# Stock Cycles

By: Michael A. Alexander | Sat, Jul 15, 2006

Progress of the secular bear market: position as of June 30, 2006

The value for R is 1380 as of June 2005. For S&P500 of about 1250 this gives P/R of 0.91

Stock Cycles Primer, Part II: Price to Resources (P/R)

In part I, we saw evidence for the existence of a long-term cycle in stock market returns.¹ A pattern was seen in which stock returns shift from high to low and back to high again over a 26-year period. I introduced the concept of valuation by simply defining markets that produce subsequent good returns as "undervalued" while those that produce bad returns are "overvalued". I then simply stated that the market in early 2000 was overvalued according to a valuation model I had developed and used the record from previous "overvalued" periods (as indicated by the model) to project the probabilities of various future returns. The story told was bad, it said an investor in early 2000 should get out of stocks completely as investments made at that time would be unlikely to outperform money market funds for the following 20 years.

In this installment I will present the valuation model I employed to make the projections in Part I. I call this valuation model P/R. it is the ratio of the index value (P) to what I call business resources (R). Business resources are simply the things (plant, equipment, technical knowledge, employee skills, market position etc.) available to the business operator that can be employed to produce a profit. For a broad-based index, the value of R is estimated as the sum of retained earnings in constant dollars as given by equation 3.1:

Eq 1.  R  =  R0  +  ∑ rrEi

Here rrEi stands for the real retained earnings in year i. That is, it is the difference between what the stocks in the index earned collectively in year i and the dividends paid out in that year, expressed on a constant-dollar basis. R0 is the value of R in some basis year. For example, R for the S&P500 in January 2002 was about 1140 (in 1999 dollars). Of this value, \$1070 represents the sum of rrE for 2001, 2000, 1999, 1998, 1997 all the way back to 1871 (all expressed in 1999 dollars). The remaining \$70 represents the value of R in 1871 (R0).

In general, retained earnings are used to purchase plant and equipment, new product lines, technology, new markets, etc. In short, retained earnings purchase the environment necessary for employees to produce profits. Without this environment, no profits could be made and the business would have no value. This environment consists of items, both tangible (office space, machinery, land) and intangible (customer relationships, brand names, managerial systems). The price of these items, like other real things, rises with inflation. This is why we estimate resources by summing previous retained earnings expressed in constant dollar terms. The focus of R is on the real environment used by workers to produce profits, not on the quantity of money that was invested back into the business, as in an accounting book value calculation.

The underlying meaning of R is subtle. Some resources are physical assets such as plant and equipment, natural resources, or land that can be counted and will show up on a balance sheet. However, most of R resides in the technical and business knowhow of workers. A company in a declining industry provides an environment less conducive to profit generation than a company in a rising industry. The declining firm becomes less able to attract and retain high-caliber employees, and loses R as a result. Companies in rising industries gain increasing numbers of talented employees and gain R. In a way the new employees bring a little R with them when they join a company.

New employees are not blank slates. They can already communicate and process information. Often they already have specialized functions and knowledge bases. That is, they are an asset (they have some R) that produces a return as well as being labor. Now where did they get this R? They got it as part of the cultural transmission they received from the previous generation. The quality of this transmission is a function of the richness of the cultural milieu in which this worker was raised. The richer the milieu, the more R. As a result of the accumulation of past retained earnings, companies grow and pay increasing wages to workers, which makes society richer over time. The richer society provides an ever-improving cultural milieu for the next generation. Hence, successive generations usually have more R than the previous generations. For example, the hard-to-explain tendency for population-average IQ scores to rise over time can be interpreted as an effect of increasing R over time.

For example, today's autoworkers and other old-economy workers have reared a generation of computer-savvy children that will be real assets for the companies of the information age. They were able to do this because they worked in an environment (created by decades of accumulated retained earnings in the auto industry) that provided a higher standard of living than their parents had growing up. This higher living standard provided a richer cultural experience for their children than the experience their parents were able to provide for them. Hence, retained earnings by the auto companies produces R, which shows up in the workers of the next generation. If the car business remains strong they will continue to attract the savvy workers of this generation and will keep the R they created through retained earnings. If not, the young workers will go elsewhere and take the R with them.

