When the stock market was reaching record new highs in 1999 and 2000, many stock valuation models began sounding the alarm, flagging what in hindsight proved to be an extremely overvalued stock market. However, most investors unfortunately chose to ignore this available information, believing instead that we had entered a "new economy," immune to past problems like long, painful bear markets.

Considering the extended rally of 2003, let's take a look at stock valuation using the so-called Fed Model to analyze the current market and determine whether it is under- or overvalued.

Fed Model Overview
Let's begin with a quick review of the basic valuation model popularized by economist Ed Yardeni who, in his own words, has dubbed it the "Fed's stock valuation model, though no one at the Fed ever officially endorsed it." This model compares two key benchmarks: the interest rate yield of the 10-year U.S. Treasury note and the forward operating earnings per share of the S&P 500 Index.

As you'll see, these variables can be tinkered with (i.e., substituted with others) to suit one's own subjective preferences regarding what works best for relative comparisons. (For example, some may substitute reported earnings or trailing earnings for the S&P 500 side of the ratio, or use a different interest rate yield in the numerator). That said, let's see what the Fed Model is telling us now and what it has indicated in the past.

The Fed model as of Nov. 14, 2003, despite a major rally off February 2003 lows, had the S&P 500 still well below fair value. You can seen in Figure 1 that the Fed Model shows the S&P fair value at 1,426.30, despite a rally of close to 30% from its 2003 lows to the latest level of 1050.35. In other words, the S&P 500 is still 26% below fair value, or undervalued by 376 points, as indicted in Figure 2.

At the historic market top of March 2000, it is worth noting that the model showed a fair value of 954.91 versus the actual closing high of 1,527.46. It's sort of like the cartoon character Wile E. Coyote, who remains suspended in midair for a few seconds before realizing he has run off the edge of a cliff. Oops!

After the major bear market plunges of 2000, 2001 and 2002, the model finally began to show the S&P 500 as undervalued. This occurred during the big swoon lower that started the summer of 2002 and continued into the month of October, as can be seen in Figure 2. But the rally of 2003 has made the S&P 500 considerably less undervalued than was the case in March this year (when the Fed Model showed the S&P 500 over 700 points undervalued). The S&P 500 remains, therefore, from a relative value perspective still a buy, according to the Fed Model. However, there are some underlying dynamics at work in the model's variables that lead to some interesting paradoxes.

Figure 1 - S&P 500 Fair value according to the Fed model\'s valuation
Source: MetaStock Professional

For example, note that the S&P 500 became more than 800 points undervalued in June of 2003, despite the major rally off the lows of March. At that point, S&P 500 fair value was over 1,800, according to the Fed Model, as can be seen in Figure 2. How could the S&P get so undervalued after it had rallied 25%? The answer can be found in an examination of the wild swings in the Treasury markets in the spring of 2003, with first a lower yield, then a reverse to a higher yield.

Economic Recovery
When it became clear to bond traders that an economic recovery was likely, long-term rates moved sharply higher, such as the Treasury 10-year note yield, which is one of the two variables in the Fed Model. Recall that the 10-year yield, however, first fell to 3.1% in June of 2003 which is what caused the spike higher in S&P 500 fair value as seen in Figure 1, despite the rally in the stock market. The yield promptly reversed course, though, and was just above 4.2% after getting as high as 4.6% in August 2003. While the S&P hovered in a trading range through most of that summer, the reversal lower again in the 10-year yield from the August highs drove fair value higher again to 1,500, with the S&P 500 getting 500 points undervalued despite climbing higher in September. This dynamic may explain why the bulls had an easier ride, since many asset allocation models are driven by Fed Model valuations or some variation of it, and that would indicate a shifting to stocks from bonds.

Figure 2: S&P 500 Overvalued and undervalued levels
Source: MetaStock Professional

Fed Model Usefulness
But is the model useful for the average investor? Taken on its own, the model could be problematic. Remember, all the Fed Model is telling us is that when the forward earnings yield on the S&P 500 (how much you would earn per dollar paid) is less than the 10-year bond yield (how much you make from holding a 10-year note), then stocks have gotten too expensive. In other words, it does not pay to hold stocks because you can earn more in a Treasury bond with less risk. Conversely, if the earnings yield on the S&P 500 is higher relative to the 10-year note yield, stocks are said to be undervalued; that is, investors are at least being compensated for taking on the greater perceived risk of stocks.

However, even if stocks still look "cheap," when we take a look at absolute value comparisons, such as the earnings yields of the S&P 500 relative to past levels, we get a very different story.

Take a look at Figure 3 below, which contains the historical reported earnings to price ratio of the S&P 500.

Figure 3: S&P 500 Earnings-to-price ratio with mean and standard deviations
Source: MetaStock Professional

Big secular bull markets begin when the earnings yield is substantially above its long-term average, preferably two standard deviations above. But as you can see from Figure 3, the reported earnings yield was considerably below its average at this point (on a reported basis at 3.29), not only a level below its long-term average, but one that preceded the long bear market that began in the late 1930s and continued into the early 1940s.

This pattern suggests that bullish investors may be in for another painful lesson about markets.

The Fed model can give us a sense of the current valuation of the market, but its timing can be problematic for investors who are seeking to avoid major losses in their stock portfolios.

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