ANYONE who has tried to swat a cockroach will know those insects' strange ability, in the heat of pursuit, to disappear. Robert Full and his colleagues at the University of California, Berkeley, have now worked out how they do this—and taught a miniature robot to copy the feat.
Dr Full had been using high-speed photography to study how cockroaches employ their antennae to sense and cross gaps. When the researchers made the gaps wider, they saw the animals flipping back underneath the ledge at the edge of the gap, rather than jumping across the empty space. As they report in the *Public Library of Science*, cockroaches running towards a gap suddenly grip the edge with the hooklike claws on their rear legs and swing 180° to land firmly underneath the ledge, upside down. They can pull off this stunt in a fifth of a second—so fast that the animals' bodies are subject to between three and five times the force of gravity, and also so fast that the movement is invisible to the human eye.
Dr Full and his colleagues have since identified similar behaviour in other animals with hooklike toes that are good at escaping pursuit: geckos, for example. They have also teamed up with members of Berkeley's robotics laboratory to program a small six-legged robot that has strips of Velcro attached to its rear legs to do the same trick. Such a robot could be fitted with a camera and used as a surveillance device. Some people, though, might prefer it to be fitted with a miniature machinegun and used as a UCPV (unmanned cockroach pursuit vehicle).
Here is an amazing spectacle. Everyone knows that the house must win and the players, over time, must lose. And yet casinos flourish all over the world. Nor, contrary to the standard arbitrage argument for efficient markets, does the smart money, the house, end up with all the capital in the world while the dumb money, the players, go broke losing the capacity to sustain inefficiencies in the market. To the contrary (and contrary to one of Jarrow’s assumptions) there is a continuous source of wealth for the house to keep winning; the dumb money is constantly replenished.
From the fantastic article: "How Big is Almost?: or why the finance professoriate is clueless about managerial effectiveness"
Stefan Jovanovich quotes from the paper:
"The paradoxical notion that uncertainty is absolute, that randomness is an objective quality, first and foremost of nature but by extension of social and economic life as well, has been rampant in our time. It was at the heart of the Copenhagen debate over the direction of quantum physics. It drove Keynesianism and Marxism and Smith’s replacement of the entrepreneur with that invisible—but oh so heavy—hand. It drove centuries of absurd debate over the relative importance of “capital” and “labor” as if they were objective fungible commodities with capabilities separable from the particular capitalists and laborers who wielded them."
"(t)here are men who consistently hit the bull’s eye at 300 yards and men who never hit it once. There are baseball players who hit .300 over a career and those who ride the bench. There are engineers with dozens of important patents to their name and those who never amount to much. There are farmers who prosper year in and year out and those for whom the weather is always bad. And generally we say the successful shooters and hitters and engineers and farmers are “good” at their jobs and the unsuccessful ones less good. We do not generally say (unless we are feeling envious), “Oh, they were just lucky,” or “they were breaking the rules.”
Can securities markets be so special among all markets, among all the arenas of our experience that in them alone diligence and skill and judgment and even raw talent do not correlate with good outcomes?"
"Randomness or “incomplete knowledge” is a subjective phenomenon. Different observers will have more or less knowledge and more or less uncertainty as a result. Moreover we can gain knowledge by dint of hard work, natural talent, and sometimes luck. We can be well prepared or poorly prepared to make a decision, discover special relativity, or buy a security. Even our best efforts to increase our knowledge may be insufficient. We may know a lot but not quite enough. We may fool ourselves about our positive expectation. There is no guarantee that our search for knowledge will bring us close enough for success. But neither is there any basis for a dogmatic ssumption of failure—or futility."
