Results May Vary

I’ve written previously about some of what I consider the shortcomings of orthodox financial economics. In general, it appears to me that economic theory is largely detached from reality in much the same way astronomy was before Copernicus and Galileo.

One instance of this detachment from reality is the “random walk” theory of financial markets. This model of market behavior was developed in the 1960s and still holds sway in the retail research departments of most U.S. brokerage firms. It’s based mainly on this:

What the chart shows is the Dow Jones Industrial Average from its creation in 1896 to the present (monthly closing prices; my apologies for the unreadability). The greenish line is a “linear regression,” that is, the straight line that is the best fit to the actual data points. Linear regression was a cutting-edge tool back in the ’60s, when computing power was rather limited. But there’s an unargued underlying assumption in applying it to a market, which makes the “random walk” theory an exercise in circular logic.

The assumption is that the graph of a stock index like the Dow in a way “wants” to be a straight line but can’t manage it. What economists actually say is that the market “seeks equilibrium,” by which they mean that it wants to go up continuously and at a consistent rate. But instead, there are “perturbations” that cause “fluctuations” above or below the idealized rate of gain. Those fluctuations are by nature random (hence “random walk”) and therefore are unpredictable.

Thus, investors shouldn’t try to guess when the market is going to have one of those “perturbations” – in other words, they shouldn’t try to practice “market timing” – but instead should simply buy stocks and hold them for the long term, because the underlying trend always goes higher. And here the logical circle is closed.

Since the 1980s, the random walk theory has come under increasing criticism, and many economists outside the Wall Street houses acknowledge that it’s not a realistic model. Many still want to cling to some variation of randomness, however, and have developed hybrid models that include some degree of self-recursiveness along with the randomness, giving us things like the exotically named GARCH model: “generalized auto-regression with conditional heteroskedacity.” However, scientific studies have shown that these models have zero value in predicting market movements.

Another argument in favor of “buy and hold” investing is the claim that the stock market consistently over the years has provided an average annual percentage return that is higher than other kinds of investments. But this depends very much on how you calculate the annual return. The usual figure is 8 percent, compared with half that return or less from interest-bearing investments such as bonds.

It’s true that if you take the closing price of an index like the Dow on a given day and calculate the percent change from the same day the year before, and you average that calculation over the past 100 years, you’ll get a figure something like that 8 percent number. But the calculation doesn’t bear any resemblance to how people actually invest: You can’t “buy the Dow” every day and sell it a year later.

I’ve constructed a model that I think represents more accurately how people really invest. I had to make some simplifying assumptions, but I believe the result is still more indicative of the kind of average returns investors can expect.

Here’s the idea: Let’s suppose that a worker sets up a program in which he or she invests a set percentage of his or her income each month. This program continues for 30 years, at which point the worker retires and cashes out. I’ve also assumed that the worker gets a cost-of-living raise at the beginning of each year, based on the nominal inflation rate (based on the Consumer Price Index) for the previous year. (That’s something few workers are actually seeing today, so the model may actually overstate the investor’s returns somewhat.)

The following chart shows the average annual return a worker would have received by following this investment strategy:

The time scale (if you can read it; right-click to open it bigger in a new window) indicates the date upon which the worker began the monthly investment program, and the vertical scale shows the percentage return at the end of 30 years for a worker who started investing on the date shown. For example, a worker who started an investment program in the very first month that Charles Dow calculated his industrial average in 1896 (i.e., the very beginning of the blue line) would have earned an average annual return of 2.86 percent over the next 30 years.

The very highest average return, 18.11 percent, would have been earned by a worker who began a monthly investment program in December 1969 and cashed out in December 1999. Obviously, the average annual return for someone who started 10 years later and cashed out last year would have been quite a bit less, just 3.92 percent at the low point in February 2009.

Worse yet, people who started investing in late 1901 to mid-1903 would have lost money, as would almost everyone who started in 1912. Perhaps most surprisingly, anyone who embarked on this kind of program in the late 1940s to mid-1950s -- which we're used to thinking of as boom times -- would have earned a fairly paltry annual return of about 2 percent or less when they cashed out in the late 1970s-early 1980s -- which were not so booming.

Overall according to this scenario, investors who have cashed out to date have earned an average annual return of 5.05 percent or a median annual return of 4.44 percent. Those figures aren’t all that much above the long-term average or median returns on interest-bearing investments. As I said earlier, the results may overstate the average returns because of my assumption about annual salary increases. In addition, the numbers don’t include any taxes or transaction costs such as brokerage commissions.

However, the real lesson of this exercise isn’t about long-term average returns, it’s about the wide variability of the real-time returns. What it boils down to is that even for a long-term investor, your results still depend entirely on when you start investing and when you cash out. If we relate that to our entry into the career world, it shows how much the decision is out of our hands: We can’t choose what year we’re born. Whether we like it or not, we’re all market-timers.

