# Stock Cycles

**Progress of the secular bear market: position as of May 31, 2006**

*The value for R is 1370 as of May 2005. For S&P500 of about 1280 this
gives P/R of 0.93*

**Stock Cycles Articles on Safehaven**

Beginning in 2001 I have written sporadic articles on a variety of financial topics on Safehaven. Over the last three years I have been writing a regular monthly article for 21st Century Investors that I called Stock Cycles. Because of financial difficulties 21st Century has dropped my column and I now plan to continue Stock Cycles on a more or less monthly basis here at Safehaven. Each month I presented an updated figure showing the current progress of the secular bear market in terms of my price-to-resource measure (P/R). The article then followed. The article usually presented information described and explaining certain historical cycles that I believe may impact the investment environment today.

My approach to cycles will be scientific and historical. There are few hard conclusions. An example of the approach is shown by the graph at the beginning of this article. This graph shows a plot of P/R for the current secular bear market and four previous ones. The present value for P/R is given. This graph shows about where we are today compared to previous times. I used a graph like this in late summer 2002 to conclude that the first bear market of the secular bear market was probably drawing to an end.¹ I wrote up the contents of this post and published it on Safehaven in October 2002.²

Today we see that this idea was pretty good; a new bull market did get started in October 2002. Thus, the story told by other valuation tools was too bearish. Reliance on those tools would have one conclude in August 2002 that the market had much further down to go. Yet an S&P500 index purchase at the average price for that month (912) looks like a reasonably good long-term position to have obtained. Even better would be the ~880 level at which the S&P500 traded on the day after my article appeared on Safehaven.2

Over the next several months I will present a primer on the concepts behind P/R in the form of a five article series. I may break the series with articles on other topics if developments warrant. I also plan to expand the topics of consideration of energy issues which I believe will be a topic of increasing interest over the next few years.

__Stock Cycles Primer, Part I: Introduction__

Figure 1 shows a plot of the total return that one would have obtained in
a hypothetical index fund over the last two centuries. The values are all shown
in terms of constant 1999 dollars, that is, the value is adjusted to eliminate
the effect of inflation. The value of the investment is shown on a *logarithmic* scale.
A fixed distance on this scale corresponds to a fixed percentage gain. Looking
at the figure you can see that multiples of ten are spaced equally apart. The
straight-line appearance shows that the stock market has tended to give the
same percentage return, on average, over the long haul. Since 1802, a stock
investment would have grown more than 500,000-fold, equivalent to an average
annual return of 6.8% after inflation. This 6.8% real return, when combined
with the average inflation rate of 3% during the 20th century, shows that stocks
have returned about 10% over the long run. This is far more than the return
available on money markets or from bonds. It is this long-term superior performance
that prompts financial advisors to recommend stocks over cash or bonds as an
investment.

Close examination of Figure 1 shows that the actual record does deviate from the trend line. In the context of the entire 200-year trend these deviations seem small, and indeed, the long-term trend does dominate over a sufficiently long time. But none of us is going to live for 200 years. If we restrict our view to shorter periods, there are clearly times, such as the period between 1982 and 2000, when returns were very good. Similarly, there were periods, such as the 16 years before 1982, when returns were rather poor.

*Figure 1. Total return on a hypothetical index fund over time (1999 dollars)*

It would appear that stocks aren't always the best investments. When I was a teenager in the late 1970's I looked into possibility of investing my college savings in mutual funds to get a better return than from my bank savings account. I went to the library and researched annual returns over the previous ten years. To my surprise, I found that the average mutual fund had returned about 3% over the previous decade, less than a savings account and less than inflation. The very top fund returned less than 12% over that decade (about 6% after inflation). This was hardly impressive.

This situation changed in the early 1980's and by the end of the 1990's, stocks had been rising strongly for almost two decades. When I was writing Stock Cycles in early 2000 the market was still going up. Were the 1970's just an anomaly, never to recur? If so, perhaps a stock index fund really is a sure-fire investment. On the other hand, if stocks are guaranteed winners, why is there a debate at all? Could all this good performance over the last 18 years be followed by a lengthy period of bad performance? If this is the case, is a stock index fund really the best retirement investment in early 2000?

__A statistical treatment of stock returns__

Rather than just noting that stocks go up in the long run as shown in Figure 1, what we really would like to know is the probability that stock investments made now will be profitable. We might be able to gain insight by compiling a list of past returns and recording the frequency at which various returns occurred. The following analysis was performed in early 2000 and is repeated here to show what historical analogy had to say in early 2000 about future stock returns.

