Stocks and homes are assets priced in US$ -- their soundly shown price histories are inflation-adjusted ("real").
Such are seldom seen, because: Well apparent therein are our nation's serial, massive mispricings.
"The public be suckered" is both this track record and keeping it unseen. Dow=DJIA.      usa2true AT posteo.de
Plot of Real DJIA, 1924-present, ca. 25 KB

Declarations
My sole purpose in authoring this web page is to facilitate rationality for the common good.

The contents of this web page are historical data, presented as specified, plus some numerical examination thereof. There is little extrapolation, no forecasting, and no offered explanation(s) of this history (but please do your own thinking).

A plot such as that above was published by The Wall Street Journal on 3/30/99, page C14, titled “Dow, Inflation Adjusted” (the agreeing overlay of the two plots is here with quoted text).

(Separately and elsewhere: for Fed Chair warnings, link from the first item in Related Work at the end of this page; for inclusion of a recent day, link from the third item.)

Description
The Dow Jones Industrial Average, the DJIA or Dow, is the U.S. stock market price indicator the media most often quote. It is reported at the close of each trading day, e.g. 8306.35 on 4/25/03; the unit of this 8306.35 Dow price is US$ on 4/25/03. Thus, comparing Dow prices from different times is comparing apples to oranges because the consumer purchasing power of the US$ depends on the time.

To make an apples to apples comparison, one must divide the Dow price for a particular time by the consumer price index for that same time, and then compare quotients. I have done this to obtain the points in the plot, which thus shows the Dow’s consumer purchasing power over time (a horizontal gridline corresponds to a constant amount of the ‘goods and services purchased by households’). Specifically: points are monthly averages starting with 1/24 (January 1924); each datum = the monthly average of daily closing Dow prices, divided by the CPI-U for that month, multiplied by 1.49629 (=100*168.8/11281.26), making the (then) all-time high in 1/00 (January 2000) equal to 100 (see plot) -- these data are designated the “Real Dow”. Note: CPI-U is the broadest, most comprehensive consumer price index published by the U.S. government. ("The CPI is generally the best measure for adjusting payments to consumers when the intent is to allow consumers to purchase at today's prices, a market basket of goods and services equivalent to one that they could purchase in an earlier period.") So, at a given time, Dow and Real Dow are both the price of the same stocks. The Dow price is in then current US$, whose consumer purchasing power much-depends on the time. The Real Dow price is in ‘constant dollars’, whose consumer purchasing power does NOT depend on the time. The (then) maximum Real Dow = 100, equals the consumer purchasing power of US$11,281.26 in January 2000, which equals the consumer purchasing power of US$15,896.15 in August 2014 (CPI-U rose 40.9% over this 14 year, 7 month interval).

To illustrate: the Dow averaged 985.93 in 1/66, and 4746.76 in 9/95 = 4.81 times higher; the CPI-U was 31.8 in 1/66, and 153.2 in 9/95 = 4.82 times higher; thus, the Real Dow for 1/66 and 9/95 are very nearly equal at 46.4 (see plot). This plot is directly inspired by the 3/30/99 publication of such a plot, titled “Dow, Inflation Adjusted”, by The Wall Street Journal (in article “The First 10,000 Points. How It All Adds Up to 10000”, page C14); the agreeing overlay of the two plots is here with quoted text.

Again to illustrate: the Dow averaged 985.93 in 1/66, and it was nearly the same 16.75 yr later, = 988.71 in 10/82; but the CPI-U increased from 31.8 in 1/66, to 98.2 in 10/82 = 3.09 times higher; thus, the Real Dow for 1/66 and 10/82 are very different, = 46.4 and 15.1 (see plot), a more than 2/3 decrease over the 16.75 yr.

And this recent illustration: the Dow averaged 11281.26 in January 2000, when the Real Dow = 100.0 = the (then) all-time high. In August 2006, 6.6 yr later, the Dow averaged just 0.2% less (at 11257.35), but the Real Dow is 17.4% less (at 82.6) -- because consumer prices rose 20.8% (CPI-U, from 168.8 to 203.9).

Observations
The plot of Real Dow since 1/24 is dramatically very far from being a steady trend. It is in fact replete with big increases and big decreases -- the Real Dow of 12.4 in 6/82 is less than that 56.6 yr earlier in 11/25 (see plot)!

