When you overestimate earnings by 20% and the growth rate of earnings by two or three times, it is easy to make stock prices look reasonable. Using measures of valuation that have stood the test of time shows stocks are overvalued and the best measure of valuation I have found says they are more overvalued than at the peak in 1929. However, in the short term, momentum trumps valuation and even though stocks are priced high they could continue going up. When momentum exhausts itself, stock prices will fall far below where they are now.

The preferred measure to show stocks are cheap is a PE (price earnings ratio) based on forward or estimated operating earnings. While the concept of using operating earnings to value stock is reasonable and theoretically better than actual or "as reported" earnings, in practice a PE using operating earnings has developed a blatant bullish bias that masks overvaluation. First of all, operating earnings have become a tool used to avoid showing an increasing share of expenses. In addition, the forward estimates are unrealistically rosy. Finally, what seems today to be a favorable level of valuation is measured against a short history in which U.S. stocks were well above normal valuations.

Operating earnings exclude certain expenses, for example, losses from a line of business that is not continuing. When they were first calculated back in 1988, operating earnings were about 1.5% higher than as reported earnings. In the first 12 years, operating earnings averaged 10% higher than "as reported" earnings. In the last 12 years they have averaged 21% higher. It seems with each recession, when earnings turn down, companies are figuring out how to exclude more expenses from operating earnings. Consider the progressively larger gaps (in the chart below) between the green line showing operating earnings and the black line showing actual earnings that occur around recessions.

By excluding an increasingly large share of expenses, the best fit growth rate through operating earnings is 6.5% vs. 5.2% for as reported earnings. Forward earnings really bring out the rose colored glasses. Forward earnings estimate growth at 14% to the end of 2013 for operating earnings and 16% for "as reported." These estimates are roughly in line with earnings growth that occurs during an expansion. However, estimated growth rates appear to ignore declines. On the eve of the big drops that began in 2000 and 2007, the estimates were still indicating 10% to 20% forward growth.

"As reported" earnings have a much longer track record; plus there are reconstructed estimates back to 1870.

The graph above shows the modern trend in earnings (green line) beginning in 1937. I use 1937 because I think this is when the modern trend of inflation began. However, calculating the best fit growth rate from 1950 gives virtually the same line. Obviously, "as reported" earnings growth has slowed since the best fit rate was 5.2% in the last 24 years, but was 6.1% for the whole period since 1937.

The rate of earnings growth in addition to being influenced by the strength of the economy is also affected by inflation. Looking at real or inflation adjusted earnings probably shows a more accurate picture of business strength.

In the last 75 years, real earnings have annualized growing about 1.9%. This is still faster than the previous period, but the difference in growth rate is not near as obvious as in the nominal earnings.

Robert Shiller uses a 10-year moving average of real earnings to calculate what is often called P/E 10. I have started using a simple exponential smoothing (ses) to calculate what I call PEses. Here is the inflation adjusted earnings with the two methods of smoothing the earnings.

A note about calculating real earnings: Shiller calculates real earnings with a CPI base of the most recent earnings so that real and nominal earnings are equal for the latest earnings period. The charts above use the CPI base year so that real and nominal earnings are equal in mid-1983 when CPI equals 100. As long as the same base is used to adjust both price and earnings, the calculation of the PE is the same regardless of the CPI base used.

Here are the three PEs discussed above.

The PE based on the average S&P 500 price in January and trailing operating earnings (orange line) was 15.2, near the low range of its 24-year history. If the last 24 years were normal, we could conclude the 15.2 PE was a sign the market was a good value. The last 24 years were not normal. The P/E 10 averaged 72% higher in the last 24 years than it did in its history prior to 1988. PEses averaged 81% higher during the time operating earnings have been available than prior to operating earnings. It seems likely that if a PE based on operating earnings had a 130-year history that it also would have averaged much lower prior to 1988.

The best that can be said for stock valuation right now is that stocks look cheap compared with the most overvalued period in history.

The importance of measuring value with PE comes from its indication of return in the future. If you buy at a high price, the future return is limited. If you buy low the future return is high. A note to the reader: all references to stock market return in the rest of the article refers to the total real return, which includes change in price of the S&P 500 with reinvested dividends and adjusted for inflation using the CPI. The change in price is calculated using monthly data points, which are the average of the daily closing prices for that month.

Shiller shows an interesting relationship in his book "Irrational Exuberance" between the P/E 10 one month and the return on the S&P 500 over the next 10 years. Here is an updated look at that relationship.

In the scatter plot on the left, each point represents a P/E 10 one month and the total real return over the next 10 years. The blue downward sloping line is the best fit of the data and shows that when the P/E 10 is high, the return in the next 10 years is likely to be low and vice versa. For example, the lowest point on the chart shows the stock market annualizing a loss of 5.9% from March 1999 to March 2009 and a P/E 10 of 41.3 in March 1999. This same data is shown on the time-series plot on the right. The black line shows the return for 10-year periods. The last point on that line shows that in the 10-year period ending January 2013 the market annualized returning 4.7%. The blue line is the inverted P/E 10. Note the inverted blue scale on the left side of the far right axis. The last point on the blue line shows the P/E 10 at 22 for January, 2013 and suggests the market will annualize a real total return of 3.7% during the next 10 years.

