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Stock Market Bubbles
Some Historical Perspective
Achla Marathe and Edward Renshaw
Los Alamos, New Mexico
and
The Department of Economics
State University of New York at Albany
An earlier version of this essay was presented at a conference on
neural networks in the capital markets sponsored by the London
Business School and the California Institute of Technology in
Pasadena, California, November 16-18, 1994 and was eventually
published in the Winter 95/96 issue of The Journal of Investing.
In this essay we examine peak to peak percentage changes in the
S&P composite stock price index involving new historic highs which
are separated by cumulative declines amounting to three percent or
more. The stock market took its sharpest plunge in five months on
the morning of December 6, 1996 after Fed chairman Greenspan
raised the specter of "irrational exuberance" on Wall Street. And
on February 26, 1997 in a speech prepared for the Senate Banking
Committee Greenspan again warned investors about the possibility
of an over valued market. His first warning followed a peak to
peak gain for the S&P index of 15.1 percent without a correction
amounting to three percent or more and his second warning came
after a peak to peak gain of 7.8 percent without a correction of
this magnitude.
The objective of this exercise is to provide readers with some historical
perspective and also test the efficient market hypothesis by examining
economic and financial environments or conditions that might enable one to
do a better job of discriminating between small and large "bubbles" and
between bubbles that are separated by relatively small "corrections" and
major stock market crashes. If the percentage changes in the S&P index from
one bubble peak to the next are sufficiently small, on the average, one can
expect modest trading profits from a simple strategy of selling a portfolio
similar to the S&P index after it has recovered to a new historic high and
repurchasing the index after the next cumulative decline amounting to three
percent or more. At that point one would really like to be able to determine
whether the decline in stock prices is likely to be a minor correction or
the beginning of a major bear market.
Bull Markets In Perspective
Since the S&P index was first computed on a daily basis in 1928 there have
so far been eleven occasions when it lost 13.9 percent or more of its value
after climbing to a new historic high. After the S&P index finally recovered
from these major bear markets and achieved at least one more new historic
high there have always been at least three minor declines or corrections of
from three to 10.6 percent (followed by a recovery to yet another new
historic high) before the stock market entered a more pronounced bear market
of greater severity. See column (4) of Table 20.1.
Five of the eleven bull markets with new historic highs for the S&P index in
the post World War II period ended on the fourth decline of three percent or
more and two bull markets on the fifth decline. In 1996 the US stock market
finally broke the 1985-87 bull market record of 12 minor peak to trough
declines of from three to 9.4 percent before a major crash. The worst
decline during the longer lasting bull market of 1991-97 has so far only
amounted 8.9 percent from February 2, 1994 to April 11 of the same year.
The most impressive aspect to the bull market of 1991-9? is its subdued
character prior to the record setting peak to peak gain of 29 percent during
1995. The bubble which peaked out on February 2, 1994 established a new all
time first peak to last peak trading day duration record of 116 days but
only increased a modest 5.63 percent above the preceding new high bubble
peak which occurred on March 10, 1993.
On December 13, 1995 this record was broken with a series of 77 new historic
highs for the S&P composite spread over a 210 day trading period without a
correction of three percent or more. The 29 percent peak-to-peak gain
associated with this bubble was more than ten percentage points higher than
the previous record of 18.8 percent which was established during the bull
market of 1985-87.
The 1991-96 bull market has already established another new all time
duration record of more than six years from its first new high on February
13, 1991. The previous record for a new high bull market without a
correction amounting to 13.9 percent or more was only about 2 and 2/3 years
from January 21, 1985 to August 25, 1987.
It is not easy to predict the demise of a bull market. The data in Table
20.1 would suggest, however, that bull markets are more likely to end after
a relatively small peak-to-peak gain in column (3) than after a spectacular
series of new historic highs that have been achieved without an intervening
decline amounting to three percent or more. There have so far only been two
cases--the bull markets of 1967-68 and 1980- -where the last peak to peak
gain in stock prices was the largest bubble in that bull market.
Further evidence in support of the conclusion that new high bull markets
usually don't end abruptly can be inferred from the number of trading days
shown in column (5) which have supported the new high portion of each
bubble. None of the major bull markets in Table 20.1 have (so far) ended
after the record number of trading days (for the most enduring bubble in
that particular bull market) without a cumulative decline of three percent
or more. The tendency for major bull markets to "fade away" instead of
ending on a big bubble, or a spectacular series of new historic highs, makes
it far more difficult to define an optimal trend chasing strategy than to
compute the profits which "might have been obtained" as a result of simpler
policies of "buying low and selling high".
