Can the Huge Advantage of Stocks over Bonds, Piled Up between 1946 and 1968, Ever Be Diluted Away?

Jeremy Siegel, in defending his thesis in favor of Stocks for the Long Run, quotes in support the international evidence compiled by Dimson, Marsh & Staunton, in their 2002 book, Triumph of the Optimists. DMS note that every stock market, in every nation, out-performed bonds—over the 100 years of the 20^th century.

I’ve elsewhere used historical US data from the 19^th century to challenge Siegel’s thesis (see my papers at ssrn.com).  I’ve also challenged the international data.  But in both cases I need carefully to pull out sub-periods to show stocks failing to out-perform bonds (e.g., in the US during the fifty years from 1793 to 1843).

France provides a good international example of the question at hand.  Over the entire 117 years from 1900 to 2016, French stocks out-performed French bonds, consistent with Siegel and with conventional wisdom (see the DMS 2017 yearbook from Credit Suisse).  But over the 57 years from 1960 through 2016, French bonds out-performed French stocks—a result which might surprise many investors.

But is it legitimate to pull out a sub-period for separate examination? That’s my topic today.

In social science generally, the norm is to use the largest (longest) available sample, and always to use the complete sample—no cherry picking. On this reasoning, the fact that French stocks out-performed French bonds over the entire 117 years makes it irrelevant to show that the reverse occurred during the last half of the period. No sub-setting allowed. Use only the best (entire) sample.

Conversely, elsewhere in social science it is considered imperative not to mix apples and oranges. If you want to predict the height of a human being whom you are about to meet, you will be more successful if you split your historical data on human height into male and female sub-samples, and determine the gender of the stranger before hazarding a prediction. And you will do even better if you know whether the stranger is of Scandinavian ethnicity.

By analogy, if market history consists of a series of regime changes, some of which favor stocks, and others of which favor bonds, then it becomes important to break out sub-periods and examine them separately. Only thus can we discover that there have been regime changes. Restricting all our analyses to results on the entire aggregate to date, which may be about to experience a regime change, or which currently includes more instances of one regime type versus another, becomes misleading. Again by analogy, if we had never noted and broken out gender or ethnicity in our historical collection of height data, we could not know that there are reliable differences in height by gender and ethnicity, and our height prediction will be that much less successful.

Still elsewhere in social science, the concept of the “outlier,” and the imperative of its removal, holds sway. Consider a reaction time experiment, where subjects press the left button if the image shows a gender-compatible action, the right button if not (the stereotype literature is rife with such studies).  The expected mean difference across experimental conditions is, say, 20 milliseconds, with an overall average response time of 50 milliseconds (= .05 seconds). But suppose in one session you have a hungover fraternity bro.  He starts to nod off during the session. When image #54 is on screen, it takes him 3.5 seconds (3500 milliseconds) to jerk awake and press one of the buttons.

His data, if retained, will destroy the experiment. Even if you double or triple the sample size, his data will overwhelm the remainder—it’s too discrepant, and whichever experimental condition he occupies must show a significantly slower reaction time, either supporting or refuting the hypothesis under test.

In self-protection, some experimenters in this field apply a rule to discard all observations more than 3 standard deviations from the mean. Other experimenters claim that this smells like cooking the data.  Debate rages.

Back to market history: the period from 1946 to 1968 was an outlier within the historical record.  To an unprecedented degree, stocks wiped the floor with bonds. As with the fraternity bro, any sample that includes the 1946 to 1968 period must conclude that “stocks beat bonds over the long-term.” Even if that sample includes a century of other data during which, say, stocks and bonds performed about the same, the huge out-performance of stocks during that one short period will drive the results measured over the entire period. If you have to include the fraternity bro—if you can’t sub-set time periods—you will have to accept the inference that stocks always beat bonds.

But, dear reader, is my assertion about stocks and bonds from 1946-1968 correct?  Is it true that not even a century of parity performance could dilute away the aberrant results seen from 1946 to 1968? How about two centuries? Put another way, Is the analogy to the fraternity bro fair? Can we treat the 1946-68 period as an outlier which it might be useful to set aside, in at least some analyses?

