, the relationship of the Fed model fails;<ref name=EC2/><ref name=EYa/> even up to 2019.<ref name=ED/>]]
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 interest rate|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.<ref name=Econ1/><ref name=Estrada2009/><ref name=Barrons/><ref name=FT3/><ref name=MH4/>

The relationship has only held in the United States, and only for two main periods: 1921 to 1928 and from 1987 to 2000.<ref name=EC2/><ref name=ED/><ref name=Estrada2009/>  It has been shown to be flawed on a theoretical basis,<ref name=FT3/><ref name="Estrada"/> fails to hold in long-term analysis of data (both in the United States, and international markets),<ref name=Estrada2009/><ref name=FT3/> and has poor predictive power for future returns on a 1, 5 and 10-year basis.<ref name=FT3/><ref name="Asness"/><ref name=MH2/> The relationship can breakdown completely at very low [[Real interest rate|real yields]] (from natural forces, or where yields are artificially suppressed by [[quantitative easing]]);<ref name=JAM1/> 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.<ref name=EC2/><ref name=Koo1/>

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.<ref name=MH/>  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<ref name=FT12/>).<ref name=FM1/><ref name=Stig/><ref name=BK3/>

The term was coined in 1997–99 by Deutsche Bank analyst Dr. Edward Yardeni commenting on a report on the July 1997 Humphrey-Hawkins testimony by the then-Fed Chair, [[Alan Greenspan]] on equity valuations.<ref name=EC2/>  In 2014, Yardeni noted that the predictive power of the Fed model stopped working almost as soon as he noted the relationship.<ref name=EYa/> The term was never formally endorsed by the Fed,<ref name=MH/> however, Greenspan made further references to the relationship.<ref name=AG/>  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 [[Wall Street Crash of 1929|1929 market bubble]],<ref name=Hill2/> due to exceptional monetary looseness by the Fed.<ref name=Bloomberg1/><ref name=WSJ4/>

==Formula==

The Fed model compares the one-year forward-looking [[I/B/E/S]] [[earnings yield]] <math>(\frac{E}{P})</math> on the [[S&P 500 Index]] to the nominal 10-year US Treasury note yield, <math>(Y_{\text{10}}) </math>.<ref name="Estrada"/><ref name=ed1/><ref name=ed2/>

:<math>\frac{E}{P}=Y_{\text{10}}</math>, means the stock market, in aggregate, is fairly valued.<ref name="Estrada"/>

:<math>\frac{E}{P}<Y_{\text{10}}</math>, means the stock market, in aggregate, is over valued.<ref name="Estrada"/>

:<math>\frac{E}{P}>Y_{\text{10}}</math>, means the stock market, in aggregate, is undervalued.<ref name="Estrada"/>

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.<ref name=ed1/>

While the Fed model was specifically named for the United States stock market, it can be applied to any other stock market.<ref name="Estrada"/>

==Origin and use==
[[File:Epr797.gif|thumb|upright=1.1|right|alt=test1|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.<ref name=Econ1>{{cite magazine | magazine=[[The Economist]] | url=https://www.economist.com/finance-and-economics/2013/08/03/a-misleading-model | title=A misleading model | date=3 August 2013 | access-date=18 December 2020 | author=Buttonwood}}</ref> 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]]":<ref name=ed1>{{cite journal |last=Yardeni |first=Ed |date=25 August 1997 | title=Topical Study #38: Fed's stock market model finds overvaluation |journal=US Equity Research, Deutsche Morgan Grenfell | url=http://www.yardeni.com/pub/t_970825.pdf | access-date=18 December 2020}}</ref><ref name=ed2>{{cite journal |last=Yardeni |first=Ed |date=26 July 1999|title=Topical Study #44: New, improved stock valuation model |journal=US Equity Research, Deutsche Morgan Grenfell | url= http://www.yardeni.com/pub/t_990726.pdf | access-date=18 December 2020}}</ref>

{{blockquote|…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 Full Employment Act|Humphrey Hawkins]] report (22 July 1997).<ref name="Estrada"/>}}

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 [[Javier Estrada (professor)|Estrada]] noting: "Any statement that justifies high P/E ratios with the existence of prevailing low-interest rates is essentially using the Fed model".<ref name="Estrada"/>