"We celebrate successful investors with other successful entrepreneurs as risk takers. This is true in the sense that the successful investor, like the entrepreneur, routinely makes judgments in the face of uncertainty. Nevertheless, the essential job of both investors and entrepreneurs is to reduce that uncertainty. Successful investors make money not by accepting risk as a given, as Modern Portfolio Theory tells us to do, but by increasing their ****
chance of making good decisions as compared to the less informed, less diligent, less talented. Admittedly how good investors, or entrepreneurs, do this is not entirely obvious. Edison helpfully told us it was 99% perspiration and 1% inspiration, but he was distinctly unhelpful in explaining how we might come by that crucial 1%. The progress from the objective uncertainty of a coin flip to sound judgment or even inspired creation is only partly a matter of quantifiable factors like more research or better math. Psychology or character or knack or what you will play an enormous role. Ultimately it does seem to matter not only what the investor or manager or entrepreneur."
Easan Katir writes:
This is the most articulate rebuttal of the random walk theory ever! Thank you for posting.
If the heat of debate contributes to global warming, then this long conversational thread alone may have raised the earth's temperature a degree or so.
Gary Rogan writes:
It still all comes down to how predictable and persistent someone's ability to outperform SOMETHING is. Whether or not the mathematics of price movements are distinguishable from brownian motion, which they clearly are, this whole never-ending argument is about whether outperformance is reliable enough to (insert your own criteria here, like "bet the house"). The world is a confusing place, for instance Victor seems to really like "Random walk down wall street" year clearly he does other things besides putting everything into some total world ETF. Even if someone has stellar history, how can you ever know that starting tomorrow they will be on a long losing streak that will either reverse all of their gains up to now or make them quit the game?
Referred to me by the folks at the Museum of Mathematics, there is a great article in NY Times that refers to M. F. M. Osborne's 1962 paper: "Periodic Structure in the Brownian Motion of Stock Prices"
Excerpt from the op-ed article "Magic Numbers" by Daniel Gilbert:
Magic “time numbers” cost a lot, but magic “10 numbers” may cost even more. In 1962, a physicist named M. F. M. Osborne noticed that stock prices tended to cluster around numbers ending in zero and five. Why? Well, on the one hand, most people have five fingers, and on the other hand, most people have five more. It isn’t hard to understand why an animal with 10 fingers would use a base-10 counting system. But according to economic theory, a stock’s price is supposed to be determined by the efficient workings of the free market and not by the phalanges of the people trading it.
And yet, research shows that fingers affect finances. For example, a stock that closed the previous day at $10.01 will perform about as well as a stock that closed at $10.03, but it will significantly outperform a stock that closed at $9.99. If stocks close two pennies apart, then why does it matter which pennies they are? Because for animals that go from thumb to pinkie in four easy steps, 10 is a magic number, and we just can’t help but use it as a magic marker — as a reference point that $10.01 exceeds and $9.99 does not. Retailers have known this for centuries, which is why so many prices end in nine and so few in one.
Gary Rogan adds:
I found this article that says a different numerical bias affects the entire universe under various guises.
Ken Drees asks:
Would it be fair to say that "deliberateness", a concept of action, is required for Benford's law to engage in natural environment. A quake, a wind, a measurable force?
Gary Rogan replies:
I don't think so. I was trying to explain to myself how something so basic yet so powerful can exist and this is the explanation I just came up with (and it's fully consistent with randomness of certain processes).
Imagine yourself shooting projectiles at an infinite log base 10 labeled axis. What are the chance that any number you hit starts with 1 if everything is completely random? My geuss was it's log base 10 of 2, and voila: I just calculated it and it's equal to .301, or the percentage they cite (30.1%). This law must characterize any truly random phenomena where the measurements are distributed over many orders of magnitude. When you don't see this law, this must indicate absence of randomness or a close concentration around some mean.
Jeremy Smith comments:
In the binary number system, all numbers save zero begin with a 1.
Gary Rogan writes:
The probability of the number starting with a 1 is log of 2 base whatever type number system you have other than of course for the binary system. It's just the ratio of the distance between 1 and 2 on the log axis divided by the distance between 1 and the number equal to the base of the system. There may be even a way to express it so that it works for the binary system since log of 2 base 2 is 0, but not right now.
