Stock Market Forecasting

Author(s): Alfred Cowles

Source: Econometrica , Jul. - Oct., 1944, Vol. 12, No. 3/4 (Jul. - Oct., 1944), pp. 206-214
Published by: The Econometric Society

Stable URL: https://www.jstor.org/stable/1905433

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 STOCK MARKET FORECASTING*

By ALFRED COWLES

The analysis reported here is a continuation of a study begun at the

end of 1927 and originally published in 1933.1 At that time were re-
ported the results achieved by 24 financial publications in forecasting
the course of the stock market during the period from January, 1928,
to June, 1932. This earlier investigation disclosed no evidence of skill
in forecasting. The present study extends the records of 11 of the fore-
casters. In the case of 7 of these the record now covers the 15A years
from January, 1928, to July, 1943, and, for the remaining 4, periods
of about 11 years ending in 1938 or 1939. The forecasters include 4
financial periodicals and 7 financial services. These organizations are
well known. Names are omitted here because their publication might
precipitate controversy over interpretation of the records. The wording
of many of the forecasts is indefinite, and it would frequently be possi-
ble for the forecaster after the event to present a plausible argument in
favor of an interpretation other than the one made by a reader.
The method used in this analysis was for each of two readers2 to grade
the forecasts independently according to the degree of bullishness or
bearishness which he thought they contained. The average of the two
interpretations was used as the basis for computing the record. It was
assumed that the reader, if the forecast was 100-per-cent bullish, would
invest all of his funds in the stock market; if the forecast was 50 per-
cent bullish, he would put three-quarters of his funds in stocks; if the
forecast was doubtful, he would put half of his funds in stocks; if 50-per-
cent bearish, one-quarter in stocks; and if 100-per-cent bearish, nothing
in stocks. The forecasts thus tabulated have been tested in the light
of the fluctuations of the stock market as reflected by the Standard
& Poor's average of 90 representative common stocks. If the forecast
is 100-per-cent bullish and the market rises 10 per cent, the forecasting
score is 1.10. If the forecaster is doubtful, the score is 1.05, reflecting
one-half of the market advance, on the assumption that the investor,
being doubtful, would place one-half of his funds in stocks and hold
one-half in reserve. If the forecast is 100-per-cent bearish, the score is

* Cowles Commission Papers, New Series, No. 6.

1 "Can Stock Market Forecasters Forecast?" by Alfred Cowles, ECONOMET-
RICA, Vol. 1, July, 1933, pp. 309-324.
2 The author is indebted to Dickson H. Leavens, Forrest Danson, and Miss
Emma Manning of the Cowles Commission for Research in Economics, The
University of Chicago, for assistance in tabulating the forecasts and computing
the records.

206

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 STOCK MARKET FORECASTING 207

1.0, regardless of the subsequent action of the mark

tion that the investor would have withdrawn all of his funds from the
market. If the forecast is 100-per-cent bullish, and the market drop
10 per cent, the score is 0.90, and if the forecast is doubtful and the
market drops 10 per cent, the score is 0.95. The compounding of the
weekly scores for each agency gives its forecasting record for the who
period. These results are compared with a figure representing the aver
age of all possible forecasting results, arrived at by compounding on
half of the percentage change in the level of the stock market for eac
period, which hereafter for convenience will be referred to as the "ran
dom forecasting record." The results presented, hereafter called the
"index of performance," are derived by dividing the actual com-
pounded record of each forecaster by the random forecasting record
referred to above and subtracting 1. The results have also been decom-
pounded so as to represent an effective annual rate. If a forecaster's
record is plus it is better, and if minus it is worse, than the random
forecasting record. Most of the agencies published forecasts every wee
and these were tabulated on a weekly basis. In other cases the late
forecast was assumed to be in effect until the next one appeared.
The process described above may be expressed in algebraic terms as
follows:
Let t = date, measured in weeks;
pt=actual market (Standard & Poor's index of
90 stocks) at date t;

P -1 =increase or decrease (rate) in actual market

from date t to date t+1;