A Trading Strategy Based on Stock Market Volatility
When the average percentage gain from one bubble peak to the next bubble
peak in column (3) of Table 20.1 is less than, or not very much greater than
three percent, it will be profitable, on the average, for a tax exempt
investor in a no load mutual fund similar to the S&P index to liquidate his
or her portfolio at the end of the day the S&P index first recovers to a new
high (after experiencing a cumulative dip of three percent or more), put the
proceeds in a money market fund, and stay out of the equity market until the
end of the day the S&P index has again experienced a cumulative decline
amounting to at least three percent.
On March 8, 1993, for example, the S&P index closed at a new historic high
of 454.71 after recovering from a cumulative dip amounting to about 3.9
percent following the preceding new high peak of 449.56 which had occurred
on February 4. Selling a portfolio similar to the S&P index on March 8 would
have been a bit premature since the index achieved another new high of
456.33 on March 10. The S&P index then proceeded to drift lower. On April 2
it lost 8.91 points and closed at 441.39. At that closing value the S&P
index was down 3.3 percent from the last new high peak on March 10 and was
about 2.9 percent lower than our assumed selling price of 454.71 on March 8.
The repurchase discount of 2.9 percent from a strategy of transacting at end
of the day closing prices, in this example, is about twice as great as the
discount that could have been obtained from an open order strategy of
selling the S&P index when it first equaled the peak value for the preceding
bubble and repurchasing after a cumulative decline of exactly three percent.
>From this example it should be clear that one really needs more information
than is actually provided in Table 20.1 to compute the gains and losses
associated with an end of the day trading strategy. The additional
information is provided in Tables 20.2 and 20.3 for two trading strategies.
It is interesting, in any event, to try to determine what kinds of economic
and financial environments are likely to create the caution and anxiety that
will produce small bubbles (or percentage gains from one bubble peak to the
next bubble peak) and make it worth while to get out of the market, on the
average, or at least refrain from buying a portfolio similar to the S&P
index after it has recover from a cumulative decline of three percent or
more and achieved a new historic high.
Devising a trading strategy of this type that will outperform a policy of
buy and hold is not an easy matter. An investor who exited the market after
every first new high and repurchased the S&P index after the first
cumulative dip of three percent would have experienced a lot of ups and down
and gone almost no where from September 22, 1954 to February 14, 1995. The
investor's net gain, before taxes and transaction costs, would have only
been a paltry 6.6 percent compared to a more spectacular gain of 1408.0
percent for a policy of buy and hold.
While most investors are probably well advised to ignore market timing
approaches to stock market participation, there are a few trading strategies
that would have outperformed buy and hold--if we ignore taxes and
transaction costs. One hypothesis, which was advanced by Renshaw in (1991)
is that new high trading strategies work best in a volatile market. Greater
volatility, other things equal, will produce more end of the day breakage
above the preceding bubble peak and below the minimum decline required for
repurchase. In so doing it will accentuate the gain to be expected from an
asymmetric relationship between percentage gains and losses. A three percent
decline from say 100 to 97, for example, requires a recovery of a little
over 3.09 percent just to get back to 100.
One indicator of stock market volatility is the percentage gain in the S&P
index the day it first recovers to a new historic high. For the 27 cases
from 9/7/29 to 7/5/96, when the first daily recovery gain to a new historic
high was equal to 1.1 percent or more, it would have been possible (for a
tax exempt investor with no transaction costs) to obtain 46.6 percent more
price appreciation, than under a policy of buy and hold, by selling a
portfolio similar to the S&P at the end of that day and repurchasing the
portfolio at the end of the day the S&P index first experienced another
cumulative new high decline amounting to three percent or more.
An investor who followed this trading strategy by selling a portfolio
similar to the S&P index on September 14, 1996--after the new high recovery
from the nerve racking correction of 7.6 percent from May 24 to July 24--
would have suffered a loss of 7.2 percent or more compared to a policy of
"buy and hold". The exuberant bull market of 1995-97, in any event, has
ruined a lot of market timing strategies.
The 1.1 percent or more gain required on the first recovery day to measure
volatility and trigger a sale was chosen in an attempt to maximize the
cumulative advantage to be obtained from this type of "three percent"
switching strategy. See those peak to peak gains in column (3) of Table 20.1
which are identified with a $ sign.