Gloom and Doom

In my first posting here a few days ago, I alluded to the belief held by many scientists (Richard Dawkins is an obvious example) that the cosmos is essentially a random process and has no overall order or purpose. I noted then that I disagree with that view and also that many scientists have come to question it.

There are two main reasons, I think, why this random model came to be prevalent. The first is Darwinism, which holds that species evolve as a result of random genetic mutations. The second is physics, which models matter as “particles” that interact randomly. I could also throw in the concept of entropy, a consequence of the second law of thermodynamics, which Victorian physicists first theorized would lead eventually to the “heat death” of the universe.

All of these things together produced an astonishing pessimism among the intellectual elite of the late 19th century, epitomized by Matthew Arnold’s marvelously gloomy 1867 poem “Dover Beach”:

Ah, love, let us be true
To one another! for the world, which seems
To lie before us like a land of dreams,
So various, so beautiful, so new,
Hath really neither joy, nor love, nor light,
Nor certitude, nor peace, nor help for pain;
And we are here as on a darkling plain
Swept with confused alarms of struggle and flight,
Where ignorant armies clash by night.

As I indicated the other day, I think the emphasis on randomness (as well as the gloom) is overwrought, to say the least. Even granting that, for example, atoms in an unconfined space move and interact randomly, as soon as they do interact, various natural laws and forces (gravity, the strong and weak nuclear forces, etc.) come into play to create structure. Similarly, even if a new, more “advanced” species emerges as a result of a random genetic mutation, that species’ existence (and success) increases the likelihood that a future mutation will produce an even more advanced and successful species.

An analogy: Suppose a rainstorm forms directly above the Continental Divide. The individual raindrops will fall randomly around the divide. But as soon as each drop hits the ground, gravity and geology kick in, and the pathways those drops take from that point on are predictable: They will flow either to the Atlantic Ocean or the Pacific (leaving out evaporation, absorption, being swallowed by grizzly bears, etc.).

Similarly, the widely held Big Bang model in cosmology holds that the initial state of the universe was a hot fog of more or less randomly distributed particles. But natural laws have gradually drawn matter into recognizable patterns or structures – galaxies, clusters of galaxies, stars, planets, etc.

Another way of putting it: The proponents of randomness claim the natural state of matter (and energy) is “equilibrium” – basically a more or less uniform distribution. That state may be disturbed occasionally by random events (stars colliding and so on), but it always returns eventually to equilibrium.

In contrast, researchers in recent decades (Nobel Prize laureate Ilya Prigogine, for example) have noted and analyzed the many instances of systems that are, as they say, “far from equilibrium” – that is, they exhibit self-sustaining and self-reproducing non-randomness. Today, there’s lots of interesting work being done on studying complex systems and creating models that take account of the wholeness of objects instead of breaking them down atomistically; one place to see some of that work is the Web site of the Center for Integral Science.

Despite these developments, mainstream economists continue to insist that financial markets are well-modeled as a random process. The leading proponent of this view is Burton G. Malkiel, a Princeton economics professor whose book “A Random Walk Down Wall Street” remains the Bible of this viewpoint. In essence, Malkiel claims financial markets tend toward equilibrium because all investors (the “particles” in this model, characterized as “rational agents” who seek to “maximize their personal good”) have access to the same information. Occasional “shocks” caused by the introduction of new information, or other “inefficiencies,” are quickly damped out as investors adjust. As a result, fluctuations in the markets are random and unpredictable, so it’s impossible to “beat the market” through timing or other strategies.

It’s a nice, neat, self-consistent theory, but in the four decades since Malkiel first published the book, there has been abundant research showing that the random walk doesn’t actually provide a good model of market behavior. A search for the phrase “random walk” in the Research Papers in Economics online IDEAS database produces one study after another showing that the random walk hypothesis fails when applied to a wide range of financial markets.

Even so, random walk theory continues to be taught in economics classes. (Malkiel himself remains unrepentant, or maybe he just isn’t keeping up with the literature; I interviewed him in the early 1990s and asked him whether any of the then-emerging criticisms of his theory from the perspective of nonlinear dynamics/“chaos theory” had given him pause, and he responded by talking about the so-called January Effect, which has nothing to do with nonlinearity.) One result is that when the stock market jumps 900 points one day and plummets 400 the next, everyone seems astounded, and we hear the so-called experts “explaining” these moves in terms of that day’s news headlines.

The alternative – or “an” alternative, at least – would be to acknowledge that financial markets exhibit some sort of orderly structure. That’s a claim that has long been made by a variety of non-academic observers and analysts (Elliott Wave Theory is a notable example). If true, the identification of the details of that order would have potentially enormously profitable implications. So far, if anyone has figured it out completely, they aren’t telling.