Pilipinas Forum 20: Turbulence, Chaos Theory and the Stockmarket

Another long exchange here (12 pages) in pilipinasforum yahoogroups more than 9 years ago, on turbulence and chaos theory, applied to business and economics, the stockmarket especially. Enjoy!
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Turbulence, Chaos Theory and the Stockmarket
Feb 2002

Our friend Fidel Nemenzo sent me this one related to Dr. Muriel's lecture tomorrow evening at WSPC, AIM re. "the application of turbulence theory in stocks trading". Fidel obtained his PhD Math from Sophia U, Japan; he's the only number theorist in this country. He's teaching now at UP Diliman.
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Pards, mukhang interesting ang lecture ni Dr Muriel sa AIM. Dr Muriel is known for his ideas on turbulence, the nature of which is one of the main problems of chaos theory. One of the characters in Jurassic Park, Ian Malcolm, was a chaos mathematician. Jurassic Park was an example of a non-linear dynam ical system. Conventional (or the common-view) science (Newtonian) says that the physical world is a machine, governed by equations. If one knows these equations, and all the "initial conditions" in a a given system, just plug in these "conditions" into the equations and you can predict what happens to the system. This is what the creator of Jurassic Park believed: if you know all the "equations" what govern everything in Jurassic Park and the behavior of its creatures, plus the most accurate observations of the system, then you can predict everything that can possibly happen, and maintain control over it. Sabi ni Ian Malcolm mahirap yan, at halos impossibleng i-predict kung ano ang pwedeng mangyari. Chaos can arise out of the most "orderly" situations. Which is what happened.

The central goal of chaos theory is the study of systems that exhibit chaotic or "random" behavior. Parang may contradiction dito: the search for order within disorder. May tula si Wallace Stevens, " ... A violent order is disorder, and a great disorder is an order. These two things are one." This describes what happens in most natural systems. (Or even "social" systems, like a crowd. The most orderly crowd can metamorphose into an unruly mob in an instant, just as the perfect storm may just be over the horizon of the calmest sea.)

Another example of a "chaotic" system is the stock market, thus the growing interest in the mathematical theory of chaos among economists. Stock brokers and currency traders know that prices quoted in any financial market can change unpredictably. Huge volumes of money are made or lost in sudden bursts of activity. Classical mathematical models of finance cannot explain this behavior, for volatility is central to the behavior of financial markets. Which is why new explanations of market behavior are being sought using ideas from chaos theory. Or even fractals-- pero saka ko na lang ito i-e-explain.

The way fluid flows, or the behavior of a plume of smoke-- these contain both order and disorder. The term physicists use is turbulence-- which is chaotic and unpredictable. The study of turbulence is a key problem in physics. Conventional theories may be able to explain the smooth flow of water when the tap is turned on lightly. But nothing explains the turbulent flow of water when the tap is strong. Dr Muriel has proposed a theory which explains such behavior. I guess that's what he hopes to do in his AIM talk-- to shed some light on the volatility and unpredictability (turbulence!) of financial markets using his ideas on fluid flow. Both types of systems exhibit essentially the same activity. I can't go to the lecture; kwentuhan mo na lang ako.

- Fidel Nemenzo

Chaos theory may well become one of the most important theoretical fields in the 21st century (aside from relativity and quantum physics). I have been fascinated with how seemingly innocous changes in the initial conditions can have multiplier effects which are often complex and unpredictable. The most popular example is known as the "Butterfly Effect" in which the flapping of a butterfly's wings for example in Germany (I'm still in a thrall with the "butterfly" ending in "All Quiet on the Western Front" flick. Thanks Gina!) could cause miniscule atmospheric changes and which, given a time horizon could affect weather patterns in Pampanga. And think of how a very small change in testosterone level of an individual could trigger a nuclear war (ala Dr. Strangelove). So it could be like goodbye mankind, hello dinosaurs kind of thing.

Anyway, the latest experiment on the chaos theory involved sending a random signal to the Pioneer 10 spacecraft which is already in the edge of our solar system (before it will get blasted into smithereens by a Trekkie in the future, he he he). As Fidel pointed out, even the random dripping of a faucet has an order behind it. In other words, there's beauty in madness. or a method behind every madness.