The above correlation has a bit of a heteroscedasticity problem in that high returns all begin with low P/E 10s, but low returns begin from a much wider range of P/E 10. This problem may be that valuation more reliably affects return over a 15- to 20-year period than over a 10-year period. Here is a chart that shows the correlation between the P/E 10 and the real return over 17-year periods.

This correlation is stronger and more consistent. The conclusion is worse implying the stock market will only annualize a 2.6% return during the next 17 years. The chart also implies the brunt of the peak overvaluation from December 1999 will be felt in the next four years.

The implications of the PEses (below) are even worse implying the stock market will annualize a loss of 0.1% the next 17 years. The PEses for January was 37.8 and shows the greatest overvaluation since May 2008. It is not as overvalued as it was in August of 1965 from which the market annualized losing 1.1% to August of 1982. It is more overvalued than the peak in 1929 from which the market annualized returning 0.3% to September 1946.

PEses appears to be a better measure of value than P/E 10. The R-squared is higher suggesting that about 66% of the variation in real return over 17-year periods is explained by the PEses at the beginning of the period, where only 53% appears to be explained by the P/E 10. The high degree of smoothing in ses earnings makes them much more consistent with the long-term growth rate in earnings than the 10-year average. I believe the stronger correlation with future return comes from being more consistent with the long-term growth rate in earnings. The ses earnings are roughly as smooth as a 50-year moving average would be, but responds quicker to a change in the direction of earnings. For example, after earnings turned up from the great recession the 10-year moving average took six months longer to turn up than the ses earnings.

A few years of either strong or weak earnings throws the 10-year moving average further off the long-term trend of earnings than it does the ses earnings. This deviation from the long-term trend is why the P/E 10 over-estimated how bad the market would be from 1929 to 1946 and under estimated how bad it would be from 1965 to 1982. The PEses was spot on for these periods. The P/E 10 currently suggests the stock market is overvalued, but not to the degree of the PEses. Based on the history I expect the return in the next 17 years to be closer to the PEses estimate.

The linear best fit (green) line from the scatter plot suggests the record PEses of 65.7 from December 1999 will correspond with the real total return annualizing an 11.5% decline for 17 years, or a total loss of 88%. If this were to happen there would be about an 80% decline in the next four years.

It is probably not wise to ignore a correlation with an extraordinary 130-year record, nor is it wise to assume a relationship continues beyond the range for which it has been tested. The PEses and the return in the following 17 years has demonstrated a relationship when the PEses is between about 7 and 39.7. However, we don't yet have data to know the nature of the relationship with a PEses above 40. The relationship could remain linear as the green best fit line suggests, but for all I know it could become curvilinear and be something like the red curved line in the chart above. If the red curved line proved accurate the real total decline from present levels would be about 50%.

The PEses was 39.9 in January 1997, which is almost within the range of historical precedent. This implies the 17-year period ending in January 2014 would annualize losing 0.94%. This would be consistent with the market dropping 55% in the next year.

At this point, it is good to remember that PEses is not a timing tool and that conclusions from it are likely to be off by two or three years. In a one-year time frame, momentum can easily trump valuation and a new nominal all-time high for the S&P 500 (SPY) is not out of the question.

Even so the market is at extreme levels of valuation where reversion to the mean will probably mean dramatically lower prices sometime in the next one to four years. The current PEses is higher than 92% of its history and higher than 99% of the history prior to 1996.

The 17 years ending January 2013 annualized returning 4.7%, or 3.1% more than the PEses estimated 17 years ago. Beating the estimate this much or more has only happened 5% of the time. In the past every time a 17-year period significantly outperformed the estimate, the market declined enough in the next few years to again return the estimated amount. This may be another indication that market performance has been at the upward extremities of what is normal.

Current valuation only looks reasonable compared with the last 20 years or so. The prevalent use of a PE ratio based on operating earnings with its limited history contributes to valuation looking reasonable. I consider the valuations of the last 20 years that peaked in late 1999 to be the result of a perfect storm where demographics, economic growth, interest rates and inflation all reached their optimal levels for stock valuation at about the same time. I believe this storm is unwinding and will have completely unwound before the end of 2016. In this unwinding I expect PE ratios of whatever kind to return to historical lows such as happened in 1982 or even 1932.

In determining whether current stock prices are high or low it seems prudent to use the measure that has the best historical record and not a measure with a limited history and an obvious bias.

**Additional disclosure:** There is no guarantee analysis of historical data their trends and correlations enable accurate forecasts. The data presented is from sources believed to be reliable, but its accuracy cannot be guaranteed. Past performance does not indicate future results. This is not a recommendation to buy or sell specific securities. This is not an offer to manage money.

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