The plot is judged dominated by three “big peaks”, each an all-time record high at the time: 31.6 in 9/29, 46.4 in 1/66, and 100 in 1/00. Each of the first two of these peak prices was not again reached for nearly 30 yr (see plot). From 10/29 to “recovery” in 4/59, the Real Dow averaged 49% of the 31.6 in 9/29; from 2/66 to “recovery” in 11/95, the Real Dow averaged 60% of the 46.4 in 1/66.

It is really amazing how unindicative of the future both of these first two peak prices were. The average of the Real Dow from 10/29 to any later time took 77.8 yr to reach the 31.6 of the 9/29 peak! At 8/14, 84.9 yr post-peak, the average is 35.9= 113.7% of 31.6. And the average of the Real Dow from 2/66 to any later time took 46.9 yr to reach the 46.4 of the 1/66 peak! At 8/14, 48.6 yr post-peak, the average is 48.3 = 104.0% of 46.4.

Remember!
“The plot shows the history of the market price of a stocks-holding. For every timely trade one stocks-holder made, there was the other side of that trade ... . The plot reflects the composite market price experience of all market participants = of the average stocks-holder.”

Executive Summary of the Remainder of this Web Page
The remainder of this web page is some detailed numerical examination of the long-term past performance of the Real Dow (exceptions: Detailed Description and Related Work are as titled; the latter has a link to “the 3 Fed Chair warnings, Real DJIA” which starts with a plot that should not be missed).

A Quantitation obtains the rate of increase +1.64%/yr compounded annually as the long-term past performance of the Real Dow. This comes from choosing the two big peak to big peak intervals as comparable periods (together = 70.3 yr), and relating them.

Market Price Volatility first defines a best-fit, +1.64%/yr compounded annually curve for these Real Dow data. The average Real Dow volatility (“+ or – difference of Real Dow from the curve”) is equivalent to ca. 20 years of the 1.64%/yr growth! A range of Real Dow market price of a factor of 2.0 is equivalent to this average volatility.

Long-Term ‘Capital Gain’ Variation is a simple, initial effort to explore for the scatter that composes the already obtained +1.64%/yr compounded annually long-term ‘capital gain’ average rate. Obtained are just four components which together compose the total. These four component long-term rates cover -0.61 to 3.21%/yr, a range of 3.82%/yr which is a factor 2.3 times the average. Much scatter does compose the +1.64%/yr compounded annually long-term ‘capital gain’ average rate.

A Quantitation
A numerical characterization of the long-term past performance of the Real Dow follows. (I attempt to avoid dependence of the characterization on choice of starting and ending dates.) I choose the big peak to big peak intervals (i.e., 9/29-1/66 and 1/66-1/00) as comparable periods (together = 70.3 yr).

During the 36.3 yr first period, the Real Dow averaged 19.3, “centered” (the first moment of the period's Real Dow prices about the “center” date equals zero) at 10/1/51. During the 34.0 yr second period, the Real Dow averaged 33.5, “centered” at 8/10/85. The ratio of these two averages is 1.735 (= 33.5/19.3), and the two “centers” are 33.9 yr apart.

This factor of 1.735 increase in Real Dow in 33.9 yr equals +1.64%/yr compounded annually. I offer this rate of increase as a fair characterization of the long-term past performance of the Real Dow. Of course, this rate is in addition to keeping up with inflation, and it includes neither the positive cash flow of dividends paid nor the negative cash flow of frictional costs paid (frictional costs = the expenses associated with the DJIA component stocks-holding and -transaction).

Market Price Volatility (refers to: up and down price movements = price fluctuations = price vacillation = neither steady nor steadily trending price)
As above in Observations, “The plot of Real Dow since 1/24 is dramatically very far from being a steady trend.”. As above in A Quantitation, “... +1.64 %/yr compounded annually. I offer this rate of increase as a fair characterization of the long-term past performance of the Real Dow.”. Now I will first aim to express average volatility of the Real Dow in terms of equivalent years of 1.64 %/yr compounded annually rate of increase.

