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The "Fed model" or "Fed Stock Valuation Model" (FSVM), is a disputed theory of equity valuation that compares the stock market's earnings yield to the 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 that stocks are over-or-under valued.

While the relationship has held over some periods, the theory has been shown to be flawed on a theoretical basis, and fails to hold in long-term analysis of data across multiple markets, and has poor predictive power for future returns. The theory can breakdown completely in situations where the treasury market yields are artificially suppressed (e.g. by quantitative easing, or post-WW2); in such circumstances, without central bank support for the stock market (e.g. use of the Greenspan put in 2020, or Japanese purchase of equity ETFs post-2013), the relationship materially diverges.

The term was coined by Deutsche Bank analyst Dr. Ed Yardeni in a 1997 report that commented on a July 1997 Humphrey-Hawkins report by the then-Fed Chair, Alan Greenspan on equity market valuation. The term was never formally endorsed by the Fed, however, Greenspan made several further references to the relationship. In December 2020, the then-Fed Chair Jerome Powell, invoked the relationship to justify stock market valuations that were approaching levels not seen since the Dot-com bubble.

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 Dr. 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 probably instructed his staff to devise a stock market valuation model to help him evaluate the extent of this irrational exuberance":

…changes in this ratio 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).

The Fed model implies the stock market is fairly valued when the one-year forward-looking earnings yield ${\displaystyle ({\frac {E}{P}})}$ equals the 10-year Treasury note yield, ${\displaystyle (Y_{\text{10}})}$:

${\displaystyle {\frac {E}{P}}=Y_{\text{10}}}$

Academics note that I/B/E/S had been publishing such a metric since 1986, called the I/B/E/S Equity Valuation Model, and that the concept had been in widespread use by Wall Street analysts 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 by the Fed, but Greenspan referenced it 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".

On 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), 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 coronavirus pandemic, could form the greatest financial bubble in history.

Support

A number of arguments are listed by different authors in favor of the Fed model, the 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 decrease, 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 research indicates support for competing assets but that the driver is "uncertainty about real growth prospects and also habit-based risk aversion".

• 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".

• Historical data argument. For a specific period in 1995-2002, 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% and in recent years the correlation has broken down completely.

Failure

Academics conclude that the model is inconsistent with rational valuation of the stock market, or past observations.

Lack of theoretical support

The competing asset argument listed above argues that only when stocks have the same yield as government bonds, 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. And how do corporate bonds (with a yield above the government bond yield) fit into this picture? A number of assumptions need to be made to go from the constant growth dividend discount model to the Fed model. Estrada starts with the Gordon growth model

${\displaystyle P={\frac {D(1+G)}{R_{\text{f}}+RP-G}}}$

where P is the current price and D the current dividend, G the expected long-term growth rate, ${\displaystyle R_{\text{f}}}$ the risk free rate (10-year treasury notes) and RP the equity risk premium. If one now assumes that 100% of the earnings are paid as dividend (D=E), the growth rate is equal to zero, and the equity risk premium is also equal to zero, one gets the Fed model: E/P=${\displaystyle R_{\text{f}}}$. The three assumptions seem unrealistic at best. It is also pointed out that the Fed model compares a real magnitude (E/P) with a nominal interest rate. Inflation should affect the bond yield, but not the earnings yield.

Data selection and international markets

The Fed model equilibrium was only observed in one market, and for a limited time window. More specifically, the relationship is observed for the S&P 500 index between ~1980 and ~2005 but data outside of this time window, or in different international markets do not show the same pattern. The correlation between earnings yield and government bond yields was only 19% over the 1881–2002 period. Over the period from 1999 to 2010 was reported to be –0.80 with statistical significance . The Fed model equilibrium specifically seemed to break down during the height of the financial crisis in 2008, when the yield on 10-year Treasuries reached an all-time low at 2.4% whereas the S&P 500 earnings yield reached a 20-year-high at more than 8%, a gap of 6 percentage points. And a study of international data showed that the Fed model equilibrium only shows up in 2 out of 20 evaluated international markets. It seems that the empirical support for the Fed model is then based on carefully chosen and limited evidence.

Lack of predictive power

If the Fed model is indeed an equity valuation theory with descriptive validity, it should be able to identify over-valued and under-valued assets. But it turns out that the Fed model has no power to forecast long term stock returns. Traditional value investing methods using only the market's P/E have significantly more efficacy than the Fed model.

As an example Tom Lauricella applied the Fed model to S&P500 index on January 19, 2008. He writes:

With the past week's downturn, stocks in the Standard and Poor's 500-stock index are trading at 13 times their expected earnings for 2008. Last June, when the S&P index was 12% higher than it is now, stocks were priced at 14.2 times this year's earnings. Meanwhile, with a U.S. recession now widely expected and the Federal Reserve thought likely to cut short-term rates further, U.S. Treasury yields have fallen sharply. The 10-year Treasury note is yielding 3.64%, its lowest level since July 2003, and down from 3.81% a week ago.

Thus S&P500 forward earning yield (1/13=7.69%) is higher than 10-year Treasury note yield (3.64%), suggesting S&P500 is significantly undervalued. However, over the next twelve months, the S&P500 index fell from 1,325.19 (January 18, 2008) to 805.22 points (January 20, 2009), a drop of more than 39%.

Is the Fed model mis-specified?