- Glenn de Guzman



Noy, May kaunting comment lang ako dito sa sinabi ni Fidel na theory ni Dr Muriel. I wish I can attend Dr. Muriels lecture so that I can comprehend his comparison of fluid turbulence inside a pipe to that of the turbulence of a stock market. I do not understand how the stock market behave but I do a lot of simulation to predict when can we achieve turbulent flow of fluid inside a pipe.

Without going into complicated mathematical equations and different fluid properties, let us look at the flow of water inside a 10 cc syringe. As you apply pressure to squeeze the water out of the syringe, the water is in laminar flow inside the syringe but in the capillary diameter of its needle the water is in turbulent flow. If we repeat the same experiment using a viscous fluid like honey or condensed milk we can not reach turbulent flow both inside the syringe in the needle opening. My point here is: we can predict fluid turbulence inside a pipe. How it compares to a financial or stock market is a very interesting lecture I really miss.

- Lorrie Gallego

Friends, Interesting discussion!

Like you, the question of "how stocks behave" fascinates me immensely. The obvious practical application of "knowing how stocks behave" is that one can profit handsomely from this foreknowledge of their movements. If you knew back in 1986 that Microsoft was going to appreciate tremendously in value to become one of the world's largest and most profitable corporations, you'd have scrounged up all your available cash and borrowed as much money from your friends as you possibly could, and bought as many shares of Microsoft you could possibly get your hands on.

If you did that, today you'd be sipping margaritas in your million-dollar yacht cruising somewhere in the Carribean instead of reading this email. :)

This, of course, is the ultimate fantasy. This was the theme of the movie "Back to the Future 2" where Marty McFly's (Michael J. Fox's) nemesis Biff (Thomas Wilson) steals a sports almanac containing results of all sports events played between 1950 to 2000, transports himself using that DeLorean time machine into the future, where he then placed winning bets and turned himself into a billionaire.

By the same token, if you could only get hold of a copy of the Wall Street Journal circa 2015, you could certainly utilize the information contained in it to buy the winning stocks and short the losing ones, ahead of everybody else. That would be ultimate investment strategy.

But, in the absence of this capacity for time travel, we'd have to make do with information we obtain by analysing the PAST. The future is an IMPENETRABLE FOG, but the PAST can be studied. This is where the financial theorists come in.

I'm no financial theorist. So, let me introduce you to Harry Markowitz. Mr. Markowitz does this for a living (I obviously don't). In fact, he was awarded the Nobel Prize in Economics in 1990 for his
work on Modern Portfolio Theory (MPT). Essentially what Mr. Markowitz said in MPT is "Don't Put All Your Eggs in One Basket".

Now, many of us would question whether such insight deserved a Nobel prize to begin with. But, to Markowitz credit, he developed his theory in the 1950s long before asset diversification came in vogue. And he did crunch the numbers to support his theory. (Which means you too can win a Nobel Prize in Economics for a theory based on an everyday saying like "A rolling stone gathers no moss" - just make sure you have the STATISTICS to back you up!).

The idea of not putting all your "eggs" in one basket flows from the observation that individual stocks behave in an unpredictable manner. Princeton professor Burton Malkiel coined the term "random walk" to describe this erratic behavior of individual stocks (chaos theory?).

This isn't to say that stock investing is a waste of time. Overall, stock investing is still superior to investing in other ASSET CLASSES. Malkiel's point is that stocks AS A CLASS produce historical annual returns of 7-10%. Those who wish to capture these more or less predictable returns are better off putting their money in stocks as a CLASS, and should stop trying to look for the next Microsoft. The problem arises when one tries to PREDICT the movement of INDIVIDUAL STOCKS - there's no way anyone can achieve this successfully short of insider trading.

Anyways, these are just my non-economist's thoughts on CHAOS THEORY. Sorry for the intrusion.

- Noel

Noy, PFers,

Chaos theory is a fascinating subject and I have enjoyed some of the various insights here. I particularly liked Lorenzo’s discussion about fluid follow through pipes because it is a fairly simple system which becomes so much more complex as the fluid exits the pipe. The dynamics of such a system as the fluid while it is in the pipe only become more complex as you introduce variables which all affect the flow. Imperfections in the pipe may cause minor turbulence, even while the flow in general remains steady. Constrictions of the pipe cause further turbulence due to the Venturi effect. Without these it is easy, with these it becomes more complex. At least in these kind of cases the turbulence is fairly regular since they don’t change much over time. I had not thought of the issue of viscosity and its effect. I would suppose that even with higher viscosity you would have more turbulence at the exit if the fluid is under higher pressure and subsequently higher velocity?