The smooth curve in the Real Dow plot below increases at exactly 1.64 %/yr compounded annually (please here ignore the six black triangles and squares). It is scaled such that, over the 9/29-1/00 interval of 845 mo, the average of all the 845 differences between the Real Dow and the curve, expressed as factors > 1, is a minimum. (NOTE: a Real Dow = twice the curve’s value, and a Real Dow = half the curve’s value, are both a factor of 2 difference -- first is times 2, second is divided by 2.) Thus, this curve is a best-fit, as described, constant rate of increase (exponential) to the Real Dow over the 9/29-1/00 interval. Notably, the Real Dow equalled: 2.53*curve in 9/29; curve/2.57 in 7/32; 2.06*curve in 1/66; curve/2.38 in 6/82; 2.55*curve in 1/00.

Plot of Real DJIA, 70 yr, best-fit trend curve, ca. 26 KB

From the preceding, the minimized average factor (difference between the Real Dow and the curve) is 1.417; the median factor is 1.344; the geometric mean factor is 1.383. These factors equal +1.64 %/yr compounded annually for 21.4, 18.2, and 19.9 years, respectively. Thus, long-term Real Dow (market price) increase of 1.64 %/yr was accompanied by average volatility (“+ or – difference from the curve”) equivalent to ca. 20 years of 1.64 %/yr! And, this accompanying volatility included the five extreme months noted above, with factors 2.57 - 2.06, equivalent to 58 - 44 years (average 54 years) of 1.64 %/yr.

Note that 1.417 is the average of factors > 1 that either multiply or divide the curve’s value to equal the Real Dow. Thus, the range of (Real Dow) market price equivalent to this average volatility (“+ or – difference from the curve”) is a factor of 2.0 = 1.417/(1/1.417) = 1.417 squared.

The 1.417 is the average of 845 factors, ranging 1.00 to 2.57, and whose highest quartile averages 1.87, which is equivalent to 38.5 years of 1.64 %/yr (see table following).

Distribution of the 845 Months’ Factors (Differences Between the Real Dow and the Curve): the Four Quartiles Equivalent to Which 25% Range Average —> 1.64%/yr for 1 (lowest) 1.00 - 1.17 1.07 4.4 years 2 1.17 - 1.34 1.25 13.6 years 3 1.34 - 1.63 1.47 23.8 years 4 (highest) 1.63 - 2.57 1.87 38.5 years
Long-Term ‘Capital Gain’ Variation (‘capital gain’ can be negative, i.e., a capital loss)
As above in A Quantitation, “... +1.64 %/yr compounded annually. I offer this rate of increase as a fair characterization of the long-term past performance of the Real Dow.”. Thus, average long-term ‘capital gain’, expressed as an annually compounded rate, is already obtained. And obviously, the already evident, very large volatility of long-term, real market price dictates very large variation of long-term, real ‘capital gain’. In fact, it would seem that (for ‘appropriately/correspondingly measured volatility and variation’) the price volatility is a lower limit for the ‘capital gain’ variation, because ‘capital gain’ is twice dependent on price.

Now I seek to explore for the scatter that composes the +1.64 %/yr compounded annually. Already done: the two comparable periods, 9/29-1/66 and 1/66-1/00 (here called 1 and 2), were used to get +1.64 %/yr compounded annually and the best fit curve (see plot). CONCEPT: for each period (1 and 2), divide into the months (with Real Dow prices) above (A) the curve and the months below (B) the curve, giving four groups total; use the four couplings possible of these four groups to represent the scatter that composes the +1.64 %/yr.

THE FOUR GROUPS (together comprising the 9/29-1/00 70.3 year interval) Real Dow Center of Group Months Average —> Average 9/29-1/66 19.31 10/1/51 1A 213.5 26.59 1/9/55 1B 223 12.33 12/26/44 1/66-1/00 33.49 8/10/85 2A 196.5 45.63 6/7/86 2B 212 22.24 1/14/84
All of the four groups have similar numbers of months.The centers of averages were calculated as above in A Quantitation. In the Real Dow plot above, for each of the four groups, a black triangle is located at its Real Dow average/center thereof (and for each of the two periods, the same is a black square).

