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April 30, 2001

P/E, P/R and Irrational Exuberance
by Michael A. Alexander

Professor Robert Shiller of Yale University published his book Irrational Exuberance at the height of the NASDAQ mania last year. Shiller made the argument that stocks were overvalued and would produce poor returns for the next ten years or longer. The principal evidence he gave of overvaluation was a P/E ratio calculated by dividing the S&P500 market index at a particular time by the average of the index earnings over the previous ten years. This ratio is shown in Figure 1 by the red line. Four peaks are noticeable in the figure. They occurred in 1901, 1929, 1966 and 2000. Each of these dates immediately preceded a lengthy period of poor stock performance and Shiller predicted that the same would be true of the peak in 2000. Notice that the same cannot be said for ordinary P/E ratios calculated using average prices and earnings from the same year (black line in Figure 1). Short term P/E values often peak during recessions, such as 1896, 1921, 1933 and 1992, when earnings are temporarily depressed. These periods of high P/E are good times to buy stocks. By using a ten year average to smooth out the earnings, fewer peaks are seen and these reflect periods when stock prices are high following substantial bull market rallies.

Figure 1. Ten-year and one year P/E values over time

Figure 2 shows a comparison between the 10-year P/E used by Shiller as a valuation tool and P/R, which I use to identify secular market trends. Both methods identify the same long-term peaks in market valuation, although P/R shows a fifth peak in 1881 also. The recent bull market peak achieved higher levels of both P/E and P/R than any previous bull market peak. In order to use these ratios to identify market peaks (i.e. points of maximum valuation) one must compare the rising values as the bull market progresses with previous high levels. In January 1997 the ten-year P/E of the S&P500 surpassed the previous record set in September 1929. This implied that the stock market was very high and that a major long-term peak was imminent. Indeed, Dr. Shiller expressed his view that valuations were extremely high by historical measures in his testimony before the Board of Governors of the Federal Reserve System on December 3, 1996. In contrast to P/E, P/R did not surpass its old high (set in 1901) until January 1999.

Figure 2. Comparison of ten-year P/E values and P/R

P/R reached an all-time two years after P/E did. The impact of this two year difference can be illustrated by two hypothetical 401K investors: Mr. A and Ms. B. Following the PE warning, Mr. A moved his assets from an S&P500 index fund to a money market fund in January 1997, when the S&P500 was at 770. Following P/R, Ms. B sold her fund in January 1999, when the S&P500 was at 1210. Ms. B enjoyed two more years of 25% gains that Mr. PE missed, yet still was out of stocks during the crash. Furthermore, Ms. B has already had an opportunity to buy back into the index fund at lower prices (if she had wished to do so) and her 401K shows a larger balance at this time than if she had left it in the stock fund. This is not true for Mr. A. [In real life, I gradually moved my 401K from stock funds to 100% cash over late spring and summer 1999. Since last fall, I have reinvested half back into stock funds. This half is worth 15% more than it would be had I left it in stock funds after summer 1999. The other half remains in cash against possible further declines in the market below the April 4 low.]

These examples show how P/R gave a better indication of true market overvaluation (i.e. the stock index should be sold by long-term investors) during the recent bull market than did the 10-year P/E. This is important because premature warnings of an impending destructive bear market destroys the credibility of bearish analysis, as those who followed the warnings miss out on additional years of excellent gains. It was early calls of a top that helped make valuation-based arguments seem irrelevant and indirectly gave credence to the "new paradigm" arguments. Nevertheless, despite its premature warning, the ten-year P/E measure does do a good job of delineating the stock cycles. Figure 3 shows why 10-yr P/E functions similarly to P/R. The ten-year trailing average of earnings (the blue line in Figure 3) shows a steady rise over time that is parallel with R. Because of this parallelism, peaks in the P/E ratio will necessarily show up at the same place as peaks in R.

The ratio E/R is also shown in Figure 3. E/R can be thought of as a return on the business resources (R) available to business management. The way R is calculated (cumulative retained earnings) makes it similar to shareholder equity, except R employs a constant dollar basis while shareholder equity is denominated in nominal dollars. Just as the management effectiveness for an individual company can be assessed using the return on equity, the collective management effectiveness for all the companies in the index can be assessed using E/R.[1] Obviously, E/R will fluctuate with the business cycle. The graph of E/R in Figure 3 is a trailing ten year average of E/R, which mostly smoothes out the effect of normal business cycles. The effect of longer term cycles, such as the Kondratiev cycle (the driver of the stock cycle) can still be seen.