Victor Niederhoffer comments:
Osborne was reporting on a phenomenon he and I studied in a number of papers see "N and O Jasa 1966" for references, and his work was not a Benford thing. it was a specialist thing with all the limit orders concentrated there. It's related to Livermore's breakthrough "the round number" and much else. By the way I consider Osborne the greatest researcher in this field to have ever graced the behavioral finance and efficient markets field. His creativity was unbounded.
October 12, 2010 | Leave a Comment
It's generally accepted that large electric utility stocks are interest rate sensitive. They also have earnings growth based on a regulator-sanctioned "acceptable return on capital." The stocks are considered cheap when they are trading near book value (not now), and also when their yields are relatively high versus treasuries and bonds (yes now). There's some economic sensitivity to electric demand of course– but the stocks are still very low beta.
I posit that at their current relative prices, a basket of quality utility stocks should outperform TIPS… with similar risk and reward. The reason is not that utility stocks are particularly cheap, but rather because many TIPS have trivial and/or negative real yields. In a rising inflation environment, utilities should be able to get regulator approval to raise prices [to maintain their statutory ROE]– and in the current status quo environment, the stock yields will exceed the TIP yield.
At this moment, the 5yr Treasury has a 1.1% nominal yield, the 5 year TIP has a -0.50 real yield, and the UTY has a 4.34% nominal yield.
What am I missing here? Other than regulatory risks, in what environment will the UTY significantly underperform a 5-year TIP held to maturity?
Mr Krisrock comments:
In his book on theory, Ray Dalio of Bridgewater theorized that "stress testing" an investment theme by asking other unsuspecting traders their views, in effect is a surreptitious poll, as we note here in this textbook case of pedestrian "street begging".
Rocky Humbert responds:
Perhaps Mr. Krisrock will be so kind as to put a penny in this beggar's cup with an insight using all of his over-sized frontal lobe (and not just the amygdala).
I thank the speclisters who kindly pointed out (offlist):
1) During the 1930's depression, utility stocks held their dividends… And people who paid their bills saw higher rates to compensate for the people who did not pay their bills.
2) The TIPS will return par at maturity — there is no similar guarantee for utility stocks.
3) Because TIPS are currently trading at a premium to par, outright deflation can be injurious to their returns.
4) Utilities are taxed as corporations — and are also subject to the risks of cap&trade etc. However, the state rate-setting boards may/may-not compensate for the increased costs of cap&trade with rate hikes.
The daily and weekly statistical correlations between utes and tips are quite poor. But as the attached chart shows, they do seem to move in the same directions.Perhaps foolishly, I'm least worried about technological innovation– because the primary motivation for investing in a regulated utility is that they set rates based on a statutory ROE….
Jeff Watson writes:
Wireless electrical power transfer has been around since Leyden, Franklin, van de Graaf, and Tesla, just to name a few. Radio waves are a wireless electrical transmission system….just ask me, as a ham radio operator I have gotten many very nasty RF burns when my system wasn't properly grounded, or I stood directly in front of a beam antenna when someone keyed up the transmitter putting 2KW through the antenna. Further back was the study of charged amber by the ancient Greeks and the ability to turn static electrical potential into kinetic energy. The thermoelectric effect has reputedly been described since the middle ages. Now, the newest commercial application of wireless electrical transfer is with those new cellphone and iPod chargers where you just lay them on the pad and it magically charges the batteries with no electrical circuit. One might expect for more practical applications as time goes by and the market demands the convenience.
Mr. Krisrock adds:
In India, for example, there are many rural areas without electricity or the likelihood of same. Some years ago we partnered with Reliance and built cell towers with solar panels that allowed locals to plug in their mobile phones into the cell towers to recharge them. Until we did this they had to send them back to the cell phone company to recharge them…clearly some pennies for the beggars cup….
