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When it comes to market forecasting, there is no perfect tool in the intelligent investor's toolbox. Time has presented new valuation metrics, as the individual investor is always looking to complement the standard valuation metrics to gain an edge in the marketplace.

The "Fed Model," brought to light in 1997 by the Federal Reserve, accurately measured stocks as overvalued in two key markets: 1987 and 1997-2002.

Fed Valuation Model Backstory: 1997 & Ed Yardini

According to the Fed on July 21, 1997, the forward expected earnings yield of the S&P 500 was noted to be "often related" to changes in the yield of long term treasury notes, as measured by the yield of the 10-year U.S. treasury bond. In this regard, Fed warned of an overpriced stock market.

In 1997 the 10-year yield was significantly higher than the S&P 500 earnings yield for the first time since 1991, where earnings were depressed due to an economic slowdown.

After this tool was brought into the mainstream, Ed Yardeni aptly coined it the Fed Model. When looking at the S&P 500 10-year performance from 1997-2006, it is noted that the Fed valuation warning in July 1997 directly preceded the infamous tech bubble of 1998-2002.

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In 2007, however, the market was deemed undervalued by 20% according the Fed Model. Clearly this did not warn against the incoming financial calamity caused by the global financial crisis.

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Contemporary Criticism Of The Fed Model

The Fed Model could be criticized for three major reasons. First, as noted above, the Fed Model missed the stock market crash of 2008/2009. Second, the current bond yields are suppressed due to the central bank's asset-purchasing program. Thirdly, due to the corporate capital structure, the market's forward earnings are more closely related to the after-tax corporate bond rate versus the 10-year treasury yield, suggesting an adjustment to the Fed Model.

Part 1: Missing The Great Recession

The Fed Model clearly suggests that the market was undervalued at the end of the 2002-2007 bull run. While the global financial crisis led to widespread bank failures and destroyed asset prices, perhaps the Fed Model should be given some credence.

If the market was not influenced by artificially higher home prices, the stock market could have been undervalued as no crisis would have occurred. If these earnings were based on unsustainable lending practices and sky-high real asset prices that threatened bank solvency, clearly the market would be at risk regardless of stock valuations.

In another example, if the S&P 500 was trading at 10 times forward earnings today, most anyone would state the market is undervalued. If a large disaster occurred, such as a new deadly plague that ran rampant in the U.S., the market would suffer.

In closing the valuation argument, it could be said that the Fed Model of valuation is very accurate, less economies based on unsustainable growth or a black-swan event. In the 2007 miss, the combination of both occurrences led a recorded undervalued market, in terms of the Fed Model valuation tool, to subsequently crash.

Part 2: Artificial Bond Yields Suggests Market Not So Undervalued

With the central bank's asset purchasing program in place, an artificial demand has constrained bond supply and thus arguably lowered yields below the natural market clearing price. As such, bond yields are suppressed and potentially higher rates should be accounted for.

In the Fed Model, the equation is

E/P = Y10

With the variables defined as:

E = Forward Earnings Estimate of S&P 500

P = Price of S&P 500

Y10 = Yield of 10-Year Treasury

Using the December 18, 2013 S&P 500 closing price of 1,810.65 and a 2014 earnings estimate of $122.29 per share, the forward earnings yield (E/P) of the S&P 500 is 6.75%. With the 10-year treasury yield at 2.88%, the equation to unlock valuation is:

(Y10 - E/P)/(E/P) = V

Valuation at these levels is -57.33%. When keeping E/P constant while adjusting Y10 for higher rates, the following metrics rate market valuation as follows:

Fed Model Valuation Analysis 12-18-13

DateS&P 500 E/P10-Year YieldFed Model
Current 12/18/136.75%2.88%-57.33%
Projection 3.75%6.75%3.75%-44.44%
Projection 4.5%6.75%4.50%-33.33%
Projection 5.25%6.75%5.25%-22.22%

If the Fed Model is given credence and a 10-year treasury equilibrium price is 4.5%, the market is still undervalued by over 33%, which would suggest a current valuation of over 2,717.

Part 3: Adjusting The Model For The Corporate Capital Structure

According to the Capital Structure Substitution Theory, public companies manipulate the capital structure to maximize earnings. As such, corporations adjust dividends, stock repurchases, stock offerings and debt offerings to maximize corporate valuation.