How much more complex is any system when the ultimate variable comes into play – the human being. I used to believe that with enough computing power to handle the huge number of variables involved one may be able to predict the stock market with some degree of certainty. Now, however, I wonder how it would it ever be possible to accurately predict how individuals will react in all of the various circumstances. Especially when each have their own motivations.

A complex system that is more in line with my own occupation is weather systems. It has always fascinated me how so many individual variables come into play which seem to make it an infinitely complex system, but we are at still able to predict in a general way what will happen in the next two or three days. Beyond that, however, it becomes just too complex. The use of historic data with which one can compare other periods when similar variables were in play has helped, but we are still a long way off. Glen mentioned the “Butterfly Effect” which has always fascinated me as well. In actual practice, however, it seems there is a tendency in weather systems for friction, or a desire to return to stasis. So, while theoretically possible, it requires a far more significant input to the system to cause major change elsewhere.

I did appreciate Glen’s comment “In other words, there's beauty in madness.” It gives me hope that there is perhaps some beauty in how I seem to manage my day to day activities J

- Cynthia

The challenge behind chaos theory and systems is to be able to discern the order behind the seemingly random behavior patterns. It posits that no occurence can be considered as completely random, but determined in a certain by some complex natural process.

Regarding Dubya and the politicians, there are some studies in their nascent stages which try to apply chaos theory with geopolitical power plays and national security concerns (like dovetailing the thoughts of Clausewitz and chaos system; think about the "fog of war" concept).
-Glenn de Guzman

Dear Lorrie, Glenn, Noel, everyone,

Well, I attended Dr. Muriel's lecture last night at WSPC, AIM, re. "Turbulence theory & applications in currency trading" (not stocks trading). The room was full of traders & AIM students (esp. Indians). So, what did Dr. Muriel say, as far as my non-physicist, non-mathematician, or non-trader mind, could comprehend?

Money is the cost of energy. For instance, you spend to have dinner with someone, energy is lost somewhere, though you gain energy in the process (info or laughter you enjoyed from your dinner date). In physics, energy is conserved. Chaos theory has no energy conservation principle in its model; his turbulence theory has.

Dr. Muriel's model - where he showed only the series of long Greek equations, not the simplified one - has a predictive capability of only 1-2 days. The data used to plug into his software are taken on hourly basis online. What he showed were the results of his model, a series of graphs depicting the exchange rate bet. US$/Euro or US$/CHF or Euro/CHF. Well, his model focused on only 3 major currencies in the world - the US$, the Euro, and the Swiss francs. Of course I think the 3rd most traded currency in the world is the Japan Yen. The results of his forecast is +/- 0.008 Euro/US$, very small indeed. Despite all of these, Dr. Muriel says he's a conservative trader.

Going out of the room after the lecture, I don't think I learned much from his speech. My economics and political-animal mind still insist on the following:

1. Currency trading, like any other commodities or stocks, is foremost a function of supply and demand. If you know for instance, i.e., you have inside information, that some big local companies, or the central bank, will be in serious need for US$ tomorrow or next week as they have to pay those corporate or govt. loans, then demand for $ will be high tomorrow or next week. How about the supply - will there be a surge of OFW $ money to be exchanged into the local currency? If you got softwares and good data base that can track movement of these supply and demand for $, chances are you'll hit a jackpot by selling your $ tomorrow or next week, then buy $ when its price goes down (lower demand, surge in $ inflows).

2. A good grasp of the world politics and economy, as well as domestic politics and economy/ business, are your insurance to make a more reliable forecast. And this reminds me of the bank analysts and economists of some foreign banks, particularly DBS (devt. bank of Singapore) and SCB (standard chartered bank). Their analysts and/or economists (based in HK or London or Singapore) who only read dispatch from Bloomberg or Reuters or the net make really bold predictions like "P55/$ by end- 2001" (DBS, sometime last Sept or Oct.) or "P56/$ by Jan. 2002" (SCB, sometime last Sept. or Oct. too). Will write a longer discussion on this when i have the time later.

3. Theories in physics and math will have to "borrow" a number of theories from economics, finance or even political science to make their models and assumptions approach the realities in the market.