Most of the more profitable volatility switches involving a first new high
daily gain of 1.1 percent or more have occurred since the invention of stock
index futures and options in 1982. These innovations have made it easier and
more profitable for traders and speculators to "short" an over valued
market. Lots of volatility associated with the first four bubbles in a bull
market may be indicative of a near term crash. The three bull markets with
three or more dollar signs attached to the first four bubbles (the 1980,
1982-83 and 1989-90 bull markets) all ended on the bursting of the fourth
bubble.
Bubble Size In Relation to Earnings and Dividends
There are a number of other environments where modest profits could have
been obtained, on the average, by employing a three percent or more
switching strategy. One of the most publicized indicators of an "over valued
market" is a dividend yield for the S&P index of three percent or less
(Renshaw 1990 and 1992). This indicator, however, has not worked very well
in recent years. See Table 20.2.
The poor performance of a low dividend yield exit strategy, by itself,
during the bull market of 1995, however, makes it clear that traders should
also keep a close eye on what is happening to earnings. From the fourth
quarter of 1993 to the fourth quarter of 1994 the quarterly earnings
associated with the S&P index increased 65.3 percent. This was the largest
fourth quarter to fourth quarter increase in corporate earnings since 1946.
The explosive increase in earnings helped to lower the P/E ratio from 21.3
at the end of 1993 to a more normal 15.0 at the end of 1994. The expectation
that earnings would continue to increase at a rapid rate set the stage for
one of the most remarkable bubbles in stock market history.
In a world where it has become fashionable for many corporations to use
their earnings to buy up other companies, or repurchase their own stock, it
is reasonable to suppose that high price/earnings ratios may be a more
reliable indication of overvaluation than low dividend yields. For the ten
cases where the P/E ratio for the S&P index at the end of the preceding
quarter was in excess of 20.50 one could have obtained eleven percent more
price appreciation with a first new high sale and buy back strategy after
the next decline of three percent, than under a buy and hold policy.
A crash indicator threshold of 20.50 for the P/E ratio was first proposed by
Renshaw in (1990). Since then we have had seven additional out of sample
cases of new high bubbles following a P/E ratio in excess of this threshold.
The average discount to be obtained from exiting the market after a P/E
ratio of 20.50 or more is enhanced somewhat, however, if one only considers
the six cases where the dividend yield was equal to 3.0 percent or less. See
those changes in the value of the S&P index in column (4) of Table 20.3 that
are identified with an asterisk.
Large Corrections
The most severe "correction" in Table 20.1 is the 10.6 percent decline in
the S&P index from September 23 to October 11, 1955 which contained a one
day drop in stock prices amounting to 6.6 percent on September 26, following
President Eisenhower's heart attack.
There have been eight large corrections in major bull markets involving
declines of from 7.9 to 10.6 percent. For the seven resolved cases an
investor could have always sold a portfolio similar to the S&P index after
the first day of recovery to a new historic high and then repurchased the
same portfolio at a discount of at least 11.8 percent during the next stock
market crash.
Whether mega buck profits from this kind of trading strategy will continue
to occur in the future is one of the more interesting questions to be
resolved with the passage of time. While the goal of most market timers is
to avoid large corrections and market crashes, the out of sample history of
crash indicators that would have produced large trading profits in the past
is not very encouraging (Renshaw, 1995a).
One reason for at least hoping that the rather spectacular bubble which
emerged after the 8.9 percent correction of 1994 won't be followed by an
horrendous crash, is evidence suggesting that the stock market is more
stable now than it used to be (Renshaw 1995b). The three smallest annual
high/low ratios for the S&P index were all recorded in the 1992-94 period.
There is also the prolonged nature of the 1991-96 new high bull market which
suggests that stock market crashes in the midst of prosperity may not be
occurring as frequently as was the case during the 1960s, 70s and 80s.
Stock Market Crashes in the Midst of Prosperity
Four of the ten completed new high bull markets in Table 20.1 ended as a
result of stock market crashes in the midst of prosperity. All of these
crashes (the debacles of 1962, 1966, 1984 and 1987) were preceded by at
least one new high, peak-to-peak gain of nine percent or more for the S&P
index in column 3 of Table 20.1. This is the only characteristic of new high
bull markets terminated by bear markets in the midst of prosperity (that we
have discovered) that is not widely shared by the six (completed) new high
bull markets which were terminated by recessions. The implication would seem
to be that crashes in the midst of prosperity can be explained, at least in
part, by "excessive" optimism or speculative enthusiasm.