Figure 1 Business resources (R) versus GDP per capita over time

So R is not conserved within an individual company. Companies on the rise can pick up "free" R, (i.e. R created by the retained earnings of other companies) while those in declining industries will lose R. On a society-wide basis, as long as there is a rising tide of cultural transmission to new generations, R is conserved. Hence if one looks at a broadly representative index, R should be conserved within the collection of companies inside that index. This is why equation 1 "works" for a broad-based index, but not for a narrow index or an individual company. The S&P500 index contains a set of the largest companies that are selected to be representative of the US economy. Collectively, the S&P500 companies carry out a substantial portion of the economic activity in the US. I assume that the S&P500 is sufficiently broad that R is conserved over time and equation 1 will give a good estimate for R.

The act of retaining (and investing) profits is what generates new R. This activity puts people to profitable work and increases productivity. Rising productivity produces rising income and a richer culture (more R) that is transmitted to the next generation. Once generated, R exists as part of the culture. It may eventually be used by a wide range of companies other than the ones that originally created the R. Recall that \$70 of the \$1140 of R today (R0 in equation 1) existed in 1871. This R0 was produced by companies before 1871. Almost all of these companies are gone today, but the R they created still lives on as part of the cultural legacy of the past.

What we are talking about by building up R is economic growth. The high standard of living we enjoy today is our cultural legacy from the investments (R accumulation) made by previous generations, just as the (higher) standard of living that our grandchildren will enjoy will reflect the investments made today. The standard of living can be measured by the real gross domestic product per person (GDP per capita). Figure 1 shows a plot of 33 times R versus real per capita GDP. Since the latter part of the nineteenth century R has tracked economic growth quite well. Since 1860 the rate of GDP per capita growth was 1.8% as compared to 1.9% for R. The index before the mid 19th century was comprised of only a handful of stocks, which were hardly representative of the economy as a whole. It is not surprising that R did not track economic growth as well then.

The stock index value is simply a price the market puts on R. All other things being equal, the index should rise at the same rate as R. Figure 2 shows that this is indeed the case. Figure 2 shows the value of the stock index in current dollars. The value of R was converted into current dollars and plotted in the figure. Finally the ratio of the index (P) to R is shown. Enormous fluctuations in this ratio (P/R) are apparent in the figure. These fluctuations reflect the long-term stock cycle. Figure 3 shows explicitly how the stock cycles show up in P/R. The market reached a record level of P/R in January 1999 and continued to move higher afterward. The high level of P/R in early 2000 suggested that the long bull market was nearing its end.

Use of P/R for valuation

In Part I, I used a new valuation tool to identify overvalued markets to produce estimates of the probability of future returns being below that of money markets. I concluded that prospects for stock returns beating money market returns were poor. The tool employed was a derivative of P/R. In this section we will see how P/R relates to the key idea of valuation of stocks in terms of their future performance. To start, we will consider, what is meant by "value" or, what is a stock worth?

Figure 2 Resources (R) compared to the index and P/R

Figure 3. P/R used as a measure of the stock cycle (annual averages)

Investors purchase stocks in order to make money. The more money an investor makes from a stock, the more that stock was worth when she bought it. That is, the value of a stock depends on what happens in the future. There are two ways in which an investor can make money from a stock. One is by collecting dividend payments. The other is by selling the stock to someone else at a higher price than what was paid for it. The value of a stock, then, is simply the present value of the two sources of money: future dividends and the proceeds from a future sale of the stock. By present value I mean the quantity of money that, if invested at a particular rate of return called the discount rate, would generate the same amount of money as the stock will. For example, suppose the stock will pay a dividend of \$1 next year. To generate this dollar next year we would need to invest ninety-one cents at a 10% rate of return right now. Thus, we say the present value of the \$1 dividend next year with a 10% discount rate is \$0.91. The present value for a series of n dividend payments made over n years is given by the following formula:

Eq 2.  PVDIV  =  ∑ divj • (1 + dr)-j   for j = 1 ton

Here PVDIV refers to the present value of the future dividend stream, divj is the dividend j years in the future and dr is the discount rate. The symbol ∑ means "sum of". The present value (PVS) of the future sale price (\$Sale) is the quantity of money invested today at the discount rate of return that will yield the sale price j years in the future. It is given by:

Eq. 3. PVS = \$Sale • (1 + dr)-j

The value of the stock is the sum of PVDIV and PVs. These equations are perfectly valid, but not very useful, as they require knowledge of the future price and dividend payments of the stock of interest, which of course, we do not know. We can use these equations to calculate the historical value of stocks (or stock indexes) based on future returns, which we do know for the historical stock index. We can call this quantity the "True Value" (TV) of the historical index based on future returns.