In other words, corporations adjust dividends, stocks and bonds to optimize the capital structure. With this in mind, the forward earnings yield would then revert closer to the after-tax corporate bond rate, thus eliminating the need to measure valuation with the 10-year treasury yield. In this regard, the adjusted model would be formulated as follows:

E/P = R[1-T]

With the variables are defined as:

E = Forward Earnings Estimate of S&P 500

P = Price of S&P 500

R = Corporate Bond Rate

T = Corporate Tax Rate

To measure the S&P 500, R will equal the Moody's Baa (investment grade) corporate bond yield, which is 5.38% (this is slightly higher than aggregate weighted S&P 500 corporate bond yield, which will lead to a slightly conservative ranking).

As the current maximum U.S. corporate tax rate is 35%, T equals .35.

After computing for R at 5.38%, which is a 250 basis point premium to the 10-year yield of 2.88%, the market is undervalued by 48%.

Debunking Contemporary Criticism

To adjust for a rise in rates, the following Fed Model and adjusted Fed Model valuations are used in conjunction with investment-grade corporate bonds maintaining a 250 basis point yield premium on the 10-year. Also, this assumes a constant S&P 500 earnings yield of 6.75%.

Fed Model Valuation Analysis 12-18-13
DateS&P 500 E/P10-Year YieldBaa YieldFed ModelAdjusted Fed Model
Current 12/18/136.75%2.88%5.38%-57.33%-48.19%
Projection 3.75%6.75%3.75%6.25%-44.44%-39.81%
Projection 4.5%6.75%4.50%7.00%-33.33%-32.59%
Projection 5.25%6.75%5.25%7.75%-22.22%-25.37%

Conclusion

Since 1997, the Fed Model has been used to determine the value of the stock market by noting the relationship between the S&P 500 forward earnings yield and the 10-year treasury yield. According to this model, the S&P 500 is fairly priced when its forward earnings yield is at equilibrium with the 10-year treasury bond yield. At current levels, the S&P 500 is 57.33% undervalued according to this model.

To adjust for the capital structure substitution theory, where the after-tax corporate bond yield replaces the 10-year treasury yield, the market is undervalued by 48.19%.

Both models could be discounted for two reasons: the failure to miss the global financial crisis and a current bond yields that are artificially suppressed due to the central bank asset purchasing program.

Regarding the global financial crisis, stocks may not have been overvalued. Earnings were based on unsustainable lending and overvalued real assets, specifically property. This suggests that a black swan event, which clearly could have been foreseen in hindsight, crushed an already-undervalued market.

In regards to suppressed bond yields, projected treasury yields of 3.75%, 4.5% and 5.25% were inserted into the model's algorithm. Both models suggest that the market would still be undervalued at the S&P 500's 6.75% forward earnings yield.

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By projecting alternate clearing prices for the 10-year bond, the valuation would be based on the investor's view of what bond price would actually be at equilibrium without central bank intervention.

Using a 4.5% 10-year treasury yield, both models suggest the market would be undervalued by close to 33%. This translates into S&P 500 levels of 2,717.55 (fed model) and 2,687.69 (adjusted fed model with 250 basis point corporate yield risk premium versus the 10-year treasury yield).

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At 4.5%, the fair value forward P/E ratio of both models would be 22.22 and 21.97, respectively. Currently the S&P 500 forward P/E ratio is 14.81.

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To make a move to S&P 500 fair valuation, assuming this model works and using a 4.5% clearing price on the 10-year and a 250 basis point yield premium on the Baa level of corporate bonds, the market would need to rise 48.4% to 50.1% from current levels to meet fair value.

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Rather than claim the Fed Model is correct and the market is undervalued by 57%, the intelligent investor could adjust the model according to the capital structure substitution theory and higher bond yields.

When projecting a 4.5% clearing price yield on the 10-year treasury bond and an investment grade 250 basis point yield risk premium, the fair price of the S&P 500 would be 2,686. This level would imply a forward P/E ratio of 21.97 and entail a 48.4% upside from current to fair valuation.

Source: Fed Valuation Model: Stocks 57% Undervalued