Tyler Mclellan comments:
You're missing this. The future nominal rates are the sum of the short rates (at least to some point on the yield curve). If you finance the position at overnight money (which many marginal buyers do), you cannot lose money if the sum of the short rates is less than the yield. I repeat, no matter what happens to inflation etc…you cannot lose money so long as the short rates one finances at are less than the yield. Through one more iteration, TIPS work the same way.
So i suspect the answer to your question has to do with the nature of "return".
David Hillman adds:
Once we could not imagine a wheel nor a printing press nor telescopes nor electricity, nor steamships, nor the camera, nor the radio, nor the automobile, nor the incandescent light, nor telephones, nor submarines, nor television, nor computers, nor endoscopic surgery, nor nanotechnology.
The 4 ounce, 4.75"x2.5"x0.5" device clipped to my belt is a GPS, a voice recorder, an 8MP camera, a calendar, an alarm clock/stopwatch, a music/video/tv player, a language translator, a dictionary, an encyclopedia, a library, an internet browser, it allows remotely operating a computer half-way across the globe, it connects to gmail, to WiFi, it recognizes touch commands and voice commands, it will both convert the spoken word to text and vice versa, and oh, yes…..it's a telephone, too. The cost of entry is $99 + $55/mo. Such a device was not imaginable as recently as 20 years ago.
A world without a power grid depends upon a collective will to have it, vision, investment, R&D, innovation, efficient production, practicality, affordability, and profitability.There are many individuals moving "off the grid" now, some adopting current [no pun intended] technology, wind, solar, water, other renewable, that allows same, others eschewing that technology in favor of more basic passive and mechanical means, horsepower and elbow grease.
But while basic technology exists, instead of pursuing advancement in earnest, we persist in taking the easy, short-sighted, petroleum-based way out, screwing ourselves in the process.Still, given the history of technological advancement, one might suggest somewhat optimistically that, someday, we will will it and the question is less "could there be?" than it is "when?" Until then, we'll just plod along from crisis to crisis as we humans are wont to do. Plus ca change…..
Jeremy Smith comments:
You wrote, "It's generally accepted that large electric utility stocks are interest rate sensitive. They also have earnings growth bas…"
"Generally accepted" is statistically incorrect, at least since 1994, which is a long time. Correlation to bond prices is actually negative. Utility dividends also increase. They can estimate 3-4% increase for an index of these, more for the better companies. Of course the longer you hold a higer yielding stock with dividend growth, the more hopeless fixed income is by comparison, especially with regard to income generated. As income rises it forces higher the value of the instrument producing the income, all other things being equal.
Phil McDonnell comments:
I do not think that it is generally accepted that utilities are negatively correlated with bonds but that appears to be the case. I picked idu for utils, tlt for 20+ treasuries and shy 1 yr treasury. For last 105 days of daily net changes we have the following co-terminal correlations:
idu tlt idu
shy - 54 74
Perhaps the utility– interest rate connection is more complicated than upon first reflection. 1. They are heavy borrowers for their capital equipment financing so one would think they are hurt by higher rates. 2. Their are regulated, so when their regulators are convinced that rates have risen they will often give them rate relief which means higher rates are eventually mitigate. 3. The stocks sell in competition for investment dollars with other income producing assets such as bonds etc. So they must be priced to yield competitive returns.
Steve Ellison writes:
Could it be that there is little interest rate sensitivity when rates are very low? Or that the correlation was arbed away when everybody knew about it? Last year, I noted a similar regime change in the correlation of stock prices and interest rates.
Tyler McLellan writes:
Look, stocks and bonds have been Correlated negatively in price terms since 1999/2000, I would bet that utilities have been correlated enough to the market as a whole that they've been at least partially along for the ride.