In the post World War II period there have been only eleven new high peak to
peak gains in column (3) of Table 20.1 amounting to nine percent or more.
Seven of these bubbles "broke" during quarters when the annualized growth of
real GDP in 1987 dollars was over five percent or during quarters when the
four quarter growth rate for real GDP was in excess of five percent.
Two of these cases occurred in 1987, before the October crash, when the
economic growth rate had slowed to a more normal pace and the stock market
was still imbued with a tremendous amount speculative enthusiasm. The
largest bubble of all broke during the fourth quarter of 1995 after real GDP
for the third quarter expressed in chain weighted dollars had increased at
an annualized rate of 3.6 after increases of only .6 and .5 percent for the
first two quarters.
It should be noted, however, that only one of these large new high bubbles,
the 11.5 percent increase in stock prices from June 15, 1987 to August 25,
was followed by a crash. The other nine bubbles only experienced minor
corrections or declines ranging from a loss of 3.1 percent for the 1964
bubble to a loss of 6.9 percent for the 1983 bubble.
The Possibility of Another Recession
In Essay 19 the emphasis was on the "good year" approach to economic and
financial forecasting. If one could have accurately anticipated years
containing a recessionary peak in business activity that information would
have been of considerable value in avoiding financial loss.
There have so far only been seven new high bubbles in the post 1953 period
that occurred during years containing a recessionary peak in business
activity. See those peak dates identified with a "P" in Table 20.1.
Investors who exited the market in these years after the first new high and
repurchased a portfolio similar the S&P after a closing dip of three percent
or more could have obtained an average trading profit (before taxes and
commissions) of 1.34 percent.
Larger gains could have been achieved by simply staying out of the market
until it was clear that the US economy had slipped into another recession.
Since the mild recession of 1960-61 the S&P composite stock price index has
consistently lost more of its value, measured on a monthly average basis,
after a recessionary peak in business activity as defined by the National
Bureau of Economic Research than before the peak (Table 14.5).
The duration of business expansions has been increasing with the passage of
time. The five business expansions from 1961-90 had an average duration of
60.8 months. This can be compared to an average duration of only 36.2 months
for the first four expansions after World War II and an average duration of
only 29 months for the 22 expansions from 1854-1945.
One of the problems that nervous investors face in relation to the business
cycle is that economists have not had very much success at identifying
recessionary peaks in business activity in close proximity to their
occurrence (Siegel, 1994, p. 180).
There is a time honored rule of thumb that a recession will soon follow
three consecutive declines in the Conference Board's index of leading
economic indicators. The lead times for this signal, however, have ranged
from only two months for the recessions of 1948-49 and 1953-54 to a grand
total of 90 months for the three declines which occurred during the stock
market crash of 1962.
In thinking about the possibility of a near term peak in business activity
it should be appreciated that modern day recessions are not a severe as they
used to be. During the recession of 1948-49 payroll employment declined by
5.2 percent and industrial production by ten percent. During the 1990-91
recession payroll employment experienced a dip of only 1.7 percent and
industrial production only declined 4.2 percent.
It should also be appreciated that the recession prone auto industry and
many other US corporations are now in better financial shape and are less
dependent on domestic sales than was the case in 1990. If speculative
enthusiasm does not lift price/earnings ratios to a dangerous level there is
a possibility that the market's response to a near term recession might be
more nearly a correction than an old fashioned crash.
Some Concluding Remarks
The relatively small stock market correction associated with the Fed's
preemptive strike against the possibility of accelerating inflation in 1994
and the rather spectacular new high bubble of 1995 have tarnished the image
of low dividend yields and a number of other market timing signals. While
most investors are probably well advised to follow the philosophy of Peter
Lynch and Jeremy Siegel, by investing in stocks for the long run, it can be
interesting and possibly rewarding to have an appreciation of how the market
has behaved over long periods of time.
The stock market bubbles identified by new high peaks that are separated by
cumulative declines of three percent or more in Table 20.1 are one of the
easiest data bases to update and maintain. They can be used to measure the
duration, stability and magnitude of both short lived and more prolonged
bull markets. They can also be used to obtain a quick, rough approximation
of the gains and losses that "might have been obtained" in connection with a
much wider range of statistical indicators, investment timing and trading
strategies than can possibly be evaluated in this essay.