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".<ref name=AG>{{Cite book|title=[[The Age of Turbulence|The Age of Turbulence: Adventures in a New World]] |page=14 |last=Greenspan |first=Alan |location=New York |publisher=[[Penguin Press]] |year=2007 |isbn=978-1-59420-131-8}}</ref>

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]]),<ref name=Hill2>{{cite web | website =[[The Hill (website)|The Hill]] | url=https://thehill.com/opinion/finance/533002-georgia-and-the-everything-market-bubble | title=Georgia and the everything market bubble | first=Desmond | last=Lachman | author-link=Desmond Lachman | date=7 January 2021 | access-date=7 January 2021}}</ref> 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".<ref name=Bloomberg1>{{cite web | website =[[Bloomberg News]] | date=17 December 2020 | access-date=18 December 2020 | url=https://www.bloomberg.com/news/articles/2020-12-16/powell-busts-out-fed-model-to-defend-high-equity-valuations | title=Soaring Stock Valuations No Big Deal to Powell Next to Bonds | first1=Sarah |last1=Ponczek |first2=Lu |last2=Wang}}</ref><ref>{{cite news | newspaper=[[The Hindustan Times]] | url=https://www.hindustantimes.com/world-news/powell-busts-out-fed-model-to-defend-high-equity-valuations/story-EaUaBbV06sYj8edEdT8FYO.html | title=Powell busts out Fed model to defend high equity valuations | first=Kanishka | last=Sarkar | date=17 December 2020 | access-date=18 December 2020}}</ref> Yardeni said Powell's actions in 2020, countering the financial effects of the [[COVID-19 pandemic]], could form the greatest financial bubble in history.<ref>{{cite web | website=[[Business Insider]] | date=23 June 2020 | url= https://markets.businessinsider.com/news/stocks/fed-bond-stimulus-risks-historic-stock-market-bubble-yardeni-outlook-2020-6-1029334701 | title=The Fed's unprecedented relief measures could form the greatest financial bubble in history says Ed Yardeni | first=Ben | last=Winck | access-date=16 December 2020}}</ref>

{{blockquote|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.|author=''[[Bloomberg News|Bloomberg]]'' (December 2020)<ref>{{cite web | website=[[Bloomberg News]] | url=https://www.bloomberg.com/news/newsletters/2020-12-18/the-weekly-fix-don-t-put-powell-in-a-corner-junk-frenzy | title=Don't Sweat Stock Valuations | date=18 December 2020 | access-date=4 January 2021 | first=Katherine | last=Greifield}}</ref>}}

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.<ref name=WSJ4>{{cite news | newspaper=[[The Wall Street Journal]] | title=Powell Won't Pop This Bubble (Yet) | first=Justin | last=Lahart | date=30 January 2021 | accessdate=4 February 2021 | url=https://www.wsj.com/articles/powell-wont-pop-this-bubble-yet-11612018980}}</ref>

==Supporting arguments==

A number of arguments are listed in favor of the Fed model, the three most important of which are:<ref name="Estrada"/><ref name=SOA>{{cite web | website=[[Society of Actuaries]] | url=https://www.soa.org/globalassets/assets/files/resources/essays-monographs/invest-fallacies/inv-ebook-2014-cantor.pdf | title=The Fallacy of the Fed Model | first1=David R. | last1=Cantor | first2=Adam | last2=Butler | first3=Kunal  | last3=Rajani | date=2014 | access-date=17 December 2020}}</ref><ref name=Econ1/>

*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.<ref name=Barrons>{{cite magazine | magazine=[[Barron's (newspaper)|Barron's]] | title=The Flaws in the Fed Model | date=9 June 2012 | access-date=24 December 2020 | first=Michael | last=Santoli | url=https://www.barrons.com/articles/SB50001424053111904470204577446371761637272}}</ref>  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".<ref name="Asness">{{cite journal | author-link=Cliff Asness | last=Asness |first=Clifford |year=2003 |title=Fight the FED model |journal= Journal of Portfolio Management|volume=30 |pages=11–24 |doi=10.3905/jpm.2003.319916 |ssrn=381480 |s2cid=155012499 }}</ref><ref name=SOA/>  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).<ref name=FM1>{{cite journal |last=Bekaert |first=Geert |author2=Engstrom, Eric |date=April 2008 |title=Inflation and the Stock Market: Understanding the 'Fed Model'  |ssrn=1125355 }}</ref> ''[[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".<ref>{{cite news | newspaper=[[The Wall Street Journal]] | first=Jonathan | last=Clements | date=1 May 2005 | access-date=31 December 2020 | title=The Fed Model: Fix It Before You Use It | url=https://www.wsj.com/articles/SB111491292409921442}}</ref>  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":<ref name=MH/>