The thought experiment proceeds as follows:

1. Between end-1946 and end-1968, an investment in stocks turned one dollar into $10.90, after adjusting for inflation, a real return of 11.47% annualized, almost double Siegel’s estimated long-term average for stocks. Long government bonds—”certificates of confiscation,” as they came to be called—with their woefully inadequate returns, turned one dollar into $0.78, a negative real return of minus 1.1% compounded (data from the Ibbotson SBBI).
2. Siegel’s long-term return estimates are 6.6% real for stocks and 3.6% real for bonds. Their midpoint is 5.1%.
3. To determine how much of an outlier the 1946-1968 period represents, let’s assume that over the ensuing century, stocks and bonds were to perform exactly the same, each returning the midpoint of 5.1% compounded.
4. When you invest one dollar for 100 years at 5.1%, you grow it to $144.63. This will be our multiplier.
5. Next, we take the $10.90 stock portfolio achieved at the end of 1968 and multiply it by $144.63. This gives us the value of our stock portfolio in 2068, after 122 years of investing.  Do the same for the bond portfolio worth $0.78 in 1968.
6. Next take, the 122^nd root of the 2068 portfolio values. This gives us the annualized return of stocks relative to bonds over the entire investment period beginning in 1946.
7. To avoid a version of Zeno’s paradox, set a stopping rule. Define “diluted away” as stock and bond returns that fall within +/- 0.125%, one-eighth of a point, of 5.1%–the true long-term average outside the outlier period.

I’ve tabled the results below. As you can see, one century of parity performance doesn’t come close to reversing the calculation that stocks will significantly out-perform bonds over the “long-term,” even though the out-performance is confined to a comparatively short span of twenty-two years.

Okay, what if we add two centuries of parity performance, giving a total sample of 222 years, not too far from the US historical sample of 211 years used in Siegel’s book (2014)? Nope, stocks still dominate bonds, with “long term returns” coming in at 5.71% versus 4.47%, despite two centuries of delivering exactly the same return.

How about 400 years, the far horizon of modern investment history, generally taken as beginning with the Amsterdam stock market in the early 1600s?  Well here we begin to see some convergence, albeit with stocks still notably in the lead, now returning a real 5.42% over the 422 years, against bonds’ 4.77%. But, like Zeno’s turtle approaching the finish line, the convergence is slowing.

To jump ahead, it will take over one thousand years of parity performance before our stopping criterion is reached; 1085 years to be exact. At that juncture our stock investor has earned 5.22% over the 1107 years, and our bond investor has earned 4.97%.  Although our stopping criterion has been met, the stock investor, with 2.99 X 10²⁴ dollars, remains well ahead of the bond investor, in fact $2.77 trillion, trillion dollars ahead (the bond investor ends up with only 215 sextillion dollars).

Oh wait—the world economy doesn’t amount to 215 sextillion dollars, much less 2.99 septillion.  So even if Rollo the Dane, first Duke of Normandy, had split his estate into a stock and bond portfolio in 934 AD, his descendants couldn’t have earned 5.1% compounded over the ensuing 1085 years. No one could (or did).

Actually the thought experiment would have blown up much earlier, probably by the 200 year test at least. My contention is not that stocks will never dramatically out-perform bonds again.  Rather, the assumption is that significant out-performance by stocks is a relatively rare event that occurs no more often than once every century or two. If, at any time during the thought experiment, we see an event on even a more modest scale, like the Civil War, when stocks first moved decisively ahead of bonds in the long-term sweepstakes, then Zeno’s turtle must return to Go, does not collect the 200 years of parity performance, and essentially, starts over.

In short, 1085 years is not going to suffice to dilute away the out-performance of stocks seen in 1946-1968, because, one or two centuries into the test, there will likely be another period of stock out-performance, even if much more modest, which will abolish the dilution achieved to that point, re-starting the clock.

As long as we are condemned to analyze only the entire historical record up to today, never a subset, we are always going to conclude that stocks beat bonds, in any sample that includes 1946-1968.  Your grandchildren will come to that conclusion, your great-great-great grandchildren will conclude the same, and your great-great-great-great-great-great grandchildren will likewise, as they analyze three and then four centuries of data which include 1946-1968. 

Mathematically, if we must only use the entire sample, the current conclusion can’t ever change. Doesn’t matter if a more fine-grained analysis would reveal that “every century or so, stocks enjoy one or two decades of exceptional out-performance, even as 80% to 90% of the time, they perform exactly the same as bonds.” Entire lifetimes could pass without an episode of stock out-performance, and the conclusion would remain the same: “the historical data show that over the long term, stocks have out-performed bonds.” Too bad about your lifetime.

Must we include the hungover fraternity bro, and accept the experimental results showing his condition to have the slowest average reaction time? Must we only take human height, and never break out male and female average height, in making our predictions? Then we can also ignore the last 57 years of market history in France, and can continue to predict, with confidence, that French stocks will out-perform French bonds, because that’s what happened over the best (longest) sample available to us, all 117 years of it.