The Four Couplings Possible, of the Four Groups Real Factor Center Dow (end/ >1 = to Avgs, start) 1.716/ Center end/ Rel. Rate —> for OR Couple /yr start Wt. %/yr 33.9yr —> /1.716 1A—>2A 31.4 1.716 .209 1.73 1.790 1.043 1A—>2B 29.0 0.837 .209 -0.61 0.812 2.113 1B—>2A 41.4 3.700 .289 3.21 2.912 1.697 1B—>2B 39.1 1.803 .293 1.52 1.667 1.029 Wtd. Avg. Rate =1.61 1.61%/yr for 33.9yr —> 1.716 Wtd. Avg. Factor of The Four Couplings =1.451
In the table preceding, the 2nd and 3rd columns combined give Rate (annually compounded) in the 5th column. Relative Weight in the 4th column comes from the product: 2nd column*start group months*end group months; all four differ only modestly from 0.25. The four Rates’ (-0.61 to 3.21) weighted average is 1.61 %/yr, which is very satisfactorily close to the best fit curve’s 1.64 %/yr (obtained above in A Quantitation, along with 33.9yr). The results in the 6th column, from the annual compounding for 33.9yr of the four Rates, are ratioed with the 1.716 from the 1.61 %/yr, to give the Factors > 1 in the last column. Their weighted average is 1.451. A Factor > 1 in the last column is the difference in total capital at the end of 33.9yr between the couple’s Rate and the 1.61 %/yr average.

Assessment
The 1.451 is the average factor difference, in total capital at the end of 33.9yr, between the four couplings and their 1.61 %/yr average. From Market Price Volatility above, 1.417 is the average factor difference over 70.3yr between the Real Dow and its best fit, +1.64 %/yr curve. These two factors are judged directly comparable: they are close, and the first does exceed the second.

Difference will NOT be recognized in the rest of this Assessment between 1.64 %/yr and 1.61 %/yr, because they are so close. Note that multi-decade ‘capital gains’ are expressed as annually compounded rates. Note that 33.9yr is merely the time between the “centers” of periods 1 and 2; it is NOT from any selection of starting/ending dates.

Much scatter does compose the +1.64 %/yr average long-term ‘capital gain’. Of the four components from the table, half are very close to average (1.52 and 1.73 %/yr), and half are very far from average (-0.61 and 3.21 %/yr)! Very notably, the four components can be condensed to these two: 0.56 %/yr for starting above the curve, and 2.37 %/yr for starting below the curve.

Note that 1.451 is the average of factors > 1 that either multiply or divide a couple’s result to equal the 1.61 %/yr (weighted average’s) result. Thus, the range of total capital at the end of 33.9yr that is equivalent to this average variation (from the weighted average’s result) is a factor of 2.1 = 1.451/(1/1.451) = 1.451 squared (the corresponding rates are 0.50 and 2.73 %/yr). This range of total capital at the end is directly equivalent to a factor of 2.1 difference in the magnitude of an income stream -- for example the difference in a monthly Social Security benefit between $475. and $1000.

The 1.451 is the average of 4 factors, ranging 1.03 to 2.11. Half are very close to 1.00 (1.03 and 1.04), and half are very far from 1.00 (1.70 and 2.11).

Detailed Description
Because (calendar) monthly averages are used, the designated date is the 16th of the month.

The month’s average of daily closing DJIA prices is used. Daily DJIA closes since 1896 available at
http://www.djaverages.com/?go=industrial-index-data
and available from a later date at
http://finance.yahoo.com/q/hp?s=%5EDJI
and at
http://www.google.com/finance/historical?q=INDEXDJX:.DJI

The Consumer Price Index for All Urban Consumers, CPI-U, is published monthly by the U.S. Bureau of Labor Statistics. Data since 1913 are available in a 12-column format at
ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt
and in a single column format at
http://research.stlouisfed.org/fred2/data/CPIAUCNS.txt

The Real Dow were calculated as specified above in Description. All Real Dow averages for periods starting or ending with 1/66 include the 1/66 Real Dow datum at one half of one month's weight. A first moment about a date is the sum of the products of a month's Real Dow and the time difference (+ or –) from that date. The TABLE shows “all the numbers” I used/computed and is self-explanatory after the preceding.

The three Real Dow big peaks are shown superimposed in the overlay. Real Dow data are shown from 1/80 to now. The Real Dow data for 1/24 to 7/32 and for 1/46 to 6/82 were shifted to later times by 70.3 yr and by 34.0 yr, respectively, and multiplied by (100/31.6) and by (100/46.4), respectively, to coincide the 9/29, 1/66 and 1/00 big peaks in the overlay.


Related Work
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