{{blockquote|The Fed Model's attraction to the Wall Street bulls is that it almost always is bullish.|[[Mark Hulbert]] (June 2020)<ref name=MH/>}}

*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,<ref name="Estrada"/> 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".<ref name="Asness"/><ref name=EC2>{{cite magazine | magazine=[[The Economist]] | title=Burying the "Fed model" | date=29 November 2012 | access-date=17 December 2020 | url=https://www.economist.com/buttonwoods-notebook/2012/11/29/burying-the-fed-model}}</ref>  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".<ref>{{cite news | newspaper=[[The Wall Street Journal]] | url=https://www.wsj.com/articles/has-the-fed-rewritten-the-laws-of-investing-11608747325 | title=Has the Fed Rewritten the Laws of Investing? | first=Justin | last=Lahart | date=23 December 2020 | access-date=25 December 2020}}</ref>

: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.<ref name=Koo1>{{cite book | title=The Escape from Balance Sheet Recession and the QE Trap: A Hazardous Road for the World Economy Kindle Edition | author=Richard Koo | author-link=Richard Koo | isbn=978-1119028123 | date=October 2014 | publisher=[[Wiley (publisher)|Wiley]]}}</ref>

*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.<ref name="Salomons">{{cite journal |last=Salomons |first=R. |year=2006 |title=A Tactical Implication of Predictability: Fighting the FED model |journal= [[The Journal of Investing]]|doi=10.3905/joi.2006.635635 |ssrn=517322 |s2cid=155042547 }}</ref> 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.<ref name=EC2/>  Academics show that outside of the United States, the evidence for a Fed model is weak,<ref name="Estrada"/> 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]]),<ref name=FM1/> or even a mistaken understanding by investors of such Fed actions.<ref name=Econ1/><ref name="Asness"/>  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".<ref>{{cite web | website=[[Bloomberg News]] | url=https://www.bloomberg.com/opinion/articles/2017-09-07/fed-model-on-stock-yields-loses-its-predictive-power | title=Fed Model Loses Its Grip on Stocks | first=Stephen | last=Gandel | date=17 September 2020 | access-date=28 December 2020}}</ref>

==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).<ref name="Estrada"/><ref>{{cite journal | journal=Journal of Financial Research | url=https://onlinelibrary.wiley.com/doi/pdf/10.1111/1475-6803.t01-1-00001 | title=The Biggest Mistakes We Teach | first=Jay R. | last=Ritter | volume=25 | issue=2 | doi=10.1111/1475-6803.t01-1-00001 | pages=159–168 | access-date=18 December 2020 | date=June 2002| s2cid=153887380 }}</ref>

=== 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.<ref name=Estrada2009/>

For example, a number of unrealistic assumptions need to be made to go from the academically robust [[Dividend discount model|constant growth dividend discount model]] of equity valuation, to the Fed model of market valuation, which [[Javier Estrada (professor)|Estrada]] broke down, starting with the [[Gordon model|Gordon growth model]]:<ref name="Estrada">{{cite journal |last=Estrada |first=J. |year=2006 |title=The Fed model: A note |journal= Finance Research Letters|volume=3 |pages= 14–22|doi=10.1016/j.frl.2005.11.002 |ssrn=841787 |author-link=Javier Estrada (professor)}}</ref>

:<math> P= \frac{D (1 + G)}{R_{\text{f}} + RP - G} </math>

P is the price, and D the dividend, G the expected long-term growth rate, <math>R_{\text{f}}</math> the risk-free rate (10-year nominal treasury notes), and RP the [[equity premium puzzle|equity risk premium]]; then making the following assumptions:<ref name="Estrada"/>
* 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=<math>R_{\text{f}}</math>. Estrada finds these assumptions seem unrealistic at best, and theoretically unsound as a form of valuation.<ref name="Estrada"/>