1 (pt+ 1 ) =increase or decrease (rate) in "random fore-

casting record," that is, one-half increase or

decrease in actual market;

r=-( P--+l_l ) +1= ratio of random forecasting record at date

t+1 to random forecasting record at date t;

i= r1rr2 * *· r= compounded random forecasting record at

date t+ 1;
qt =fraction of funds kept in market on advice of
forecaster from date t to date t+1;

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208 ALFRED COWLES

ft = qt ( P+-- 1 +1 = ratio of value of above investme

\ Pt /
idle cash) at date t+1 to value
t

I fi =fJ2 · ft = compounded value of investment at date t + 1;

1

HIfi
I1t -1= ="index of performance" of forecaster from
fi ri date 1 to date t+ 1, that is, ratio of compounded
value of investment to compounded random
forecasting record.

Work sheets for the computation have the form shown in Table 1
(using hypothetical values and working to only 2 decimals as compared
with 4 used in the actual study):

TABLE 1

1 2 3 4 5 6 7 8 9

Ratio of Forecaster A
Rate of random Com-
increase fore- pounded Frac- Ratio
Weeks Actual or casting random to of of o- Index
Market decrease record fore- un value of
in at t+l casting s att+1
in to pounded
that lue rfor
actual to that recordmarket
r to that value mance
market at t at t

Pt+i
t prt-- 1 r qt ft If. Ilt
Pt 1 1

1 50 +0.20 1.10 1.10 1.00 1.20 1.20 +0.09

2 60 +0.25 1.12 1.23 0 1.00 1.20 -0.02
3 75 0 1.00 1.23 0.50 1.00 1.20 -0.02
4 75 -0.20 0.90 1.11 1.00 0.80 0.96 -0.14
5 60 -0.10 0.95 1.05 0.50 0.95 0.91 -0.14
6 54

Thus the hypothetical forec

casting record in the first we
in the market instead of onl
by staying out of a rising ma
move and he just held his ow
of his position in the mark

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 STOCK MARKET FORECASTING 209

bullish in a bear market; and in the fifth week he lost but maintained
the same relation to the random forecasting record as the week before.
Figure 1 indicates that 6 of the 11 forecasters met with some degree
of success and that 5 were unsuccessful in their forecasts. The 11 fore-
casters were on the average only 0.2 per cent a year better than the

INDEX OF PERFORMANCE OF 11 FORECASTERS

+5 [ jANNUAL RATE +5

0 FM ~~~~~~~~~~~0

-5 -5

FIGURE 1.-The index of performance is the per cent by which the com-
pounded record of each forecaster is better or worse than the random forecasting
record.

random forecasting record. That one of the forecasters had an average

annual rate 6.02 per cent better than the random forecasting record is
to be discounted by the fact that it is the best of the 11 records ex-
amined. Assuming a complete lack of ability, if one had the opportu-
nity to make 11 attempts, the best of these by chance might show a
considerable degree of success. In this analysis, the least successful of
the forecasters, with an average annual rate 5.62 per cent worse than
the random forecasting record, was wrong almost as much as the most
successful one was right.
Figure 2 depicts the result of dividing the 15a-year period into 17
major swings and for each of these computing the average index of