The smoothed E/R plot shows that return from resources declined from about 7% before WW I to a little over 4% after WW I. A given amount of R will produce about 40% less earnings it did a century ago. This implies that for equal peak market valuations (as measured by P/R), peak P/E values of today should be about 50% higher than those of the past. Thus, whereas in the 19th and early 20th century a P/E of 20 would be considered very high, today a P/E of 30 would be considered as equivalently high. This is the reason why P/R gave a closer prediction of the timing of the bull market peak than did 10 year P/E.

Figure 3. Smoothed earnings vs. R, and E/R compared to real interest rate

Comparison of E/R with a 50-yr trailing average of real interest rate shows that real interest rates have also declined with time. Overall, the returns businessmen have extracted from R are higher than real interest rates. This spread, which is sort of a "risk premium" for business investments relative to moneylending, was about 3% prior to WW I and about 2.5% for the fifty years after WW I. Over the last 35 years it has averaged around 1.5%. Real economic activities have gradually become less profitable relative to financial activities since WW I. This trend has accelerated since the 1960's.

Additional financial ratios involving R are presented in Figure 4. Here we see a 10-yr trailing average of owner income (dividends) from resources (D/R). Also shown is capital accumulation, or the real rate of growth in R. By definition, since R is simply accumulated retained earnings in constant dollars the rate at which R rises is equal to the difference between earnings and dividends divided by R, that is, (E-D)/R. As described in Stock Cycles, this growth rate in R is equal to the long-term rise in the stock index in real terms. It is also roughly equal to the long term growth rate in GDP per capita.

Note that while E/R and D/R have fallen over the last century, there has been no corresponding drop in the rate of capital accumulation. It has remained around 2% over the entire period in the figure. What this means is the drop in profitability of American business over the last century has had no adverse effect on the rate of growth of R. That is, it has not affected the rate at which stocks rise in price or the rate at which the economy grows. As long as E/R remains above 2% there will be no adverse effect on either economic growth or long term stock price appreciation resulting from a lack of capital accumulation. Figure 4 shows that the decline in business returns (E/R) has shown up as a decline in the income (dividends) available to owners of publicly-held businesses (i.e. D/R).

Figure 4. Earnings, Dividends, and Capital Accumulation with Real Interest Rate

So far we have seen that the decline in the rate of return from business (E/R) has had no effect on either real economic growth or real stock price appreciation. The primary impact of the decline in business profitability was a dramatic drop in dividend income (D/R). Consider, D/R has fallen from 1% above real interest rate in the 1871-1911 period to 0.6% below real interest rates[2] in the period since1960. Since dividends are responsible for the majority of long-term stock returns, one would think that a 55% decline in D/R would have resulted in a sizable decline in total return from stock investments. But this did not happen. The reason is the relevant dividend yield for calculating investor returns is the dividend divided by the stock index market price (P) not equity (R). That is, it is D/P that determines investor return, not D/R. We can express investor dividend yield as the product of dividend income from resources (D/R) and R/P, the reciprocal of P/R. The advantage of this formulation is D/R over long periods of time can be considered as roughly constant, just as is capital accumulation. This means that long-term stock return is almost solely a function of the prevailing level of P/R. The lower is P/R, the higher is the total return on stocks. Since investors collectively determine P by their bidding for shares on the stock exchange they control the total return they receive over the long run.

What this means is the long-term return on stocks is determined not from economic fundamentals, but rather by investor behavior, or perhaps we might say investor culture. An investor culture that demands high returns will manipulate P/R in such a way as to increase the returns available from even rather lackluster economic fundamentals (E/R). Let us consider the stock returns for the four decades after 1871 with those obtained during the most recent stock cycle (1966-2000). E/R averaged 7.1% in the 1871-1911 period, much higher than the 4.2% return seen over 1966-2000. As a result, dividends (D/R) averaged 4.8% from 1871-1911 compared to 2.0% over 1966-2000. But when we look at how investors priced the stock index we see that in the first period, P/R varied in a narrow range from 0.63 to 1.34, and R/P averaged 1.02. During the 1966-2000 cycle P/R varied from 0.27 to 1.46 with an average R/P of 1.79. Thus, we see than investors dramatically lowered the average market price of the stock index relative to R, without affecting its upper range. That is, the amplitude of the stock cycle grew much larger.

Long-term real capital gains return is roughly equal to capital accumulation, which was at 2.0% and 2.2% during the two periods. In the 1871-1911 period, a very high D/R of 4.8% was reinvested in a high-priced index, giving an average dividend return of 4.9%, that when added to the 2% capital accumulation gives a 6.9% long-term real return. For the 1966-2000 stock cycle, a much smaller level of D/R (2.0%) was reinvested in a lower-priced stock index giving an average dividend return of 3.6%, that when added to the 2.2% capital accumulation, gives a 5.8% long-term real return. In actuality, real return over the cycle was 6.8%, reflecting the rise of P/R from 1.07 to 1.46 that occurred over this period.