Our attempt to differentiate between small and big bubbles and between minor
corrections and major crashes would strongly suggest that beating the market
is not an easy matter. We are inclined, however, to stick with the notion
that the jury is still out as to whether changes in the S&P composite stock
price index resemble a random walk and are truly consistent with the
efficient market hypothesis. The nice thing about our tables is that they
provide readers with enough history and cases to be in a better position to
make an independent judgment with regard to a profound idea that has
revolutionized courses in economics and finance but will no doubt remain
controversial, forever and ever.
References
Renshaw, Edward (1990). "Some Evidence in Support of Stock Market Bubbles,"
Financial Analysts Journal, March/April, 71-73.
-----, (1991). "A Formula Plan for a More Volatile Stock Market," Financial
Analysts Journal, January/February, 85-87.
-----, Editor, (1992). The Practical Forecasters' Almanac(Burr Ridge,
Illinois: Irwin Professional Publishing).
-----, (1995a). "There is No Big Picture, Or, That Is the Big Picture," The
Journal of Investing, Summer, 56-61.
-----, (1995b). "Is the Stock Market More Stable than it Used to Be?"
Financial Analysts Journal, Nov./Dec., 81-88.
Siegel, Jeremy (1994). Stocks for the Long Run(Burr Ridge, Illinois: Irwin
Professional Publishing).
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Table 20.1
Declines of Three Percent or More in the S&P 500 Stock Price Index After it
Has Achieved a New All Time High Since September 7, 1929
Percentage Change S&P
Date of Value S&P Index --------------------- Trading
------------------- --------------- Peak to Peak to Day
Peak Trough Peak Trough Peak Trough Duration
(1) (2) (3) (4) (5)n
9/ 7/29 6/ 1/32 31.92 4.40** --- -86.2
10/ 6/54 10/29/54 32.76 31.68 2.6 - 3.3 10
1/ 3/55 1/17/55 36.75 34.58 12.2$ - 5.9# 40H
3/ 4/55 3/14/55 37.52 34.96 2.1$ - 6.8 19
4/21/55 5/17/55 38.32* 36.97 2.1 - 3.5 7
7/27/55 8/10/55 43.76 41.74 14.2 - 4.6# 37
9/23/55 10/11/55 45.63 40.80 4.3 -10.6 13
11/14/55 1/23/56 46.41 43.11 1.7$ - 7.1 0
3/20/56 5/28/56 48.87 44.10 5.3$ - 9.8 7
8/ 2/56 10/22/57 49.74 38.98** 1.8 -21.6 13
11/17/58 11/25/58 53.24 51.02 7.0 - 4.2# 37
1/21/59 2/ 9/59 56.04 53.58 5.3$ - 4.4# 27
5/29/59 6/10/59 58.68 56.36 4.7 - 4.0# 61H
8/ 3/59 10/25/60 60.71* 52.30** 3.5 -13.9 22
4/17/61 4/24/61 66.68 64.40 9.8 - 3.4# 54H
5/17/61 7/18/61 67.39E 64.41D 1.1 - 4.4 2
9/ 6/61 9/25/61 68.46E 65.77D 1.6 - 3.9 22
12/12/61 6/26/62 72.64E* 52.32D** 6.1 -28.0 35
10/28/63 11/22/63 74.48 69.61 2.5 - 6.5 39
5/12/64 6/ 8/64 81.16 78.64 9.0 - 3.1# 101H
7/17/64 8/26/64 84.01 81.32 3.5 - 3.2# 15
11/20/64 12/15/64 86.28* 83.22 2.7 - 3.5 17
5/13/65 6/28/65 90.27 81.60 4.6 - 9.6 81
2/ 9/66 10/ 7/66 94.06 73.20** 4.2 -22.2 94
5/ 8/67 6/ 5/67 94.58 88.43 .6 - 6.5 2
8/ 4/67 8/28/67 95.83 92.64 1.3 - 3.3 4
9/25/67 3/ 5/68 97.59 87.72 1.8$ -10.1 8