No cherry-picking, right? 

No possibility of regime change?

Table for the Thought Experiment

	Stocks	Bonds
[Real] value of $1.00 invested from 1946 to 1968	$10.90	$0.78
Annualized return over these twenty-two years	11.47%	-1.1%
After one century of parity performance at 5.1%, portfolio value now:	$1,576	$113
Annualized return over the entire 122 years:	6.22%	3.95%
After two centuries of parity performance at 5.1%, portfolio value now:	$228,014	$16,393
Annualized return over the entire 222 years:	5.71%	4.47%
After four centuries of parity performance at 5.1%, portfolio value now:	$4,769,857,350	$342,918,863
Annualized return over the entire 422 years:	5.42%	4.77%
. . .	. . .	. . .
After 1,085 years of parity performance at 5.1%, portfolio value now:	$2.99 X 1024	$2.15 X 1023
Annualized return over the entire 1,107 years (stopping criterion met):	5.22%	4.97%

 

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That’s the main meal; now for a cheese plate to wrap up. With the framework in hand, we can vary the assumptions to address alternative scenarios that may have occurred to you.

1. What if returns were lower during the parity period—1.9%, say, instead of 5.1%? That’s the average of the worst 20 year period for stocks in the SBBI with the worst 20 year period for bonds (not coincident). Would a lower parity rate change how long it would take to reach the point of dilution?

Not by much; at those lower parity returns I make it 1,050 years instead of 1,085.

2. What if an ordinary bear market had occurred in 1969, before testing for dilution? Say, a 50% decline in stocks accompanied by a 10% rise in bonds.

That makes some difference: the point of dilution is now reached after only 750 years.

3. What if the Great Depression had been replicated following 1968? SBBI data show a stock market decline from August of 1929 through June of 1932 of almost 84% (total return), accompanied by a rise in bonds of 14% (also total return). If those returns are inserted after 1968, and then parity performance commences, how long afterwards until the point of dilution would be reached?

Now that does make a considerable difference: time to dilution is cut to 270 years.  But of course, a Great Depression would be particularly likely to see a stock market bounce in the years after, so this shorter time span is also highly unlikely to be reached before the clock must be reset.

4. Now, something a little different: in France, from 1960, stocks under-performed bonds by about 1% per year in annualized terms. Unlike all the previous examples, in this final piece I consider how long a modest stock under-performance would have to be sustained, to dilute away 1946-68. Here I set the bond return at 5.6% and the stock return at 4.6% (approximately what occurred in France from 1960 through 2016). For consistency I use the same stopping criterion of +/- 0.125% (although here Zeno’s paradox doesn’t apply; given enough years, the bond portfolio value must eventually surpass that of stocks).

Does a century of modest stock under-performance suffice to dilute away the 1946-1968 outlier? Nope.  Two centuries?  Not quite—it takes almost 220 years to reach the stopping point. A few years later, some time before the 3^rd century is complete, the bond portfolio will finally overtake the stock portfolio in size.

For perspective, 242 years is a few years longer than the US stock market has been in existence.  It follows that even if stocks in the US had under-performed bonds by 1% per year, every year, outside the 1946-68 period, through their entire history, it would still be correct, if we are obliged to use the entire sample, to state that “Stocks have out-performed bonds over the long-term.” This holds, even as that statement would also be false, the reverse of the truth, for 220 of the 242 years, or 90% of the time.

That’s the price of “no cherry-picking allowed.” 

Face it: the stock advantage booked from 1946-1968 is never going to fade out of the data. As long as we must look only at the entire available sample, it will always be true that stocks have out-performed bonds. Forever. Even if no period like 1946-1968 ever occurs again.

Jeremy Siegel can never be proved wrong!

* * *

Now a glass of port to finish the meal. I invite the reader to consider the futility of calculating compounded returns, over a period of centuries, and expecting these numbers to provide a useful guide to what your investment experience might be over the next ten, twenty, thirty or fifty years.

Note also the absurdly large portfolio sizes that occur once we compound over more than two centuries—a reminder that in the real world, nobody makes 6.6%, or even 3.6%, over the very long-term.

Please consider: What if using the entire historical sample was less illuminating than taking out sub-periods to study the range of investment outcomes that you, finite human, might experience during your life?

For additional thought experiments in this vein, please see my paper “Stock Market Charts You Never Saw.”