In short, I think turbulence theory as what I gathered from Dr. Muriel's brief lecture, will still need a long way to make it more applicable to a different turbulence in the currency and finance markets. That is, if I should gamble my money in currency trading, i would prefer consulting a good economist like ozone or glenn, than a physicist.

I want to be honest to Dr. Muriel in my comment on his lecture, so I cc him. You may write him at dtsny@.... yeebbaa!!

-Nonoy

Dear Noy, PFers,

I've noticed that no topic prompted much and diverse reactions (and counter-reactions) as the topic of Turbulence & Chaos theories, well since I joined PF as few weeks ago. I wonder whether last night's lecture will become some mathematician's passport to unimaginable wealth. Even if all the Field's Medal awardees develop some complex mathematical systems in the future which will enable us to do far complex and powerful computations,

will we finally conquer risk, and finally tame Wall Street's bear? If some mathematical genius will finally develop a really workable Grand Unified Theory will our view of the future be any more accurate than Babylonian astrologers? Can we, like Paul Dirac's god, [re]create the [financial] world with our beautiful mathematics? Even then, I will not count on it.

It was said that Newton's determinism rules the physical world, while the fuzzy sub-atomic world is best understood by quantum physics Yet what system is best to understand man? Thus far, even the best effort of political science, psychology, sociology, and all the other 'ogies has yet produce a system that can fully capture the full complexity of human behavior. Clearly man is far more complex than the summation of his experiences, and his reaction to environmental stimuli far more diverse social science anticipates. Religion seems to fare better here than all of the sciences in attributing man's behavior to his "indwelling personality," "intensions," "self-determinism," and his "free will."

How will you capture these attributes, unique to homo sapiens, in mathematical models? Yes, of any sophistication. Unfortunately, this is the man which inhabits the trading floor, not the homo economicus we freely assume in economics.

I agree with you that traders will be better off consulting with economists (Oops, forgive us, our biases are showing!) that some physicists. Yet, that advise too must be taken with a proverbial grain of salt. You may recall Noy that economists' dealings in the stock market aren't immune to her whims after all. Isn't it that Irving Fisher lost much of his wealth in the financial crash of the 1930s, and no longer recovered from it. In 1998, just a year Merton and Scholes received the Nobel Prize for their work (yes, of the famed Black-Scholes formula on options pricing), Long Term Capital Management, a hedge fun in which they were among the principal shareholders had to be rescued at a cost of $3.5 billion dollars.

- Ahmed Mendoza

Nonoy,

Dr. Amador Muriel, I think, uses three currencies in his model, not necessarily based on whether these currencies are the most traded ones. He does claim that his use of the Swiss Franc is solely based on the fact that he loves living in Geneva (where he lives for a substantial portion of each year).

From what I gather, his turbulence/energy conservation principle measures the changes in the relationship between two currencies US$-Swiss Franc for example, against the changes in the US$-Euro exchange rate, to predict the probable movement of the Euro-Swiss Franc. His idea is based on the concept that changes in the relationship between two currencies will be reflected in the relationship between those two currencies and the rest of the currencies in the world market. The 'rest of the world currencies' is easiest and best approximated by the use of a third (which probably has to be a major) currency.

I assume you only need two highly tradable currencies -- US$ and Euro - or US$/Yen perhaps, and a third currency from which to trade from to run the model. Which is why I think Dr. Muriel is looking to applying his theory to the lowly Philippine Peso (pardon my lack of monetary nationalism). I assume he'd use the changes in the Peso-Yen and Yen-US$ to predict the Peso-US$ exchange rate.

As for your preference of economics over physics in predicting currency market movements, despite my being an economist (or probably BECAUSE I am an economist), I will have to disagree with your stance. Economists (and bankers for that matter) have been constantly making extremely horrible predictions, going nowhere as near as Dr. Muriel in terms of precision power.

My favorite 'study' regarding this predictive capacity is the Asian Wall Street Journal's annual battle pitting stock tips from so-called experts (bankers and economists) against humble taxi drivers and janitors. Each year, the taxi driver has a better tendency of making more money from his or her portfolio than the million-dollar-salaried guy who does this for a living. If a taxi driver can beat an economist on predictive power, I'd bet on the guy with a PhD in physics any day than a team comprised of Sachs, Summers, Greenspan, Samuelson, etc.