7/11/68 8/ 2/68 102.39* 96.63 4.9 - 5.6 44H
11/29/68 5/26/70 108.37 69.29** 5.8 -36.1 38
4/12/72 5/ 9/72 110.18 104.74D 1.7 - 4.9 24
5/26/72 7/20/72 110.66 105.81D .4 - 4.4 2
8/14/72 10/16/72 112.55 106.77D 1.7 - 5.1 4
12/11/72 12/21/72 119.12* 115.11D 5.8 - 3.4# 26H
1/11/73P 10/ 3/74 120.24 62.28D** .9 -48.2 6
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Table 20.1 (continued). Declines of Three Percent or More in the S&P 500
Stock Price Index After it Has Achieved a New All Time High Since September
7, 1929
Percentage Change S&P
Date of Value S&P Index --------------------- Trading
------------------- --------------- Peak to Peak to Day
Peak Trough Peak Trough Peak Trough Duration
(1) (2) (3) (4) (5)n
8/22/80P 8/28/80 126.02 122.08 4.8$ - 3.1# 26H
9/22/80P 9/29/80 130.40 123.54 3.5$ - 5.3 13
10/15/80P 10/30/80 133.70 126.29 2.5$ - 5.5 7
11/28/80P 8/12/82 140.52* 102.42** 5.1$ -27.1 11
11/ 9/82 11/23/82 143.02 132.93 1.8$ - 7.1 4
1/10/83 1/24/83 146.78 139.97 2.6$ - 4.6 2
6/22/83 8/ 8/83 170.99 159.18 16.5 - 6.9# 94H
10/10/83 7/24/84 172.65* 147.82** 1.0$ -14.4 0
2/13/85 3/15/85 183.35 176.53 6.2$ - 3.7# 17
6/ 6/85 6/13/85 191.06 185.33 4.2 - 3.0# 29
7/17/85 9/25/85 195.65 180.66 2.4 - 7.7 13
1/ 7/86 1/22/86 213.80* 203.49 9.3$ - 4.8# 37
3/27/86 4/ 7/86 238.97 228.63 11.8 - 4.3# 37
4/21/86 5/16/86 244.74 232.76 2.4$ - 4.9 3
5/29/86 6/10/86 247.98 239.58 1.3$ - 3.4 2
7/ 2/86 7/15/86 252.70 233.66 1.9 - 7.5 5
9/ 4/86 9/29/86 253.83 229.91 .4$ - 9.4 6
12/ 2/86 12/31/86 254.00 242.17 .1$ - 4.7 0
3/24/87 3/30/87 301.64 289.20 18.8 - 4.1# 53H
4/ 6/87 5/20/87 301.95 278.21D .1 - 7.9 0
8/25/87 12/ 4/87 336.77 223.92** 11.5 -33.5 50
9/ 1/89 9/14/89 353.73 343.16 5.0$ - 3.0# 27H
10/ 9/89 1/30/90 359.80 322.98 1.7$ -10.2 4
6/ 4/90P 6/26/90 367.40 352.06 2.1$ - 4.2 4
7/16/90P 10/11/90 368.95* 295.46** .4 -19.9 0
4/17/91 5/15/91 390.45 368.57 5.8 - 5.6# 43
8/ 6/91 8/19/91 390.62 376.47 .0$ - 3.6 0
8/28/91 10/ 9/91 396.64 376.80 1.5 - 5.0 4
11/13/91 11/29/91 397.41E* 375.22 .2 - 5.6 1
1/15/92 4/ 8/92 420.77E 394.50 5.9 - 6.2 14
8/ 3/92 8/24/92 425.09E 410.72 1.0$ - 3.4 3
9/14/92 10/ 9/92 425.27E 402.66D .0$ - 5.3 0
2/ 4/93 2/18/93 449.56E 431.90 5.7 - 3.9# 51
3/10/93 4/26/93 456.33E 433.54D 1.5$ - 5.0 2
2/ 2/94 4/ 4/94 482.00E 438.92D 5.6 - 8.9 116
12/13/95 1/10/96 621.69 598.48D 29.0 - 3.7# 210H
2/12/96 4/11/96 661.45 631.18D 6.4 - 4.6# 10
5/24/96 7/24/96 678.51 626.65D 2.6$ - 7.6 9
11/18/96 12/16/96 757.03 720.98D 15.1G$ - 4.8# 51
2/18/97 816.29 D 7.8G ? 26
Footnotes for Table 20.1
(5)n. Number of additional trading days after the recovery to a first new
high to the last new high or peak date.
* Fourth new high to be followed by a three percent decline for the bull
market in question.
**A major bear market low.
$ identifies cases where the first new high was associated with a daily gain
of 1.1 percent or more.
#Cases where the peak to trough decline in column (4) is less than the
preceding peak to peak increase in column (3).