One reason to suspect this? Maybe if equity price are set my marginal preferences of equity investors if tech stock a goes down and that makes people want to sell some ute b to buy more, it might not matter that bonds are twenty bps lower, especially when the bond buyers don't care about either.
Rocky Humbert writes:
I played with the data a bit more, and it looks like the Tyler and Steve's observations account for most of the the regime change. The Ute's stock market beta/correlation dwarf their bond market beta/correlation (notwithstanding the low stock mkt beta of Utes.) Since stocks versus bonds have gone their separate ways over the past 12 years– the ute's regime change riddle is mostly solved.
There is one last data point worthy of mention: more than 65% of the UTE's total return is due to their dividends…and the attached chart graphically illustrates investor preference for utility dividends versus bond market dividends. This chart highlights the fact that the mean dividend yield for utes is 69% of the bond yield … and we are currently 3 sigma cheap…on a yield comparison basis. But that's true of many stocks…
My intuition remains that Ute's will probably outperform 5-year TIPS from these relative prices, but it appears that this intuition is a restatement of my bias that stocks overall should outperform bonds from these relative prices. If Ute's get whacked because of a hike in dividend tax rates, this may provide an attractive entry point for Ute's on their own absolute-return merits.
I'd like to thank everyone for contributing their thoughts (especially when they disagree with my thesis). It's a pleasure and privilege to interact with a group of such intelligent, independent-thinking people.
Jim Sogi comments:
Undistributed power using local generation, solar, wind, battery, water will be what undermines the monopoly just as cell phone undermined the phone land grid.
Stefan Jovanovich replies:
I think it is an exaggeration to argue that the cell phone has "undermined" the phone land grid. The "land" grid is, in fact, the backbone that now connects all the cell towers; if wireless were truly able to handle the data rates, the towers would be off the grid. They are not; and the "wholesale" wireless technology– microwave– has been the greatest single casualty so far during this wireless revolution.
When you maneuver a ship, there are controllable forces, such as propeller and rudder effects. There are also uncontrollable forces, such as wind, current, sea conditions. Moreover, each vessel has different characteristics and reacts differently. You have also to take into account the characteristics of your ship that may not be constant and given, such as ship loading and hull conditions. As a result, a captain works in an environment where a ship's behavior is not observed in exactly the same way and each situation is different from another. A maneuver is a dynamic process. You have your plan and when you execute it, you want to have a continuous update to understand the effect that your order has achieved and the next course of action in order to be able to follow your plan. Each time you find yourself in situations where your ship reacts differently due to everchanging combinations of speed, rudder, wind, current, sea state.
You need to be adaptable to the environment. Often, a too frequent assessment of your orders is not good because you need some time to let the ship react to your order because of its inertia. At the same time, if your feedback cycle is too slow, you might not have enough time to correct your action. You might end up not being able to follow your plan any more. In that case, the wisest thing you can do is give up and start again the maneuver from scratch instead of trying improbable corrections.
In markets, you do not have controllable forces, but you have expected crowd behaviors. In this context also each situation is different. A trader establishes a plan and during the trade execution, as new data come in, he/she assesses the market's behavior. The frequency at which this feedback process is done is critical. Traders may overreact and be deceived by the short term noise (you need time for the trade to develop), or they may be too slow to realize that the trade is not going as expected. How much data do you need, how often? How is the behavior different from what is expected is an interesting parameter. What is the threshold that makes you realize the trade went wrong? A ship maneuvering characteristics can be modeled mathematically, but in real life captains have to apply their experience and judgment to work in an observe-evaluate-decide-act cycle, which is very similar to what a trader does in a real time environment. Similarly, the market can be modeled, but most of the times expected outcomes require judgment and interpretation. It is all about the human dimension, where the action-effect cycle is matched against broad assessments of a generic "system" behavior.
Jeremy Smith comments:
“Consider how often a vessel must change its course in leaving a harbor, yet once on the high seas a single heading may bear it to its destination. Only
a major navigational hazard could change it.”