- Robby Galang

Noel:

Just a quick follow-up to your earlier posting on chaos theory and random walks (two very different things, by the way):

>But, in the absence of this capacity for time travel, >we'd have to make do with information we obtain by >analysing the PAST. The future is an IMPENETRABLE FOG, but the PAST can be studied. This is where the >financial theorists come in.

Agreed, but as they say, "past performance is no guarantee of future results". More on this below.

>I'm no financial theorist. So, let me introduce you to >Harry Markowitz. Mr.
Markowitz does this for a living
>(I obviously don't). In fact, he was awarded the Nobel >Prize in Economics in
1990 for his work on Modern >Portfolio Theory (MPT). Essentially what Mr. Markowitz
>said in MPT is "Don't Put All Your Eggs in One Basket".

I wish it were as trivial as that!:) Markowitz got the Nobel (which was shared with Merton Miller and William Sharpe) for expressing, in a tractable form, the problem of finding portfolios with maximum expected returns per unit variance, and, most importantly, for providing the earliest mathematical solution to this problem. (Incidentally, his solution was not based so much on crunching through actual data and statistics on portfolio returns, but on nonlinear optimization techniques of a non-statistical character). Granted, it was based on a simple, commonsensical idea--most useful economic theories are--but applied to the problem of stock-picking, it is an idea that back then was difficult to SOLVE and apply. The Nobel committee also prefers to give its award to work that has fostered substantial practical applications, and Markowitz's highly influential work (as well as that of Miller, Sharpe, Black, Scholes, and Merton) did in fact lead to the creation of entire industries (mutual funds, financial derivatives,
financial engineering, risk management, etc.)

I agree that the balance of the evidence is that insider trading and asymmetric information are the most likely sources of predictable, persistent, above-normal returns. There are still anomalies in asset-returns like the "January" effect, the predictability of forward-spot exchange rate premia, etc. But the balance of the evidence does point to insider knowledge as a major candidate explanation behind most cases of abnormally high or predictable returns.

As you point out it is also an established empirical fact (but one based mostly on U.S. data) that the historical returns of a diversified basket of stocks has produced higher long-run returns than other assets (e.g., bonds). However, I should alert one and all that there are some good reasons to question the stability of this historical pattern. Here two references come to mind: one is Robert Shiller's popular (2000) book, "Irrational Exuberance". The other is a recent NBER technical paper (March 2001) by Jagannathan, McGrattan, and Scherbina entitled "The Declining U.S. Equity Premium", in which they document that the 7-10% stock return advantage over bonds that was true of the period 1926-70s has now become more like 0.7%! This last paper is inordinately technical for most tastes, so I would recommend leafing through Shiller instead for this new view of long-run stock market returns.

Incidentally, the term "random walk" comes from mathematicians not from Malkiel. The term "random walk" (meant to describe the kind of behavior similar to that of a drunk trying to walk home) already appears in books on stochastic processes from the 60s, two decades before Malkiel wrote his popular book.

Sincerely,

- Butch Arroyo

Butch, Noel, Nonoy, Fidel and other PFers following the discussion on chaos theory:

I believe that what Dr. Muriel is trying to do is to mathematically model via series of Greek equations the behavior of complex variables, specifically investor pyschology in order to make sense of the apparent chaos/turbulence in financial markets. This to me implies nothing else but using historical information to explain possible future outcomes. This would NOT be different at all from what economists currently do in running input-output, general equilibrium and other econometric models to forecast macroeconomic performance in the short run. Nor would this be different from technical analysis used by analysts in predicting stock performance.

The only real value of PAST data is providing investors clue about the quality, robustness and certainty of the firm's FUTURE cash flows. Companies like Ayala, San Miguel and other blue-chips have so-called GOOD FUNDAMENTALS because their historical performance provide solid basis for projecting their FUTURE cash flows. There is lower uncertainty over their ability to deliver the FUTURE income and therefore they are charged lower risk premium: their equity promises relatively lower return, while their debt enjoys lower spread vis-a-vis T-bill benchmark. In contrast, many tech firms have NO HISTORICAL TRACK RECORD. Therefore, there is high uncertainty over the probability of these firms delivering on their promised cash flows. The higher risk premium is translated to higher required return to compensate for the risk or if they are issuing debt, they would be charged higher spread by the banks to cover additional risk.

But what determines FUTURE performance? This can easily be explained by economic theory. Let me try to explain as simple as possible.