The data in Figure 1 were used to calculate total returns over successive one-year periods starting with January 1802 to January 1803 and ending with December 1998 to December 1999. There are 2359 such periods (the market was closed for four months in 1914). Similarly, total returns were calculated for successive five-year periods starting with January 1802 to January 1807 and ending with December 1994 to December 1999. The same thing was done for ten-year periods and twenty-year periods. The returns for each holding period were ranked in order of return and the values plotted against the percentile frequency in Figure 2. Note that Figure 2.2 is scaled to show returns between -10% and +25%. A significant fraction of the one-year returns are outside this range and do not appear in the figure.

*Figure 2. Probabilities of various real returns over 1, 5, 10 and 20 year
periods*

Figure 2 is interpreted as follows. The vertical axis gives total annualized
returns after inflation for various holding periods as a function of probability.
On the horizontal axis is the probability that the return will be equal to
or better than the value given by the curve. For example, the last five years
have shown an average annual return of more than 20%. What is the probability
that the next five years will show a real return of 20% or greater? Consulting
Figure 2, we find the dashed horizontal line representing a 20% return and
follow it along until it intersects with the five-year line. The intersection
occurs at a percentile value of about 4%. This means there was a 4% chance
that we could have seen five more years of 20% or better returns. Another interesting
exercise is to determine what are the chances of actually losing money to inflation
in a stock index fund over the next one, five, ten or twenty years after 2000.
Proceeding as before, we find the 0% return line and follow it along, noting
the percentile values at which each curve is crossed. Over a single year there
is a 70% chance of an index fund giving a positive return. By holding for five
years, the odds of success rise to 85%. For ten years the odds exceed 90%.
Finally, there is a 0% chance of losing money over a 20 year period; a negative
real return over a 20 year period has *never* happened in all 2131 such
periods over the last 198 years.

A useful way to use this figure is to consider the probability that a stock index investment will outperform a money market. In January 2000, money market funds were yielding about 5%, and the inflation rate was about 2.5%, meaning that money markets were returning about 2.5% after inflation. What we would like to know is how often will this safe 2.5% real return beat the return available from a randomly-placed stock index investment? To do this we consult Figure 2 and follow along a 2.5% return line. The intersections give the results: 63% over one year, 74% over 5 years, 82% over ten and 93% over twenty years.

As Figure 2 shows, stocks beat money markets most of the time over all the holding periods. The longer the period, the higher the chance of stocks beating money market funds. This is not surprising. The long-term trend in Figure 2 becomes more dominant as holding time increases and the return necessarily shifts to the mean. Since this mean is more than twice the money market return, stocks must necessarily beat money markets if they are held long enough. This is why financial advisors urge substantial investments in common stocks. It is also why stock market experts say now is the best time to invest. When they say this they don't mean that by investing now you will get the best return possible, but rather, that the odds of a good return are better with stocks than any other investment.

Is this always true? The assumption behind the above statement is that all periods are alike. Although periods of good and bad performance do occur, they are unpredictable and random, hence your best bet is to go with stocks, especially if you have a long time in which to invest, since the odds improve with holding time. If stock returns are random, we should expect the range of returns depicted in Figure 2 to be scattered randomly. That is, in any given time interval we should expect all sorts of returns to occur. It turns out that over the short run (weeks to a few years) stock returns do appear to be random. But over longer periods a pattern in stock returns can be seen.

Let us expand on this idea. If stock returns are random, we should expect periods of above and below average performance to appear randomly, like flipping a coin. What we can do is determine is calculate stock returns over sequential periods of a particular length and then note whether the return is above or below average. For example, we can look at ten-year returns by calculating the total return from 1802-1812, 1812-1822, 1822-1832 and so one. We then compare the return to the long-term average of 6.8% and denote whether it is above or below the average.

This is equivalent to carrying out a series of coin flips and noting the *sequence* of
heads and tails obtained. The sequence is then examined for signs of non-randomness.
For example, if we flipped eight coins in sequence and got the result HTHTHTHT,
THTHTHTH, TTHHTTHH or HHTTHHTT we would be surprised. Strictly alternating
patterns like these are unlikely. The probability of any of these patterns
arising from eight random coin flips is 1 in 64. A similar unlikely pattern
in stock returns from sequential periods would also suggest non-randomness.

Stock returns were calculated over sequential periods 9 to 20 years in length. For each return in sequence it was determined whether it was above (heads) or below (tails) the median value. The results of this assessment were recorded in Table 1. For example, consider the first entry for 20 years. There were 10 sequential 20-year periods. The return during the first twenty-year period was below median and so it is marked as a tails (T). The next return was above average and so it is marked as a heads (H) and so on to give the sequence THTHTTHHTH. In each sequence in Table 1, special alternating patterns are marked in bold. What we would like to know is whether any of the patterns are sufficiently "special" that its appearance would likely not be the result of chance. In this case, we can surmise that there is some non-random phenomenon that produces these alternating patterns of good and bad returns.