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 210 ALFRED COWLES

performance; that is, the average result of the 11 forecasters3 as a per-

centage of the random forecasting record. Any rise exceeding 33 per
cent, or decline of more than 25 per cent, was designated as a major
swing, the daily highs or lows being considered rather than weekly or
monthly averages. The last swing was arbitrarily terminated in July,
1943, because when the analysis was made the market in that month
had reached its highest point since the low of 1942, and subsequent to
July, 1943, it had not declined as much as the 25 per cent necessary
to establish a major down-swing. It appears that the consensus of
opinion was always right in the case of bull markets, and wrong in
the bear markets. Of the 6904 forecasts recorded, 4712 were bullish,
1107 doubtful, and 1085 bearish. Yet only 88 months of the period are
occupied by bull markets and 98 by bear markets, and in July, 1943,
the end of the 152-year period, the market was at only about two-thirds
of its level at the beginning of this period in January, 1928. In the case
of every one of the 11 forecasters the number of bullish predictions far
exceeded the number of bearish ones. The persistent and unwarranted
record of optimism can possibly be explained on the ground that readers
prefer good news to bad, and that a forecaster who presents a cheerful
point of view thereby attracts a following without which he would
probably be unable to remain long in the business of forecasting. In
extenuation, however, it may be said that the last 15 years is the longest
period on record in which the industrial stock averages failed to move
into new high ground. During the 57 years from 1871 to 1927, the
average rate of gain for industrial common stocks in the United States
was 3.8 per cent a year in addition to dividend income, and the longest
period in which a previous all-time high was not exceeded was 91 years
from June, 1889, to March, 1899. This background may have exerted a
strong influence during the last 15 years on the minds of the forecasters.
It was found possible to extend back to 1903 the published record of
the forecasting agency with the most successful record for the period
from 1928 to 1943. While three individuals were for different periods
responsible for the forecasts throughout those 40 years, the general
principles followed by them all were similar and the succeeding fore-
casters were avowed disciples of their predecessors. It therefore seems
justifiable to treat the combined record as a continuous one for the
40 years in question. In analyzing this record, the same method was
used as in the case of the 11 forecasters previously reported except that
corrections were made to include cash dividends, brokerage charges,
and interest which could have been earned on idle funds. Also, the

3For the period subsequent to 1939 only 7 of the 11 forecasting records were
available.

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 STOCK MARKET FORECASTING 211

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 212 ALFRED COWLES

Dow-Jones industrial average4 was used in computing the market gain

or loss on each forecast instead of the Standard & Poor's average of
90 stocks since the latter is not available prior to 1926. The resulting
figure was reduced to the actual effective annual rate of gain instead of
to the index of performance. The rate of gain computed as above indi-
cated is 14.2 per cent a year, of which about 4.2 per cent is dividend
and interest income. In the same period a continuous investment in the
stocks composing the Dow-Jones industrial average would have shown
a return, including dividends, of 10.9 per cent a year. Following the
forecasts, therefore, would have resulted in a gain of 3.3 per cent a year
over the result secured by a continuous investment in the common
stocks composing the Dow-Jones industrial average.
Breaking the record down into four periods of 10 years each, we find
that following the forecasts would have shown an average annual capi-
tal gain of about 13 per cent from 1904 to 1913, 7 per cent from 1914
to 1923, 13 per cent from 1924 to 1933, and 7 per cent from 1934 to
1943. This is without including the cash dividends and interest earned
on idle funds which would have averaged around 4.2 per cent a year.
There were two fairly long periods in which following the forecasts
would not have resulted in profits. One of these was the 51 years from
the fall of 1909 to the spring of 1915 when losses averaging about 3 per
cent a year would have been incurred. The other was the last 6 years of
the record from June, 1937, to June, 1943, when little if any profit
would have been secured. Both of these were, however, periods in which
stock prices were lower at the end then at the beginning, so that follow-
ing the forecasts would not have been less successful than a continuous
investment in common stocks.
In view of this moderately but consistently successful result over
such a long period it may be of interest to consider the forecasting
method used and some statistical evidence as to the soundness of the
principles involved. The theory of these forecasters was that there was
a prevalence of sequences over reversals in the movements of stock
prices5 and that it was, therefore, desirable to swim with the tide. They
evolved various devices for recognizing when the tide had turned, no
attempt being made to anticipate such an event. The magnitude of the
cycles to be identified apparently was of several years' duration and par-
ticular significance generally was not attached to developments requir-
ing less than a few weeks to materialize. A detailed discussion of the
statistical devices employed in the forecasts will not be attempted here

4Where needed in order to preserve the continuity of this average, corrections

were made to offset the effect of stock dividends and changes in the list of stocks
included.
6 The word "sequence" is used here to denote when a rise follows a rise, or a
decline a decline. A "reversal" is when a decline follows a rise, or a rise a decline.