PROFIT is the relationship between REVENUES and COSTS. The higher the revenues vis-a-vis the costs, the higher the profits. In turn, REVENUES depend on both PRICE and QUANTITY. We know that the ability to price and generate sales is governed by factors such as price elasticity of demand, degree of competition, presence of substitutes, threat of forward or backward integration, etc.

These factors are summarised by Michael Porter in his classic Five Forces Model. A complement to the static Porter model is Gary Hamel & CK Pralahad's dynamic concept of competencies and strategic architecture in their COMPETING FOR THE FUTURE book, while Adam Brandenburger & Barry Nalebuff further adds game-theoretic aspects of competition in their classic book COOPETITION.

On the other hand, COSTS depend on both MACROECONOMIC variables such as INFLATION, INTEREST RATES, FOREIGN EXCHANGE RATE, WAGES and TAXES, as well as the firm's own working capital needs, technology and HR spending, R&D, etc.

Therefore it should not come as a surprise why the financial markets react immediately to news about employment indicators, Greenspan's testimonies, introduction of new technology, etc. All these information fundamentally affect the various variables that impact on the firm's profitability.

The volatility or "chaos/turbulence" in the financial markets simply reflect investors perception of the impact of new information on fundamental values of various assets. The "overshooting" of FX rates, for instance, is largely due to risk perceptions by investors - as more information becomes available then the uncertainty subsides and value moves up/down to more "normal" or stable levels.

Problem with using past data is when one relies entirely on these information alone to make investment decisions or management strategies. One faces danger of missing non-linear trends, discountinuities and the like. The on-going Enron/Andersen scandal and cloud of doubt it has raised on reliability of audit and accounting information should also convince us of danger of taking at face value claims by companies in their published annual reports.

- Ronald Villanueva

Butch, Thanks for your comments. May I respond:

You quoted the oft-repeated statement "Past performance is no guarantee of future results."

This statement is so intuitively correct that I even wonder why mutual fund companies and brokers include this in their prospectuses. We all know that there's no such thing as an iron-clad guarantee of getting a specific outcome to ANYTHING we do - not in governance, not in marriage, not in medicine, certainly not in investing. We can only go by the probability that certain patterns we see in the past will repeat themselves in the future. I'm fairly confident that when I wake up tomorrow morning, the earth will still be here and it'll be business as usual for me. But who knows: there's a chance of 1 in 50 million that an asteroid about 1 kilometer in diameter will strike earth overnight, killing everything in it.

But, I'll take my chances. And get myself a good night's sleep.:)

That's why I'm still bullish on stocks. I've read Robert Shiller's book and I agree that US stocks had become overvalued during the late 1990's. This wasn't the first time that a stock market bubble had occurred and it most certainly won't be the last.

The take home message from Shiller's book (to me anyway) is that IT PAYS TO DIVERSIFY YOUR PORTFOLIO. I don't think Shiller ever advocated abandoning stocks altogether, especially not if you're in your late twenties/early thirties (which happens to be my age group), and therefore have a long term horizon ahead of you. I could understand the reservations our older colleagues would have with respect to investing in equities: they won't have much time to recover from a prolonged bear market. I'm willing to take that risk. To each his own RISK-APPETITE.

I think this way because I've examined the historical record: the long term performance of US stocks HAS BEEN superior to other asset classes. Between 1802 to 1997, stocks returned AFTER INFLATION 7.2% annually. During the same period, bonds returned 2.0% after inflation annually, while gold returned -0.1%. That's based on 200 years of historical data. In the absence of a time machine or Nostradamus-like powers of clairvoyance that can show me what'll happen in the FUTURE, I'm stuck with studying the PAST.

(Interestingly, the data for international stock returns - UK, Germany, Japan - from 1926 to 1997 come to within 1% of US stock returns - fairly competitive.)

With regards to "random walk", you're absolutely right. Malkiel didn't invent that term. But he did POPULARIZE it through his bestseller "A Random Walk Down Wall Street".

- Noel

Noel:

Don't get me wrong-- I myself follow a similar strategy (heavy on stocks and mutual funds). And the time-series econometrician in me respects the forecasting power of history, logically modeled.