Table 1. Patterns of above and below average returns for various investment periods

Period
| Pattern of return: above average (H) or below average (T) |
No. of periods |

20 | THTH TTHH TH |
10 |

19 | THTH TTHT HH |
10 |

18 | THTH HHT THTH |
11 |

17 | THHTHHT HHTT |
11 |

16 | TH HTHT THTHTH |
12 |

15 | THTTHHH THTHTH |
13 |

14 | TH TTHHTT HTHHTH |
14 |

13 | THTHTHTHTHTHT TH |
15 |

12 | THHHT HHTT T HTHT TH |
16 |

11 | T HHTTHHTT T THTH HTH |
17 |

10 | THH THTH HTHT THTH HTTH |
19 |

9 | TTHH HTHH HTHT TH TTHHTTHH |
22 |

The thirteen-year returns show 13 strictly alternating good (H) and bad (T)
returns. The probability of such a pattern appearing in *any* of the entries
in Table 2.1 is only 1.6%, strongly suggesting that the pattern exhibited by
the thirteen-year period is nonrandom. The shortest repeating sequence in the
special pattern for the thirteen-year case was two periods long, or 26 years,
implying a 26-year cycle might be operating in stock returns (or at least once
was operating, as the pattern stopped around 1960). Here we see evidence of
non-random behavior on a multi-decade time scale.

*Figure 3. Sequential thirteen-year returns over time*

None of the other patterns in Table 1 show strong evidence of non-randomness. We would expect 1.2 eight-character special patterns purely by chance and there are two. We would expect 5.3 six-character special patterns and there are three. Finally we should expect 22 four-character special patterns and there are seventeen.

Figure 3 shows a plot of these thirteen-year returns. Differences in stock returns, such as the oscillating pattern in Figure 2.4, are caused by changes in stock prices (and hence index values). It has happened on some occasions, such as in 1929-32, that stocks fell a long ways in price, taking a long time to return to their previous levels. Stock market analysts would say that stocks in the period immediately before these price drops were "overvalued". A stock is overvalued when it falls in price afterward and doesn't recover for a long time. Similarly, entire indexes can become overvalued.

Stocks and stock indexes can be undervalued too. If a stock or stock index is undervalued, it will rise in price afterward at a greater than normal rate, and not fall back down. If one buys an index fund when the index is overvalued, the subsequent return will be below average. Conversely, if one buys an index fund when the index is undervalued, the return will be higher than average. So the range of returns shown in Figure 2 actually reflect the range of market "valuations" over time, running from very undervalued (high subsequent return) on the left side of the figure to very overvalued (low subsequent return) on the right side. Since returns are, for the most part, randomly distributed, it would seem that market valuation is largely random too, with the exception of the sequence of thirteen-year returns. Figure 3 is highly suggestive of a cyclical pattern in the stock market in which the market shifts from overvalued to undervalued and back to overvalued again about every 26 years.

__Projection of future returns from overvalued markets__

A lot of effort has been put into developing methods of predicting the valuation
on the stock market (i.e. an index) because valuation has a big effect on performance.
Since one does not know precisely the valuation of the market until after it
either falls or rises, what people have done is develop models that correlate
with past valuations (which we do know since we have seen what happened afterward).
A common valuation tool is the *price to earnings* *ratio *(P/E)
which is the price of a stock or index, divided by its earnings per share.
The idea behind P/E is that investors are actually buying an earnings stream
when they buy stocks. The value of these earnings (P/E) will then depend on
how reliable the earnings stream will be in the future, whether it will grow
in the future, and what sort of returns are available from other sorts of investments
such as bonds or money markets. In the late 1990's use of the P/E to make investment
decisions fell out of favor. Many stocks didn't have earnings so a P/E could
not be calculated for them. Also many stocks and indexes that appeared overvalued
on the basis of their high P/E rose substantially in price, suggesting that
they were actually undervalued. At the same time, presumably undervalued stocks
(low P/E) fell in price, suggesting that they were in fact overvalued.

I will present a valuation model in Part II that is quite different from the P/E ratio. Here I will use this model to estimate future returns that take into account the overvalued market of early 2000. We will see that overvaluation lowers future returns on the S&P500.

Figure 4 shows a new version of Figure 2. The returns following the 200 most overvalued months were used to produce Figure 4. My valuation model was used to pick the 200 months. The idea is that the selection of returns from just overvalued markets (like early 2000) should provide a better idea of the situation facing an investor at that time than does Figure 2, which includes all markets.