The Fed model equilibrium remains an enigma. On one hand 30 years of data is available that shows how S&P earnings yield and 10-year government bond yield move in tandem. On the other hand, there is no theoretical foundation to explain the relationship, and the best explanation academics came up with is that investors collectively suffer from 'money illusion'. A number of questions remain unanswered. Why was the relationship observed in the US and not in most other international markets? Do investors in the US (the world's largest equity market) suffer more from 'illusions' than investors in for example Austria and Finland? Why did the relationship not exist in the US before 1980 (or 1965) and why did the equilibrium break down during the financial crisis of 2007–2008? And if government bonds and stocks are competing assets, what is the role of corporate bonds?

The recently proposed capital structure substitution theory argues that the Fed model indeed needs to be re-specified. It suggests that supply (company management), rather than demand (investors) drives the relationship between E/P and interest rates. Stock market earnings yield tends to equilibrium not with the government bond yield but with the average after-tax corporate bond yield as companies adjust capital structure (mix of equity and bonds) to maximize earnings per share. If managements consistently optimize capital structure by substituting stocks (repurchasing shares) for bonds or vice versa, equilibrium is reached when:

${\displaystyle {\frac {E_{\text{x}}}{P_{\text{x}}}}=R_{\text{x}}\ }$

where E is the earnings-per-share of company x, P is the share price, R is the nominal interest rate on corporate bonds and T is the corporate tax rate. For a long time the after-tax interest rate on corporate bonds was roughly equal to the 10-year Treasury rate. But during the 2008 financial crisis this relationship broke down, as Baa rated corporate bonds peaked at over 9%, and 10-year treasuries bottomed under 2.5% (see figure 3). In the US, SEC Rule 10b-18 (explicitly allowing share repurchases) enabled fine adjustment toward equilibrium as of 1982, explaining why the equilibrium emerged around that time and not before. And in many other countries share repurchases were prohibited until 1998 or are still considered illegal, explaining why the Fed model equilibrium was observed in the US but not in many other international markets.

See also

• Greenspan put

References

1. Buttonwood (3 August 2013). "A misleading model". The Economist. Retrieved 18 December 2020.
2. ^ Yardeni, Ed (25 August 1997). "Topical Study #38: Fed's stock market model finds overvaluation" (PDF). US Equity Research, Deutsche Morgan Grenfell. Retrieved 18 December 2020.{{cite journal}}: CS1 maint: year (link)
3. ^ Yardeni, Ed (26 July 1999). "Topical Study #44: New, improved stock valuation model" (PDF). US Equity Research, Deutsche Morgan Grenfell. Retrieved 18 December 2020.{{cite journal}}: CS1 maint: year (link)
4. ^ Estrada, J. (2006). "The Fed model: A note". Finance Research Letters: 14–22. SSRN 841787.
5. Greenspan, Alan (2007). The Age of Turbulence: Adventures in a New World. New York: Penguin Press. p. 14. ISBN 1-59420-131-5.
6. Ponczek, Sarah; Wang, Lu (17 December 2020). "Soaring Stock Valuations No Big Deal to Powell Next to Bonds". Bloomberg News. Retrieved 18 December 2020.
7. Sarkar, Kanishka (17 December 2020). "Powell busts out Fed model to defend high equity valuations". The Hindustan Times. Retrieved 18 December 2020.
8. Winck, Ben (23 June 2020). "The Fed's unprecedented relief measures could form the greatest financial bubble in history says Ed Yardeni". Business Insider. Retrieved 16 December 2020.
9. ^ Cantor, David R.; Butler, Adam; Rajani, Kunal (2014). "The Fallacy of the Fed Model" (PDF). Society of Actuaries. Retrieved 17 December 2020.
10. ^ Asness, Clifford (2003). "Fight the FED model". Journal of Portfolio Management. SSRN 381480.
11. Bekaert, Geert; Engstrom, Eric (April 2008). "Inflation and the Stock Market: Understanding the 'Fed Model'". SSRN 1125355. {{cite journal}}: Cite journal requires |journal= (help)
12. "Burying the "Fed model"". The Economist. 29 November 2012. Retrieved 17 December 2020.
13. ^ Salomons, R. (2006). "A Tactical Implication of Predictability: Fighting the FED model". The Journal of Investing. SSRN 517322.
15. Feinman, J. (2003). "Inflation illusion and the (mis)pricing of assets and liabilities" (PDF). Journal of Investing: 29–36.
16. Ritter, J.R.; Warr, R.S. (2002). "The decline of inflation and the bull market of 1982–1999" (PDF). Journal of Financial and Quantitative Analysis: 29.
17. Lauricella, Tom (19 January 2008). "When Is It Time to Buy Stocks Again?". Wall Street Journal.
18. Timmer, Jan (2011). "Understanding the Fed Model, Capital Structure, and then Some". SSRN 1322703. {{cite journal}}: Cite journal requires |journal= (help)

Further reading

• Lander, Joel; Orphanides, Athanasios; Douvogiannis, Martha (1997). "Earnings, Forecasts and the Predictability of Stock Returns: Evidence From Trading the S&P". Journal of Portfolio Management. 23 (4): 24–35. doi:10.3905/jpm.1997.409620. .

External links

• The "FED Model" theory of equity valuation- A blog discussion of the "Fed model" and how to apply it to the S&P 500 index.
• Investopedia: The Fed Model and Stock Valuation
• Investopedia: Breaking down the Fed model
• Seeking Alpha: Debunking the Fed model

• Finance theories
• Investment