D identifies cases where the first new high occurred after a month when the
dividend yield for the S&P index was equal to 3.0 percent or less.
E identifies cases where the first new high occurred after a quarter when
the P/E ratio for the S&P index was equal to 20.50 or more.
G identifies peak to peak gains that may have encouraged Fed Chairman Alan
Greenspan to warn investors about the possibility of irrational exuberance.
H identifies the trading day duration record, without a cumulative decline
of three percent or more, for each bull market separated by cumulative
declines of 13 percent or more.
P identifies declines of three percent or more that occurred during years
containing a recessionary peak designated by the National Bureau of Economic
Research.
Source of basic data: The Practical Forecasters' Almanac(Burr Ridge,
Illinois: Irwin, 1992), Table 3.05 and Standard and Poor's Security Price
Index Record.
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Table 20.2
The Sell and Repurchase Values for the S&P Composite Stock Price Index
Associated with a Strategy of Selling the Index after a First New Historic
High--if the Preceding Month's Dividend Yield Was Equal to 3.0 Percent or
Less--and Repurchasing It after the Next Cumulative Decline of Three Percent
or More.
Daily Closing Values
S&P Stock Price Index
Sell Buy Div. Yield P/E Ratio --------------------- % Change
Date Date Previous Previous Sell Buy S&P
Month Quarter Date Date Index
(1) (2) (3) (4) (5)
5/15/61 6/16/61 2.95 21.1 66.83 65.18 - 2.5
8/04/61 9/25/61 3.00 21.3 67.68 65.77 - 2.8
10/20/61 1/05/62 2.93 21.9 68.48 69.66 1.7
3/06/72 5/01/72 2.92 17.9 108.77 106.69 - 1.9*
5/24/72 6/08/72 2.83 18.5 110.31 107.28 - 2.7
8/08/72 9/12/72 2.90 18.0 110.69 108.47 - 2.0*
11/01/72 12/21/72 2.82 18.0 112.67 115.11 2.2*
1/03/73 1/26/73 2.70 18.4 119.57 116.45 - 2.6
4/06/87 4/09/87 2.90 19.3 301.95 292.86 - 3.0
9/14/92 10/02/92 2.97 23.9 425.27 410.47 - 3.5
3/08/93 4/02/93 2.81 22.8 454.71 441.39 - 2.9
8/19/93 2/24/94 2.81 22.3 456.43 464.26 1.7
2/14/95 1/10/96 2.87 15.0 482.55 598.48 24.0*
1/29/96 2/29/96 2.30 18.1 624.22 640.43 2.6*
5/13/96 7/05/96 2.24 19.0 661.51 657.44 - .6
9/13/96 12/12/96 2.22 19.2 680.54 729.82 7.2
1/10/97 2/28/97 2.01 759.50 790.82 4.1
*Percentage change in the S&P index when the P/E Ratio in the previous
quarter in column (2) was less than 18.4.
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Table 20.3
The Sell and Repurchase Values for the S&P Composite Stock Price Index
Associated with a Strategy of Selling the Index after a First New Historic
High--if the Preceding End of the Quarter P/E Ratio Was Over 20.50--and
Repurchasing It after the Next Cumulative Decline of Three Percent or More.
Daily Closing Values
S&P Stock Price Index
Sell Buy P/E Ratio --------------------- % Change
Date Date Previous Sell Buy S&P
Quarter Date Date Index
(1) (2) (3) (4)
5/15/61 6/16/61 21.1 66.83 65.18 - 2.5*
8/04/61 9/25/61 21.3 67.68 65.77 - 2.8*
10/20/61 1/05/62 21.9 68.48 69.66 1.7*
11/12/91 11/15/91 21.8 396.74 382.62 - 3.6
12/24/91 2/18/92 21.8 399.33 407.38 2.0
7/29/92 8/24/92 23.9 422.23 410.72 - 2.7
9/14/92 10/02/92 23.9 425.27 410.47 - 3.5*
11/20/92 2/16/92 22.2 426.65 433.91 1.7
3/08/93 4/02/93 22.8 454.71 441.39 - 2.9*
8/19/93 2/24/94 23.3 456.43 464.26 1.7*
Average Percentage Change from Sell Date to Buy Date - 1.09
*Identifies cases where the dividend yield in the preceding month was equal
to 3.00 percent or less. The average decline associated with these six cases
is 1.38 percent.
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Essay 20:
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