Figure 4. The stock index divided by its discounted-future or "true value"

Equations 2 and 3 were used to calculate TV for the stock index for the period 1802-1969. I chose a rather long period of 30 years for the investment time (n = 30) in order to minimize the effects of the business cycle on dividends and stock prices. \$Sale was simply the annual average of the index thirty years in the future. The long-term return on stocks (in constant dollars) over the entire period has been 6.8%. Thus, the discount rate used was 6.8% plus the prevailing inflation rate over the thirty-year investment period. The actual value of the market index was divided by the true value and the resulting ratio plotted in Figure 4.

Examination of Figure 4 shows that the market rarely prices stocks "right". At times, such as the 1940's the market underpriced stocks. Long term investments in stocks made at these times will yield average real returns higher than 6.8%. Other times such as the late 1920's and mid 1960's, the stock market overpriced stocks. Long term investments made during these times will yield average real returns lower than 6.8%. The propensity for the market to over or under price stocks is a consequence of the tendency of the long-term stock cycle that was discussed in Part I. Although this tendency has always been present in the market, it seems to have grown more extreme in the twentieth century as compared to the nineteenth.

A question naturally arises. Is there some way to estimate what the true value of the market is today? To use equations 3.2 and 3.3 directly we would have to wait thirty years to obtain future dividends and stock prices. One way to get around this would be to find a valuation method that can be calculated today that correlates with the true value for historical markets. Figure 5 shows P/R plotted along with Price/TrueValue (P/TV). There is a reasonable correlation; peaks and valleys in P/R and P/TV tend to coincide. There is less agreement between the absolute values of P/R and P/TV. P/R was fairly small at the 1960's market peak, yet the market was very overvalued then. We note that the P/R values before and after the 1960's peak were very low, much lower than in the nineteenth century. Relative to the "neighboring" values of P/R, the mid-1960's P/R was quite high. Using a relative value of P/R might be a more effective indicator of value.

Figure 5. Price to resources ratio (P/R) compared to price to true value ratio

To test this idea, relative P/R values were calculated by dividing current P/R by its average value over the previous cycle. This relative P/R was then plotted along with the price/true value in Figure 6. The correspondence between the price to true value and the relative P/R is excellent. The highest value of relative P/R prior to 1970 occurred in 1929, when P/TV was also at a maximum. The second highest value of relative P/R occurred in the mid-1960's (when absolute P/R was fairly low). P/TV was at its second highest level then. Both P/R and relative P/R indicate that the price to true value in the early 1980's was probably much less than one, indicating that stocks at that time were underpriced relative to their future 30-year performance. The enormous bull market since then is strong evidence that this was indeed so.

Another interesting observation is to compare the market in 1929 versus 1987. Both years were similar in that a massive bull market driven by disinflation was terminated by a stock market crash. Furthermore, the market was similarly valued in terms of P/E in both years, suggesting an equivalent degree of conventional overvaluation. In terms of relative P/R, the 1929 market was extremely overvalued. In contrast, the 1987 market was not overvalued in terms of relative P/R. In actual fact, the 1929 market was extremely overvalued, as shown by the extremely high price to true value. It required 25 years for the market to recover its 1929 highs. The performance of the market since 1987 strongly suggests that the 1987 market was not overvalued like in 1929, although we will not be able to determine a definitive answer to this question until 2017. Nevertheless, had one employed the relative retained earnings as a market value proxy one would have known to sell into the rally following 1929 crash, but to hold after the 1987 crash, which as it turned out, were the correct strategies for the long term investor.

The valuation model employed to identify overvalued markets in Part I was relative P/R The 200 months with the highest relative P/R in history were used as the sample of "overvalued" markets. Figure 6 implies that the market in 1999 was quite possibly more overvalued relative to future performance than it was in 1929, implying very dismal future returns. The behavior of the market since 1999 is consistent with this assessment.