*Figure 4. Probabilities of various real returns in "overvalued" markets*

Interpretation of Figure 4 is the same as for Figure 2. Annual returns between
-5% and +15% are presented. As with Figure 2, a significant fraction of the
one-year returns fall outside this range and do not appear in the figure. We
can ask the same questions as before, but will get different answers. For example,
using Figure 2, which includes all market history regardless of valuation,
we determined that the chance of a 20% annualized return over the next five
years was 4%. Using Figure 4, which includes only those markets that have been
identified as "overvalued" by my valuation methodology, we find that there
is a *zero* chance of the S&P500 index returning even a 15% annualized
return over the five years after 2000.

Looking at the chance of loss, we see that the curves start moving down much further to the left than they did in Figure 2. Consider the chances of the index beating the 2.5% money market return. Over a one-year period the index beats the money market return 55% of the time in an overvalued market as compared to 62% of the time in

all markets. This finding suggests that valuation has little effect on short-term performance, exactly what we would expect for a random process. Over a five-year period, the stock index beats the money market return 58% of the time in overvalued markets as compared to 74% of the time for all markets. Over a ten-year period the index beats the money market return 54% of the time in overvalued markets as compared to 82% of the time in all markets. Finally, over a 20 year period the stock index beats the money rate 52% of the time in overvalued markets compared to 93% of the time in all markets. Notice that holding for longer periods of time does not improve the chances of stocks returns beating a money market fund. Overvaluation temporarily suspends the benefits of the long-term upward trend shown in Figure 1. Nevertheless, even in overvalued markets an investment in an index fund still outperforms the money market return more often than not.

The historical returns shown in Figure 4 come primarily from dividends, which were a lot higher in the past than they are today. Over the long haul, about two-thirds of total return has come from dividends. The market in early 2000 showed an extremely low average dividend yield of about 1.2% compared to the historical average of 4.6%. To deal with this low-dividend market, returns from capital-gains were calculated for the overvalued markets. The results appear in Figure 5. To these returns one can add 1-2% for dividends to get an idea of what sort of returns might be forthcoming from the overvalued, low-dividend market in early 2000.

*Figure 5. Probabilities of various real capital gains returns in "overvalued" markets*

Figure 5 can be used just like Figures 2 and 4. For example, what is the chance that the market will be lower (in inflation-adjusted terms) in 2001, 2005, 2010 or 2020 than it was in early 2000? A lower market implies a capital-gains return of 0% or less. We find the 0% value on the vertical axis and follow the dashed horizontal line at 0% and noting the probability values when it intersects each of the curves. The 20 year curve was intersected at a probability value of 25%, meaning there a 75% that the S&P500 index in constant dollars will be lower in 2020 than it was in early 2000.

Following along the 0% return line shows probabilities of 65%, 55% and 50% that the constant-dollar index would be below its 2000 level in 2010, 2005 and 2001, respectively. This means that there was a 50:50 chance that the market would be lower one year after 2000. This probability of decline would rise to 55% by 2005, to 65% by 2010 and to 75% by 2020. Over one year the probabilities are essentially random, yet as the time rises the projected behavior becomes less and less random.

The effect of holding time on stock returns in overvalued markets is the opposite
of what it is for all markets. Normally, holding stocks for longer amounts
of time increases the probability that they will beat other types of investments
such as money markets. This observation led to the commonly held belief that
for long-term investors, any time is a good time to invest since the long term
trend in Figure 1 dominates over time. In the case of overvalued markets (like
2000), holding for longer times, up to twenty years, does *not* increase
your odds of success. That is why it was wise to move assets from large cap
stocks, mutual funds and index funds in early 2000 and put them in an alternate
investment such as a money market fund.

Increased holding time does not improve the probability of a good return in
overvalued markets. This is a natural consequence of the position in the stock
cycle represented by overvaluation. In early 2000 (when I was writing *Stock
Cycles* and doing this analysis) we were close to the time of trend change
from up to down. Any long-term investment made at that time would necessarily
extend into the coming downtrend. The longer the holding time, the more of
it would fall into the downtrend. Hence increasing the holding period of an
investment made in an overvalued market fails to improve the performance of
that investment compared to money markets. This is why a money market was to
be preferred to stocks in early 2000, even though the market might have continued
to go up for a while longer.

In Part II, I will show the development of what I call price to resources (P/R), the valuation model I invented to track the progress of longer term stock cycles. This model and two others will be used to defined the stock cycle that defines the secular bull and bear market trends that can greatly affect investment performance.

__References__

1. Alexander, Michael A, post on the Longwaves Discussion List, August 25,
2002 (http://www.longwaves.net/2002/msg02047.html)

2. Alexander, Michael A., "How Low Can We Go? What Several Valuation Methods
Have To Say" *Safehaven,* October
20, 2002.

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