– Louis Auchincloss, The Embezzler 
J.T. Holley adds:
In the spirit of Patrick O'Brian I would have to disagree or at least add to this quote. Pirates, Enemies and Gov't can cause navigational changes in both the ships directions and destinations as well as in the markets. Seamanship by David Dodge is a excellent book that discusses the navigational patterns as well that the U.S. Navy utilizes. Having served onboard the U.S.S. Stark I can assure you that rarely is "a single heading" utilized to reach a destination. Sure it is the broad direction, but there are other directions that are in between when going from point A to point B.
Pitt T. Maner III writes:
Let me add a nice quote from The New Dictionary of Thoughts (1963). I wish I knew who "Anon" was:
A smooth sea never made a skilful mariner, neither do uninterrupted prosperity and success qualify for usefulness and happiness. The storms of adversity, like those of the ocean, rouse the faculties, and excite the invention, prudence, skill, and fortitude of the voyager. The martyrs of ancient times, in bracing their minds to outward calamities, acquired a loftiness of purpose and a moral heroism worth a lifetime of softness and security. Anon.
The pdf of the book is searchable and many a fine old quote can be found there.
Jim Sogi adds:
Jeff is right. A sailing ship in particular will sail the best course made good, rather than rhumb line. For example, it will take the best angle to the wind, for the ship best speed, even though off rhumb line, for best course made good. A catamaran, for example, will go faster tacking down wind, zig zagging rather than shortest distance. I think day traders know this instinctively. It's quantified in markets in the absolute volatility numbers, or in Sharpe result numbers.
Another curious effect is when there is a strong current setting the vessel down. The vessel aims at a different point than where it intends to go, and 'crabs' along its course. This is hard for people to understand, as they can't really see the current, but one has to be aware of the motion of the ship in relation to the course, which is a derivative function. I suppose this might be thought of as Sharpe as opposed to gross dollars in trading or percent.
Another odd effect I experienced last weekend up in Alaska skiing was during a white out, a sense of vertigo. There is no visual reference point to balance, and its easy to lose balance in total white out conditions. While standing still, a small avalanche passed by, and though I was standing still, seeing the snow pass by gave the impression of motion, and threw me off balance. Or there is the feeling of standing still, then all of a sudden hit a bump and realize the skier was moving, but couldn't see it. The idea is that sometimes the perception is not correct and some other reference is needed. Pilots know this. This was one of the main points in survival. Loss of a reference point often lead to panic and death. In the markets, it's easy to lose reference. Chair's international numbers, I believe, are an attempt to get some sort of reference point. I had guides skiing up in the wilderness, who have a lifetime of experience and reference. Like markets, if you lose your reference point, you'll be dead in short order.
The use of fixed mechanical resting stops seems to be an admission of inability to trade your way out of a paper bag. It is also an admission you are undercapitalized. It is one thing to realize you were wrong. It is another thing to give up on the bottom tick.
Isn't it better to trade your way out of a bad situation rather than give more of your money to the opposition in defeat? It is a harmful mechanical crutch. It is better to watch for a better opportunity to exit with some grace. It is better to know the market, and know yourself.
Larry Williams objects:
What if you cannot exit with grace — market goes limit down 10 days? No way to trade your way out of that…
Stops prevent failures and allow one to regulate the size of the loss.
I'm talking trading here; not investing… value investors buy and hold until value changes or overall market gives a sell, that seems to be best strategy.
Shui Kage adds:
The old Japanese market proverb: "Mikiri senryō".
"To ditch a small loss is worth a thousand ryō" (In today's language: is worth one million dollars).
Most amateurs are unable to take losses at small size and most amateurs are not very good traders.
Phil McDonnell dissents:
If the market goes limit down (or up) against you then stops will not help either. The stops will not be executed. In that case only proper position sizing in the beginning or an option hedge will protect your position. There is no guarantee a stop will be executed at your price or anywhere near your price in the event of a gap open.