Figure 6. Relative P/R versus Price / True Value over time

So far we have seen how long-term cycles in the stock market can be identified using P/R. We have also seen how relative P/R provides a good estimate for index valuation with respect to long-term future returns. That is, when P/R is high relative to is average value in over the previous cycle, returns over the next few decades will be lower than average. Similarly, when P/R is high relative to its average over a cycle, returns over the next few decades will be higher than average.

P/R is not the only valuation model that can be used to characterize long-term stock cycles. Another valuation model is the Q ratio originally developed by the late Yale economics professor James Tobin. Figure 7 compares P/R with Tobin's Q and shows that they are very similar. Particularly, the both define the same basic long-term stock cycle.

The Q ratio measures the ratio of the market value of factories and other corporate assets to their replacement cost. When Q is low, as it was in the late 1970's and early 1980's, companies tend to expand by acquiring other companies instead of building plants or buying equipment. When Q is high it makes better sense to build new assets directly. Obviously, if one can buy an asset more cheaply by buying the stock of the asset-owning company than buying the asset directly, the stock is undervalued. This is the basis of the use of Q as a measure of stock valuation. When Q rises much above one, stocks should be sold as being overvalued. Q is very similar to P/R. Both measure asset values on an inflation-adjusted basis and so it is not surprising that they show the same cycles.

Figure 7. P/R compared to Tobin's Q

Tobin's original presentation of his ratio only covered one stock cycle peak, in which Q indeed reached a value just over one before beginning a long-term decline. Thus, advocates of this ratio would be warning of an overvalued market in late 1993 as Q was approaching one. The enormous rise in the market after 1994 served to decrease interest in Q. In their recent book, Valuing Wall Street, Smithers and Wright extend the record of Q back to 1900, covering three previous secular bull market peaks. They found the value of Q at the 1960's peak (1.06) was the lowest of the three, with the highest (1.35) occurring in 1929. Thus, markets tend to rise significantly above one at major market peaks and so the Q value just below one in late 1993 did not necessarily signal a top in 1994, stocks could well rise further

Table 1. Trend changes in three valuation methods and the stock cycle defined by them
 P/R Tobin's Q Shiller's P/E Stock Cycle 1802 -- 1802 (P) 1815 -- 1815 (T) 1835 -- 1835 (P) 1843 -- 1843 (T) 1853 -- 1853 (P) 1861* -- 1861 (T) 1881 -- 1881 1881 (P) 1896 -- 1896 1896 (T) 1901 1906 (P) 1901 1906 (P) 1921 1921 1921 1921 (T) 1929 1929 1929 1929 (P) 1949* 1949 1949* 1949 (T) 1966 1968 1966 1966 (P) 1982 1982 1982 1982 (T) 2000 2000 2000 2000 (P)
*These dates represent the last of several lows, which was followed by a significant rise.

Figure 7 shows that P/R and Q closely track each other. There are a few differences; the most interesting was the tendency for Q to be higher than P/R since 1990. Tobin's Q focuses on the replacement value of a company's assets (less liabilities) or net worth, as its measure of what the company is worth. This measure places stress on tangible assets, for which a replacement value can be obtained. Intangible assets, such as goodwill, are not counted. To the extent that retained earnings are used to purchase intangible assets, R captures intangibles. With the development of the "information economy", a greater impact of intangible assets on the value of the stock market is to be expected. It is reasonable to think that net worth underestimates the true value of a business, and that Q might be "reading high" today. Part III of this series will present a detailed comparison of Q, P/R and Shiller's P/E, a third valuation measure, as to what they had to say in about market values in 1999-2000 and late 2002.

For the present we simply note that there exist other valuation models, like Tobin's Q that can be also be used to define the long-term stock cycle. Table 1 summarizes the turning points obtained from the three different valuation models. For these data, a composite stock cycle was obtained. This cycle averaged 26 years in length between 1802 and 1966, strongly suggestive that it was responsible for the 13 year cyclical pattern described in part I.