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 STOCK MARKET FORECASTING 213

because the forecasters never reduced their method to terms which

could be defined precisely in a mathematical sense or which made pos-
sible its application by two independent operators with any assurance
of securing identical, or at least similar, results. It will suffice to say
that they tried to recognize when the long-term trend of the market
had reversed itself simply by the superficial appearance of the general
pattern presented rather than by any precise statistical test.
What statistical evidence is there as to why such an apparently naive
procedure should be successful? The author and the late Herbert E.
Jones once made an investigation of the evidence as to the element of
inertia in stock prices as follows:6 In a penny-tossing series there is a
probability of one-half that a reversal will occur. If the stock market
rises for one hour, day, week, month, or year, is there a probability of
one-half that it will decline in the succeeding comparable unit of time?
In an attempt to answer this question, sequences and reversals, as de-
fined in footnote 5, were counted.
A study of the ratio of sequences to reversals will probably disclose
structure as previously defined, if it exists within the series, and the
significance of this structure can be investigated by ordinary statistical
methods. For instance, the probability can be determined that any
ratio occurred by chance, from a random population of possible price
series. Also, from the frequency distribution of these ratios one can
estimate the probabilities of success in forecasting a rise or decline in
stock prices. Samples of adequate length, where available, were ex-
amined, the intervals between observations being successively 20 min-
utes, 1 hour, 1 day, 1, 2, and 3 weeks, 1, 2, 3, * * *, 11 months and
1, 2, 3, . . . , 10 years. It was found that for every series with intervals
between observations of from 20 minutes up to and including 3 years,
the sequences outnumbered the reversals. As a result of various con-
siderations it appeared that a unit of 1 month was the most promising
from a forecasting viewpoint. In the case of the 100-year monthly series
of common-stock prices from 1836 to 1935, a total of 1200 observations,
there were 748 sequences and 450 reversals. That is, the estimated prob-
ability was 0.625 that, if the market had risen in any given month,
it would rise in the succeeding month or, if it had fallen, that it would
continue to decline for another month. The standard deviation for such
a long series constructed by random penny tossing would be 17.3;
therefore the deviation of 149 from the expected value 599 is in excess
of 8 times the standard deviation. The probability of obtaining such
a result in a penny-tossing series is infinitesimal.
An investigation of the average amount the stock market moved in

6 "Some A Posteriori Probabilities in Stock Market Action," by Alfred Cowles

and Herbert E. Jones, ECONOMETRICA, Vol. 5, July, 1937, pp. 280-294.

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214 ALFRED COWLES

each month, a consideration of brokerage costs, and determination of

the degree of consistency revealed by the data, were used to supple-
ment the information as to the ratio of sequences to reversals. This
further analysis indicated an average net gain of 6.7 per cent a year
with a probability of a net loss in 1 year out of 3. To this should be
added the expected dividend and interest income which for the period
analyzed would have been about 5 per cent a year. The anticipated
degree of success in forecasting should be modified by a consideration
of the fact that the unit of time employed, 1 month, was selected by
hindsight after investigation of various other possible units of time. The
investigation, however, discloses evidence of structure in stock prices
sufficient to account in large measure for the success of the 40-year
forecasting record herewith reported.

CONCLUSION

(1) The records of 11 leading financial periodicals and services since

1927, over periods varying from 10 to 151 years, fail to disclose evi-
dence of ability to predict successfully the future course of the stock
market.
(2) Of the 6904 forecasts recorded during the 15a-year period, more
than four times as many were bullish as bearish, although more than
half of the period was occupied by bear markets, and stocks at the end
were at only about two-thirds of their level at the beginning.
(3) The record of the forecasting agency with the best results for the
151 years since 1927, when tabulated back to 1903, for the 40 years
showed results 3.3 per cent a year better than would have been secured
by a continuous investment in the stocks composing the Dow-Jones
industrial average. Under present laws the capital-gains tax might wipe
out most of this advantage. While prospects for the speculator are,
therefore, not particularly alluring, statistical tests disclose positive
evidence of structure in stock prices which indicates a likelihood that
whatever success may be claimed for the very consistent 40-year record
is not entirely accidental. A simple application of the "inertia" princi-
ple, such as buying at turning points in the market after prices for a
month averaged higher, and selling after they averaged lower, than for
the previous month, would have resulted in substantial gains for the
period under consideration.

Cowles Commission for Research in Economics

The University of Chicago

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