Fed Model

Charts with SP500 Risk Premium, Estimated and Yield

You can see the updated and interactive data in our Fed Model Page

1. Introduction

In 1997 Fed Chairman Alan Greenspan indicated that changes in the SP500 earnings yield have often been inversely related to changes in the long term Treasury yields. This concept has been studied and extended by Dr. Edward Yardeni who coined it the "Fed Model". In its simplest form, it states that if the forward earnings yield of a stock market is higher than long term treasury yield the market is undervalued, and vice-versa. A stock market's equilibrium can, therefore, be stated as: 

Current Estimated Yield (CEY)  = 10 Y T-Note Yield (TBY)

The premise is that if the expected earnings yield of the market is equal to or lower than what you can earn risk-free on a 10Y note, then it does not pay to hold stocks. Conversely, if the S&P yield is higher than the 10Y note, then investors are receiving a “Risk Premium” for taking the additional risk inherent in stocks. The “Risk Premium” is therefore defined as:

Risk Premium (RP) = CEY - TBY

Values of RP less than 1% normally indicate an unfavorable risk/reward environment for stocks relative to bonds. 


About Analysts Estimates 

Analysts typically report current & next fiscal year estimates. The Fed Model literature is not specific as to what “Current Estimates” means. In Portfolio123 we decided to use a “blend” of the analyst’s Current & Next fiscal year. This “blended” estimate represents the Next Twelve Months (NTM) and creates a smoother transition when the analyst “next” fiscal year becomes the “current” one when Q4 is announced. The formula to blend the two estimates uses the latest quarter number to “scale” in the next year estimates. For example, if Q1 was just announced the blended estimate adds together 75% of CurrYEPS with 25% of the NextYEPS

2. The Fed Model in Portfolio123

We have created several data series to recreate the Fed Model historical and current values. All historical values were created using Portfolio123’s point-in-time engine and are, therefore, void of any biases.  Here's a screenshot of our Fed Model Chart:

NOTE: To use the data directly within your systems and rules please see section 5 “Accessing The Data in Rules”

Market Risk Indicator

This gauge shows the current value of the Risk Premium (RP), color-coded by the level of risk. Also shown are arrows indicating whether the trends of two S&P500 metrics are above or below their 40-week averages. In Figure 1 the indicator paints a mixed message: the Risk Premium indicates a bargain in the market (“future yield” higher by 4%+ than 10Y Note), but the future and past EPS trends are down. An extreme RP reading doesn't necessarily mean that the market will move to reach 'equilibrium' nor should it be considered a ‘leading indicator’. An RP reading is best used in conjunction with other confirming signals.

Historical Charts

These three charts show 1) the historical values of the Risk Premium superimposed with the S&P500, 2) the Future EPS estimates for the SP500 (weekly values) with moving averages (20,40) , and  3) the 10Y T-Note Yield superimposed with the S&P500 Yield.

  1. Risk Premium vs SP500. You can quickly see the overvalued market of the internet bubble (around 2000) and the undervalued market after the 2008 crash.

  2. This chart helps to identify trends. You can see your selected series, in this case, blended SP500 estimates, and the 20 and 40-week moving average.

  3. The SP500 Yield and the 10 Year T-Note

3. Pros and Cons

Theoretical rigor

Recall that the phase "Fed Model" was coined by Dr. Yardeni, not by anyone at the Fed. And within the Fed, it's not clear that anyone really saw this as a market timing or equity valuation model. It was just an observation near the bottom of Section 2 of a report to Congress with a small two-paragraph section entitled "Equity Prices" being just one of many other economic and financial topics covered. In commenting on a recent rise in stock prices to a greater degree than would be implied by consensus estimates alone, the report observed that "changes in this ratio have often been inversely related to changes in long-term Treasury yields, but this year's stock price gains were not matched by a significant net decline in interest rates." (Suggesting that the P/E is inversely related to changes in treasury yields is equivalent to stating that earnings yields are directly related to treasury yields.)

That's it. No data is presented. And in fact, there is no suggestion that the earnings yield should equal the treasury yield. The phrase used was "related to." The nature of the relationship is not discussed, but there is no reason to believe the Fed ignored considerations that should make this yields unequal: the fact that corporate earnings grow over time while interest payments remain fixed (a rational explanation for lower earnings yields), and the fact that corporate earnings streams are more risky than treasury interest payments (suggesting earnings yields should be higher).

An issue the Fed expressly acknowledged was estimate revision: "One important factor behind the increase in stock prices this year appears to be a further rise in analysts' reported expectations of earnings growth over the next three to five years." In other words, when the Fed looked at "model," it was well aware of how estimate revision would impact day-to-day stock prices, separately from risk premium.

Accuracy of estimates

As noted, the Fed was mindful of the fact that estimates change. And by now, estimate revision has become so thoroughly embedded in our market culture, as to become a cottage industry in its own right. Research organizations have been built up on the basis of statistical models that study and quantify links between revisions and stock prices, the financial media often gives short shrift to the levels of corporate earnings preferring instead to emphasize where the numbers stand relative to estimates (in other words, shares of companies that report earnings which are weak, but less weak than expected, often get more favorable mention than do shares of companies whose earnings were great, but a bit less greater than expected).