Figure 8. The real stock index with the secular bull and bear markets identified

The stock cycle consists of two opposing trends. The period during which valuation (be it P/R, Tobin's Q or Shiller's P/E) rises from a trough to a peak is called a secular bull market. Conversely the period during which valuation falls from a peak to the next trough is called a secular bear market. Figure 8 shows a plot of the S&P500 index and its precursor indices expressed in constant 1999 dollars. The turning points from Table 1 are drawn on the figure. From Figure 8 a second interpretation can be seen. Secular bull markets are times during which the real value of the stock index shows a rising trend. Secular bear markets are the period in between the bull markets, when the real value of the index is either flat or actually falling. Examination of the period around 1906 shows why 1906 and not 1901 was chose as the end of the 1896-1906 secular bull market. Although both Shiller's P/E and P/R peaked in 1901, the real index was significantly higher in 1906, hence the Tobin's Q date was used for this trend change. On the other hand, 1966 and not 1968 was selected as the top for the 1949-1966 secular bull market. This was done because the 1968 peak was not sufficiently high in real terms to represent a continuation of the bull trend.

The impact of secular trends on long-term investment performance is very great. To illustrate this, consider two investors, Mr. A and Ms. B. Mr. A is fully invested during the secular bear market periods whereas Ms. B is invested during the secular bull periods (see Table 2). All transactions occur in January, so Mr. A bought a hypothetical index fund in January 1802 and sold it in January 1815. Ms. B bought the fund in January 1815 and sold in January 1835, at which point Mr. A bought it again. This continues down until the present. The performance of the two investors is shown in Table 2.

Note that despite being invested for 95 years in lengthy chunks of time running from 8-20 years in length, Mr. A's overall return is barely positive in real terms. In contrast, Ms. B gains an average real return of over 13% for her 103 years in the market. Half of the time, such as the 1982-2000 period, index fund investors are in Ms. B's enviable situation. With an average return of more than three times the real interest rate, an index fund is always a better investment during a secular bull market than bonds or money markets. A rational strategy during the secular bull market is then to buy those stocks that are most strongly participating in the bull market, regardless of their price. The faster a stock is rising relative to the average stock (called the relative strength) the more the stock is worth. This observation has given rise to what is called relative-strength or momentum investing. The incredible performance of tech stocks (and especially Internet stocks) in the late 1990's can be seen as direct evidence of the popularity of momentum investing.

Table 2 Performance of investments during secular bear versus bull markets
 Mr. A (Secular Bear Markets) Ms. B (Secular Bull Markets) Period Duration Real Return Period Duration Real Return 1802-1815 13 2.8% 1815-1835 20 9.6% 1835-1843 8 -1.1% 1843-1853 10 12.5% 1853-1861 8 -2.8% 1861-1881 20 11.5% 1881-1896 15 3.7% 1896-1906 10 11.5% 1906-1921 15 -1.9% 1921-1929 8 24.8% 1929-1949 20 1.2% 1949-1966 17 14.1% 1966-1982 16 -1.5% 1982-2000 18 14.8% Overall 95 0.3% Overall 103 13.2%

The other half of the time, most recently the 1966-1982 and post-2000 periods investors are in Mr. A's frustrating situation. An index fund under these situations gives a poor return and may actually lose ground to inflation. This was the case in 1966-1982 and since 2000. Since the market has little, if any, uptrend during these periods, one might expect that momentum-based investment strategies will fare particularly poorly during these periods. It is the secular trends that cause the wide variation in returns seen over lengthy periods of time like 10 or 20 years. A 10-year period falling completely within a secular bull market will have high returns of 11-15%, whereas one completely within a secular bear market will show close to a zero return. Which return one receives then depends on the timing of the initial investment with respect to the secular bull and market markets. Secular trends also explain why the returns over the last few years of the 1990's were so good despite the high valuations on the stock market. Until the secular bull market ended, the trend was up and high returns were the norm. Since 2000, they have been spectacularly bad.

Adjacent secular bear and bull markets define the 18-37 year stock cycle (average 28 years) of stock performance. The returns over the entire cycle tend to be close to the long-term average return on stocks of 6.8% (Table 2). The combination of secular bull and secular bear markets largely cancel each other out, leaving the underlying long term trend.

Part III of this series will compare two common valuation methods with P/R and show why P/R is the best valuation measure.

References:
Alexander, Michael A., "Stock Cycles-June 2006" Safehaven, June 3, 2006.

## Author: Michael A. Alexander

Michael A. Alexander
Stock Cycles

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.