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.<ref name="Asness" /><ref>{{cite journal |last=Feinman |first=J. |year=2003 |title=Inflation illusion and the (mis)pricing of assets and liabilities |journal= Journal of Investing |pages=29–36|url=http://web.iese.edu/jestrada/PDF/Research/Refereed/FedModel-Note.pdf }}</ref><ref>{{cite journal |last=Ritter |first=J.R. |author2=Warr, R.S. |year=2002 |title=The decline of inflation and the bull market of 1982–1999 |journal=Journal of Financial and Quantitative Analysis |volume=37 |issue=1 |pages=29–61|doi=10.2307/3594994 |jstor=3594994 |s2cid=154940716 |url=http://bear.warrington.ufl.edu/ritter/publ_papers/the_decline_of_inflation.pdf }}</ref>

=== 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.<ref name=Estrada2009>{{cite journal | journal=The Quarterly Review of Economics and Finance | volume=49 | date=May 2009 | issue=2 | pages=214–238 | first=Javier | last=Estrada | title=The fed model: The bad, the worse, and the ugly | doi=10.1016/j.qref.2007.03.007 | url=https://www.sciencedirect.com/science/article/abs/pii/S1062976907000853 | issn=1062-9769 | author-link=Javier Estrada (professor)}}</ref><ref name=FT3/><ref name="Estrada" />
 
The correlation between the forward earnings yield and government bond yields was only 19% over the 1881 to 2002 period.<ref name="Salomons" /> Over the period from 1999 to 2013 the correlation was negative, with the Fed model incorrectly giving a rare "sell signal" in 2003 (turned out to be a poor signal), and a strong "buy signal" in 2007 (also turned out to be a poor signal).<ref name="Estrada"/> An academic study of international data showed that the Fed model equilibrium only shows up in 2 out of 20 evaluated international markets, with the author concluding that "evidence from 20 countries that seriously questions its empirical merits".<ref name=Estrada2009/>

In 2014, former [[S. G. Warburg & Co.]] chief investment officer, Andrew Smithers, writing in the ''[[Financial Times]]'' said of the statistical support for the Fed model: "It is not only nonsense but is the most egregious piece of "data mining" that I have encountered in the 60-plus years I have been studying financial markets".<ref name=FT3>{{cite news | newspaper=[[Financial Times]] | first=Andrew | last=Smithers | date=25 July 2014 | url=https://www.ft.com/content/2cafe1e1-21ec-3842-b5d7-8cc05bb2f850 | title=The fallacy of the Fed model | access-date=28 December 2020}}</ref>

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".<ref name=FT8>{{cite news | newspaper=[[Financial Times]] | url=https://www.ft.com/content/25201e10-3ca2-11e8-b7e0-52972418fec4 | title=Relationship between bond and dividend yields has no grounds | first=Stuart | last=Kirk | date=April 2017 | access-date=2 January 2021}}</ref>

=== 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.<ref name=MH4>{{cite news | newspaper=[[The Wall Street Journal]] | author-link=Mark Hulbert| first=M.J. | last=Hulbert | title=FED MODEL: Can Low Rates Explain High Stock Prices? Not So Fast. | url=https://www.wsj.com/articles/can-low-rates-explain-high-stock-prices-not-so-fast-11562637960 | date=8 July 2019 | access-date=31 December 2020}}</ref><ref name="Asness" />

In April 2014, Dr. Yardeni wrote of his Fed model:<ref name=EYa>{{cite web | website=[[Business Insider]] | date=28 April 2014 | first=Dr. Edward | last=Yardeni | url=https://www.businessinsider.com/the-fed-model-buybacks-and-ma-2014-4?r=US&IR=T | title=The 'Fed Model' Is Better At Predicting Corporate Financial Behavior Than Investment Returns | access-date=24 December 2020}}</ref>

{{blockquote|[..] I discovered [the Fed model] buried in the Fed's Monetary Policy Report of July 1997. It showed a close fit between the earnings yield and the 10-year Treasury bond yield from 1987 through 1997. That's just about when the model stopped working as a useful investment tool. It did show that the S&P 500 was overvalued during the late 1990s. But it has been significantly undervalued ever since then according to the model, which never gave a sell signal in 2007 or 2008.|Dr. Edward Yardeni (April 2014)<ref name=EYa/>}}