This would make it very hard to rigidly rely on any point-in-time comparison between earnings and treasury yields. It's important to temper the earnings yield with further consideration of how revisions may cause the numerator in the calculation to change going forward.

This does not diminish from the usefulness of the model. In fact, a case can be made that it makes the model more useful for day-to-day investing. But one thing is clear; it's very difficult, if not impossible, to treat the model as an expression of core financial theory. It seems preferable to treat it instead as a practical framework within which the rules based on the data inputs can be studied, tested, and refined.

Analyst optimism

It has often been observed that analyst estimates tend to be optimistic based on human nature and/or other agendas. Much has been written on the topic. But the contemporary reality is not so clear.

Look at the earnings section of the above chart. Notice that the estimates trends are choppy showing periods in which they decline to approach a less-favorable reality, but also periods when analysts need to chase reality upward.

In this day and age, with the estimate-revision "industry" now thoroughly entrenched, other factors have gained prominence: another cottage industry based on the practice of issuing formal earnings guidance, class action lawyers crawling out of the woodwork, Regulation FD, and Sarbanes Oxley. So it's getting harder and harder for even the more cynical analysts to publish overly optimistic numbers in order to pursue some other agenda. And considering the consequences of shortfalls, there's less reward than ever and more in the way of adverse consequences for companies or analysts who try to pump up expectations, so much so that some firms get criticized for habitually "low-balling."

That doesn't necessarily mean the estimates have become more accurate. But it may mean that errors are based on bona fide failures, on the part of analysts, the corporate executives who guide them, the econometric forecasting services used by both, and company in-the-field rank-and-file personnel to accurately predict near-term business trends, something that becomes much more pronounced when business cycles transition. Much attention has been paid in the past to ethical shortcomings. But the bigger issue, the extent to which basic human frailty colors outcomes every step of the way, has been largely ignored.

So it's unreasonable to expect the problem of forecast error to ever vanish. This will continue to be very irritating to investors and it definitely damages the Fed Model's Ivory tower stature. But on a practical basis, it reinforces the soundness of using the model as a top-down framework within which we can study trends in estimates and in estimate revision and create buy and sell rules.

Long periods of Under/Over valuation

We do see this with the Fed Model.

We also see it with Price/Earnings ratios, with Price/Book ratios, with dividend yields, with discounted cash flow, and so on and so forth. With any valuation measure anyone might use, assets (the market, individual stocks, etc.) tend to be overvalued or undervalued for prolonged periods of time.

If one could invest successfully based on valuation alone, we'd all be exceptionally wealthy since the valuation formulas are actually very easy to use. However, in real life, it's not so easy. That's because the key to successful value-based investing is recognizing which erroneous valuations are most likely to be corrected within reasonable time frames. Sometimes, the reconciliation will occur when the market recognizes that an asset really is much better or worse than its price implies, in which case, the price will adjust. Other times, the reconciliation occurs when the asset itself changes, for better or worse, in such a way as to match its price (examples: a company that deteriorates such that what once appeared to be an excessively low price now looks to be on target, or a seemingly overpriced shares that later look more plausible after the company "grows into its valuation").

Hence prolonged under or overvaluation suggested by the Fed Model should be treated the same was as any other instance. Use it as one factor, but not the only factor, in developing an overall analytic view.

4. Using The Model

We suggest that one not rigidly relies on the most simple view of the Fed model, the one that suggests stocks should be purchased if earnings yields are above treasury yields and vice versa. There's no evidence the Fed ever viewed the relationship this way, and there's been no research elsewhere that would support its viability as a day-to-day investment strategy.

Instead, we suggest using the Fed model as a framework around which you can create and test buy and sell rules based on the relationship between earnings and treasury yields as well as trends in the model's underlying components. When you use Technical Analysis or Price & Volume rules having benchmark as a parameter, you can if you wish to identify your benchmark as the 10-year treasury yield, the S&P 500 risk premium, TTM S&P 500 EPS, the Current-Year S&P 500 EPS estimate, the Next -Year S&P 500 EPS estimate, or the S&P 500 yield.

Using these, you can add market timing to your simulation, i.e., rules requiring that market conditions be favorable before any stocks can be purchased.

5. Accessing The Data in Rules

You can access the data within your strategies and rules by using a technical function (like Close or SMA) and the appropriate series ids ( series ids usually start with a # for P123 defined ones, and ## for external ones). You will find the complete list of Fed Model IDs for the weekly time series in the rules reference: TIME SERIES IDS->S&P500 IDS




Risk Premium



EPS Blend Curr & Next Y






SP500 Yield






6. Rule Examples:

Latest Risk Premium:  Close(0,#SPRPBlend)

Risk Premium 4 weeks ago:  Close(4,#SPRPBlend)

The SP estimates are above their 20 week average: Close (0,#SPEPSCNY) > Close (20,#SPEPSCNY)