But hear me out on this one: if a long-term (say 25 year) stock market investment is as superior as investment professionals paint it, then one would have to say that at some point risk aversion or risk preference no longer matters, only expected time till death does. So referring to an actuarial table and discovering that with 97% probability, I, at age 30 (not my true age) will reach age 55, I (or my heirs) would then be blessed with a one-way bet. I could take out a really cheap loan (nowadays, a 25-year home equity loan would cost me effectively about 4% interest a year after tax), and invest the proceeds of the loan in some diversified stock mutual fund, or say some S&P depository receipts, which track the return of the S&P500. (If I really wanted to juice it up, I would pick a fund consisting say, of small companies, since going with history, their long-run return is even higher than the broad market.) If history is any guide, then I should expect, with a high degree of confidence, a cool 3-6% spread over the 4% cost of funds.

Is this really a one-way bet? Would you actually do it, borrow like this and leverage the proceeds into a long-term investment in equities? I ask myself, and honestly, I can't be sure if I would actually do it. But it seems this is a logical implication of believing that the long-run return on equities is superior to that of interest-bearing bonds, or a bank loan.

That's my practical question. But inasmuch as this discussion was originally inspired by chaos theory, along those lines I also have a more metaphysical (yet less serious) question.

As I understand it, chaos theory proposes that the long-run of certain dynamical systems, like the weather, are highly sensitive to small perturbations in initial conditions. One implication of this is that even if you knew for sure the exact equations that govern the behavior of a chaotic system, the presence of infinitesimally small changes in the initial state of the system, or small measurement errors, will produce enormously different long-run results, or forecasts. (This is why analysts only produce short-run forecasts from chaos models). In short, the long-run state of a chaotic system is, for all practical purposes, unpredictable even with complete understanding of how the system works.

So now, if asset and stock markets, like the weather, turn out to be a chaotic dynamical system (some people actually believe this, I myself don't, or at least hope not), then could we really trust 25-year point estimates of future stock returns based on our initial assessment of current market conditions (and realized historical returns)? What if some sleepy accountant accidentally misstated last quarter's earnings on AT&T? Would that be like the Chinese "butterfly" affecting the weather in North America?

Wow, that's heavy. In any event, thanks for your earlier response. And happy investing.

Sincerely,

- Butch A.

"I could take out a really cheap loan (nowadays, a 25-year home equity loan would cost me effectively about 4% interest a year after tax), and invest the proceeds of the loan in some diversified stock mutual fund, or say some S&P depository receipts, which track the return of the S&P500."

Butch, it's interesting that you make this point since this is similar to the conclusion that Wharton's Jeremy Siegel arrived at. Moderate and aggressive investors (whom Siegel defined as those having holding periods of at least 10 years) should be able to achieve their financial goals with a reasonable probability of
success by allocating "over 100%" of their portfolios to equities. This means borrowing or leveraging an all-stock portfolio. So, yeah, this is the logical implication of the observation that the long-run return on equities is superior to that of bonds or cash. Actually, borrowing against your home equity to buy stocks probably makes more sense anyway because of the lower interest rates involved in it than if you bought stocks on margin. I know someone who has successfully implemented this strategy. (No, he hasn't lost his house yet.)

Whether I personally would leverage my own portfolio this way, well, that really depends on my time horizon and goals, wouldn't it? I think you would agree that there's no boilerplate asset allocation strategy that's applicable to EVERYBODY. Even the hypothetical situation you described above which you label as a "one-way bet" isn't really the most "efficient" portfolio in real life. The reason I say this is that as YOU the investor get OLDER, your holding period gets SHORTER. D-Day looms larger and larger. The 100% stock portfolio that you started out with when you were 30 years old will have to be reconfigured gradually as you age. By the time you're 45 years old, the 100% stock portfolio will obviously no longer be appropriate for you (assuming of course that you intend to cash out at age 55.) Reallocation of part of the portfolio to bonds and cash will have to occur.

With respect to your statement that "infinitesimally small changes in initial state of systems will produce enormously different long run results", I perfectly understand what you mean. In fact, this is vividly demonstrated by the comparative genomic sequences of humans and chimpanzees (our closest "relative" in the animal kingdom). The human genome and the chimp genome are 98.77% identical. An "infinitesimally small" difference of 1.23% in genetic constitution separates our species from the chimps.

Thank God for infinitesimally small differences! :)

- Noel
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See also

Pilipinas Forum 12: Origin of Zero, Nothingness, Big Bang... September 25, 2011

Pilipinas Forum 14: Math, Infinity and Limit, October 04, 2011