By reducing the average level of P/R investors were able to moderate the effect on investment return of a 40% drop in fundamental business profitability (E/R) to a mere 16% drop in basal long term return (from 6.9% to 5.8%). The 6.9% real return of a century ago was 3% above the average real interest rate. Similarly, the 5.8% real return for the modern stock market is also 3% above the average real interest rate. Thus, relative to the alternative, stocks produce the same basal return today as they did a century ago.

Stocks have maintained this 3% risk premium at the cost of the large swings in P/R associated with modern secular market trends. I should point out that while average P/R values were reduced, maximum values of P/R have not declined. On the other hand, the minimum level of P/R is much lower than it was before 1911. Cycle amplitude is vastly increased from what it was a century ago. Index investors today can actually lose money over a 20 year period if they pick the wrong points at which to buy (when P/R is high like in 2000) and to sell (when P/R is low like in 1982). Clearly long-term stock investing in the modern market entails much more risk than it did 100 years ago, yet stock investors receive no additional risk premium from their basal return.

Although the basal return from stocks over the last cycle was 5.8%, in actual fact, the S&P500 index returned 6.8% after inflation. The extra 1% came entirely from the "irrational exuberance" after September 1997, when P/R reached 1.07, its level at the beginning of the cycle. That is, during the last cycle stocks actually delivered a risk premium of about 4%, higher than the level in the19th century. To maintain this higher premium, all that is required is for the market to operate at a sufficiently low value of P/R during the next cycle. To accomplish this from current high levels of P/R will require a more powerful secular bear market decline than in the past. To generate a sufficiently powerful decline, stocks must first reach extremely high levels, from which a long confidence-destroying, multi-decade decline can then occur. The remarkably panic-free collapse of the NASDAQ in what is so far not even a recession, suggests that our present investor culture has developed a tolerance for a level of volatility beyond anything seen in 19^th century panics. Thus, we can say that the recent irrational exuberance served two purposes. First, it provided the extra return for the last stock cycle to bring it up to the historical norm. Second, it set the stage for the type of P/R decline necessary to maintain these high returns in the future.

[1] Provided the index is sufficiently representative of the entire economy, we do not have to worry about changes in index composition. (This is a subtle point and is discussed further in Stock Cycles). Based on successful application of R for the S&P500 it appears that this index meets this criterion (which is not all that surprising; the S&P500 index is intended to be representative and does contain the bulk of total market capitalization ). The NASDAQ index, for example, would not meet this criterion, despite containing far more individual stocks.

[2] For reinvested dividends/interest payments, dividend yields should be compared to real interest rates. When one reinvests bond dividends in a bond portfolio or simply accumulates interest in a bank account or money market fund, one reinvests into dollar-denominated debt instruments. The real value of these obligations will fall with inflation. When one reinvests stock dividends in a stock portfolio, one reinvests into equity (i.e. R) which is a real thing that retains its value against inflation. Thus, a 5% interest payment used to buy more dollar-denominated debt is a 5% nominal return because what one is buying is money (dollars). In contrast, a 2% equity (R) dividend used to buy 2% more equity (R) is a real return of 2%. For an inflation rate of 3%, a 2% value of D/R is equivalent to a 5% nominal interest rate. Even in the case when dividends and intrest payments are not reinvested, stock dividends can still be considered as a real return, whereas interest is nominal. The reason for this is that an interest payment will lose value to inflation, whereas a dividend payment will increase with time, more than keeping up with inflation over the long run.

Mike Alexander

Mike Alexander is the author of four books: (2000) Stock Cycles: Why stocks wont beat money market over the next 20 years; (2002) The Kondratiev Cycle: A generational interpretation; (2003) Retiring Rich: The ultimate IRA and 401(k) investing guide (now available in paperback under the title Investing in a Secular Bear Market) and (2004) Cycles in American Politics: How political, economic and cultural trends have shaped the nation.

Michael is not a registered advisor and does not give investment advice. His comments are an expression of opinion only and should not be construed in any manner whatsoever as recommendations to buy or sell a stock, option, future, bond, commodity or any other financial instrument at any time. While he believes his statements to be true, they always depend on the reliability of his own credible sources. Of course, we recommend that you consult with a qualified investment advisor, one licensed by appropriate regulatory agencies in your legal jurisdiction, before making any investment decisions, and barring that, we encourage you confirm the facts on your own before making important investment commitments.

Copyright © 2000 - 2008 Michael A. Alexander

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