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 [[Coefficient of determination|r-squared metric]] of 0.5%, compared poorly that those of other ratios, including [[price-earnings ratio|P/E]] (56.3%), [[Price–sales ratio|P/Sales]] (67.2%), and Households' equity allocation as a % of Total Financial Assets (88.4%).<ref name=MH2>{{cite web | website=[[MarketWatch]] | date=9 March 2018 | access-date=24 December 2020 | author-link=Mark Hulbert |first=Mark | last=Hulbert | title=This is what the Fed Model says about the outlook for stocks as the bull market turns 9 | url=https://www.marketwatch.com/story/this-is-what-the-fed-model-says-about-the-outlook-for-stocks-as-the-bull-market-turns-9-2018-03-09}}</ref>

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.<ref name=MH>{{cite web | website=[[MarketWatch]] | date=27 June 2020 | access-date=24 December 2020 |  author-link=Mark Hulbert | first=Mark | last=Hulbert | url=https://www.marketwatch.com/story/the-fed-model-is-almost-always-bullish-which-makes-it-a-perfect-face-for-this-too-good-to-be-true-stock-market-2020-06-23 | title=The Fed Model is almost always bullish, which makes it a perfect face for this too-good-to-be-true stock market}}</ref>

=== 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,<ref name=JAM1>{{cite journal | journal=Journal of Asset Management | first1=Andreas | last1=Humpe | first2=David | last2=McMillan | title= Equity/bond yield correlation and the FED model: evidence of switching behaviour from the G7 markets |volume= 19 | pages= 413–428 | date=2018 | issue=6 | doi=10.1057/s41260-018-0091-x | quote=We demonstrate that at low levels of the real bond yield, the correlation between the equity and bond yields turns negative. This arises as the lower bond yield implies heightened macroeconomic risk (e.g. deflation and economic stagnation) and causes equity and bond prices to move in opposite directions. | hdl=1893/27892 | s2cid=158210939 | hdl-access=free }}</ref> either from natural effects or by deliberate central banking actions such as quantitative easing.<ref name=EC2/><ref name=Econ1/>

Economist [[Richard Koo]] noted that in post-1990 Japan, the bursting of an asset bubble led to a balance sheet recession that compressed Japanese long-term government bond yields to almost zero.  However, the forward earnings yield on the Nikkei rose steadily for several decades post the 1990 collapse, only falling during periods of deliberate intervention by the Bank of Japan (BOI), and only really gaining traction post-2013 when the BOJ began to directly purchase Japanese equity ETFs in large quantities.<ref name=Koo1/> Koo explained that in Japan the rise in the earnings yield was due to a collapse in long-term growth prospects for Japanese equities (per Gordon's growth model, above), which was compounded by the dramatic rise in the value of Japanese government bonds (from the 10-year yield falling to almost zero), which "crowded-out" equities in the allocation of investor capital.<ref name=Koo1/>  By December 2020, the BOJ had become the biggest owner of Japanese equities, acquired with printed funds.<ref>{{cite web | website=[[Bloomberg News]] | url=https://www.bloomberg.com/news/articles/2020-12-06/boj-becomes-biggest-japan-stock-owner-with-434-billion-hoar | title=BOJ Becomes Biggest Japan Stock Owner With $434 Billion Hoard | date=6 December 2020 | access-date=22 December 2020 | first1=Min | last1=Jeong Lee | first2=Toshiro | last2=Hasegawa}}</ref>

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.<ref name=EC2/><ref name=ED/>  Only after the then-Fed chair [[Ben Bernanke]], launched a longer-term quantitative easing program called [[Quantitative easing#US QE1, QE2, and QE3|QE3]], did the S&P500 earnings yield begin to move in a weak correlation with the 10-year nominal interest rate (although the gap between the E/P metric and the 10-year nominal rate remained considerable for at least the next decade).<ref name=ED>{{cite web | website=Yardeni Research | title=Fed's Stock Valuation Model (Monthly Research) | access-date=22 December 2020 | author=Dr. Edward Yardeni Research | url=https://www.yardeni.com/pub/valuationfed.pdf}}</ref>

