From the February low to the May close, the S&P 500 rallied 22%. However, in recent RealMoney sentiment polls, the bulls averaged only 25% vs. 75% neutral or bearish. Money-flow services such as Trim Tabs and AMG Data show only modest investments in equity mutual funds: inflows about $2 billion a week since April, about the same amount into bond funds, and $2 trillion sitting in money markets.

If you're a long-term investor, do you remain on the sidelines or do you put your equity allocations back to work?

To answer this question for my clients, I refer to several models of stock market behavior, including the ones we'll discuss in today's column.

This chart shows year-over-year changes in the S&P 500 since 1950. This time period encompasses what I call the "Modern Economic Era," including the Cold War, Korean War, Vietnam War, Gulf War, Iraq War, 1987 stock market crash, Sept. 11 attacks, resignation of Nixon, impeachment of Clinton and a host of other crises.

Despite all these events, the S&P 500 gained an average of 8.9% a year, not including dividends. About 75% of the time, year-over-year returns were positive.
Reversion to the Mean
S&P 500 Year-Over-Year Change Since 1950 -- 8.9% Average

The nearly unbroken streak of positive returns from January 1991 through October 2000, followed by nearly three years of negative returns, is aberrational. Even after the recent rally, the S&P 500 is still 10% below May 2002.


S&P 500 Since 1950
Source:

This chart shows actual results of the S&P 500 vs. two trend lines. After getting ahead of itself in the late 1990s, the S&P 500 appears to be about 40% undervalued, at least compared with the long-term trend.

It's instructive, however, to convert such graphs to log scales (which make similar percentage moves look the same).


S&P 500 Since 1950
Log Scale

This chart shows that the S&P 500 grew above trend for most of the 1950s and 1960s, then grew below trend for the following 20 years. Because the two above-trend periods were the great economic boom of the 1950s and 1960s and the Internet bubble of the late 1990s, it is quite conceivable that future growth in the S&P 500 will be less than the 8.9% average, more like 6% or 7% a year.

Fed Model

Simply examining long-term growth rates doesn't take into account changes in interest rates. The Fed model attempts to value the S&P 500 on the basis of the yield on the 10-year Treasury, combined with one-year forward expectations about S&P 500 earnings.


% Diference Between S&P 500 vs. Fair Value
Source: Economy.com

In this chart, we see that the last time the S&P 500 was as much as 40% undervalued was after the great bear market of 1973-4, which makes sense given that the recent peak to trough decline in the S&P 500 was about the same magnitude, and the Nasdaq fell by an astounding 75%. Even after the recent rally, this model estimates that the S&P 500 remains undervalued by 33%, assuming yields of 4.75% and could be undervalued as much as 50% if yields remain around 3.5%.

The two drivers are forward one-year estimates of S&P 500 earnings and estimates of yields on the 10-year Treasury. If you play with the Economy.com stock market calculator , you'll see that a 1% rise in interest rates reduces the valuation of the S&P 500 by about 10%, which is disturbing, considering that the yield on the 10-year is trading at a 43-year low. The valuation is reduced by 2% for every 1% decline in estimated earnings growth.

One of the interesting things about this model is that it confounds the theory of the efficiency of markets. Given arbitrage activity, I would expect the hypothetical value to hover around the actual value. Instead, we see long periods of overvaluation, followed by long periods of undervaluation. This makes sense to me only in terms of behavioral economics. Investors "remember" when they made money in stocks and overbought when stocks prices were high, and also "remember" when they lost money in stocks and oversold.


Tobin's Q
Source: Smithers, Wright -- Valuing Wall Street

Tobin's Q is a model which says that the value of the overall stock market should equal the replacement value of the publicly traded companies -- i.e. (Market capitalization) / (net assets - net liabilities) = 1. The 1970s and early 1980s was the era of the leveraged buyout because it was cheaper to buy assets than build them. As with other models, the peak divergence occurred around March 2000. Now that the ratio has fallen back to 1, this model indicates that the risk of investing in stocks has been reduced substantially but still may be high.
Ratio Stock Market Capitalization/GDP
Ratio Stock Market Cap to GDP -- Average 64%
Source: BiancoResearch.com

Like Tobin's Q, this model assumes that there should be some link between stock market valuation and something tangible -- in this case the gross domestic product (GDP) of the U.S. The ratio averaged 64% over the last 50 years, then tripled during the Internet bull market. Through the March GDP report, the ratio fell back to 91%, which implies that the S&P 500 is still overvalued by about 50%. The counterargument is that because a large portion of stock market earnings are now derived from overseas activities, perhaps this model needs to be adjusted to take into account world GDP.

Conclusions

These models don't tell you much for daytrading -- they're based on quarterly data points, after all. During the great Internet bubble, I began to doubt whether the models were still valid as, with each passing quarter, these models pushed higher and higher into the danger zone. However, the higher into the danger zone, the greater the bear market to follow. At this point in time, these models are saying "buy," which is why I'm taking my clients to "fully invested." But I'll be watching these models for the next time the values diverge from "low risk."
David Edwards is a portfolio manager and president of Heron Capital Management, a New York management firm. Edwards was a contributor to Harry Domash's Fire Your Stock Analyst: Analyzing Stocks On Your Own available at Amazon. At the time of publication, his firm was held no positions in the stocks mentioned in this column, though positions may change at any time. Under no circumstances does the information in this column represent a recommendation to buy or sell stocks. Edwards appreciates your feedback and invites you to send it to David Edwards.