==Impact of Fed put==
{{see also|Greenspan 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.<ref name=FM1/>  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.<ref name=FM1/>

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).<ref name=Stig/>  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,<ref name="Estrada"/> and financial authors,<ref name=MH/> as some of the strongest supporters of the rationale for the Fed model relationship).<ref name=FM1/><ref name=BK3>{{cite book | title=The Everything Bubble: The Endgame For Central Bank Policy | date=October 2017 | isbn= 978-1974634064 | first=Graham | last=Summers | publisher=[[CreateSpace]]}}</ref><ref name=Stig>{{cite book |first=Joseph E. |last=Stiglitz |title=Freefall: America, Free Markets, and the Sinking of the World Economy |location=New York and London |publisher=W. W. Norton & Company |year=2010 | isbn=9780393075960 |url-access=registration |url=https://archive.org/details/freefallamericaf00stig/page/135 }}</ref>  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,<ref name=FT12>{{cite news | newspaper=[[Financial Times]] | url=https://www.ft.com/content/2fbc32ca-5e3d-38a7-ad6f-bf9fe4bd89fa | title=LTCM and the Greenspan put | first=Helen | last=Thomas | date=22 May 2007 | access-date=30 January 2021}}</ref> and was the additional use of the Greenspan put to rescue those Wall Street banks after LTCM's collapse.<ref>{{cite web | website=The Big Picture | url=https://ritholtz.com/2020/04/unintended-consequences-ltcm-rescued/ | title=Unintended Consequences, Part II: What if LTCM Was Not Rescued in 1998? | author-link=Barry Ritholtz | first=Barry | last=Rithhotz | date=22 April 2020 | access-date=30 January 2021}}</ref>

==See also==
*[[Cyclically adjusted price-to-earnings ratio]]
*[[Equity risk premium]]
*[[Everything bubble]]
*[[Greenspan put]]

==References==
{{Reflist}}

===Further reading===
*{{cite journal | title=Fight the Fed Model: The Relationship between Stock Market Yields, Bond Market Yields, and Future Returns | author-link=Cliff Asness | first=Clifford S. | last=Asness | doi=10.3905/jpm.2003.319916 | journal=[[The Journal of Portfolio Management]] | volume=30 | issue=1 | date=Fall 2003 | s2cid=155012499 | url=https://jpm.pm-research.com/content/30/1/11}}
*{{cite journal | journal=The Quarterly Review of Economics and Finance | volume=49 | date=May 2009 | issue=2 | pages=214–238 | first=Javier | last=Estrada | title=The fed model: The bad, the worse, and the ugly | doi=10.1016/j.qref.2007.03.007 | url=https://www.sciencedirect.com/science/article/abs/pii/S1062976907000853 | issn=1062-9769 | author-link=Javier Estrada (professor)}}
*{{cite web | website=[[Society of Actuaries]] | url=https://www.soa.org/globalassets/assets/files/resources/essays-monographs/invest-fallacies/inv-ebook-2014-cantor.pdf | title=The Fallacy of the Fed Model | first1=David R. | last1=Cantor | first2=Adam | last2=Butler | first3=Kunal  | last3=Rajani | date=2014 | access-date=17 December 2020}}

==External links==
{{scholia}}
*[https://www.yardeni.com/pub/valuationfed.pdf Fed Stock Valuation Model], Monthly Update, Dr. Edward Yardeni 
*[http://www.investopedia.com/articles/03/112703.asp Investopedia: The Fed Model and Stock Valuation]
*[http://www.investopedia.com/articles/stocks/08/fed-model.asp Investopedia: Breaking down the Fed model]
*[http://seekingalpha.com/article/222632-debunking-the-fed-model Seeking Alpha: Debunking the Fed model]
*[https://www.ft.com/content/25201e10-3ca2-11e8-b7e0-52972418fec4 Relationship between bond and dividend yields has no grounds], ''[[Financial Times]]'' (2017)
*[https://www.youtube.com/watch?v=8E-ZFmgw4dg (Video presentation) Fed Up with the Fed Model | Charts that Count], [[John Authers]], ''[[Financial Times]]'' (September 2018)

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