There is no theoretical basis that stops should work either. I have written about this here on numerous occasions. Thus the best advice is to back test, taking stops into account explicitly. When testing stops one should use great care to increae the assumptions regarding slippage. Invariably stops will be hit during fast markets when slippage is the greatest. Compare that to a back test without the stops. If the test using stops gives a superior overall risk reward profile then it is reasonable to use stops. One should never think of stops as the sole money management technique because of the slippage and gap issues discussed above. Rather stops are more of a trading tool to reshape your risk reward profile.
There is another reason to consider stops and that is psychological. Many of us are simply unable to pull the trigger when we get into a losing situation. Suppose you had a trading model that predicted that tomorrow would be up by the close. The obvious way to trade that would be to get in and get out by the close tomorrow. But if your system was wrong (and they all are sometimes) then you may find yourself holding the position simply unable to admit the loss and freezing on the trigger. It is easy to come up with all sorts of rationalizations for this behavior. "The drift will bail me out" might be one. Suddenly your plan has changed from a one day trade to hold it for ten years until the long term drift bails me out. So if you find yourself doing this too often then having a preset stop may be the psychological crutch you need to be successful. Better than that, of course, might be to simply write your plan down and execute it as planned.
Dr. McDonnell is the author of Optimal Portfolio Modeling, Wiley, 2008
Janice Dorn adds:
I would add to this that placement of stops is both art and science. It is among the most difficult concepts for a trader to grasp, and there is more confusion surrounding stops than almost any other aspect of trading. How often do we hear: “They see my stops” or “There is clear stop-running going on” or something similar re: stops. That is why when I trade ( not invest), I use multiple contracts, keep taking profits and trailing stops ( on a good trade) and get out as quickly as possible when the trade is not going right for me. Also, I am prepared to lose on a certain percentage of all trades per my trading plan. I used to hate and could not accept getting “stopped out” but now accept it as part of the cost of doing business.
Also, it is very challenging for most traders to “stop out” and then get back in again. Part of the reason for this is inexperience, and the other part is the way that losses are seen by the brain. Losses are weighed about 2.5 times as heavily as gains. This means that if you are down 10% on one position and up 10% on another position, you are break even on paper, but are down 25% in your brain. There is a complex process that goes on inside the brain of the trader that is looking at losses. But that is another topic and I have already digressed from the “stops” thread.
Dr. Dorn is the author of Personal Responsibility: The Power of You, Gorman, 2008
Jeremy Smith tries for the final word:
Everyone uses stops.
Some put them in immediately.
Some keep them stored in gray matter for later deployment.
Some wait for the margin call.
Kim Zussman exclaims:
If you trade less than 100% of your investable capital, that is a stop.
If you trade predominantly the capital of others, that is a stop.
If you let the account blow up without borrowing against your home or retirement accounts, or hitting up friends/family, that is a stop.
If you decide to trade small enough to preserve your marriage, sanity, or life, that is a stop.
Even the Kamikaze had stops.
Nigel Davies suggests extending the discussion:
What about broadening this discussion still further to include the 'reverse-stop', ie a profit target? I don't see much difference between the two from a conceptual point of view, the issue here being psychological (one represents a loss, the other a win).
Can one be ideologically opposed to stops without also being unable to take a profit? I don't see how we can discuss one without the other and they all come under the category of 'planned exits'.
This graph shows moonshot one-year growth of Money of Zero Maturity, a proxy for money supply.
Jeremy Smith adds:
In contrast to this, the year-over-year change in the real Monetary Base has been negative lately.
Bill Rafter explains:
Yes, Monetary Base growth is still hugely negative. But George is also correct that MZM growth is hugely positive. The missing connection is lag. MZM significantly leads Monetary Base.
I would like to offer some simple thoughts on non-linear relationships. The usual way to study non-linear correlations is to transform one or more of the variables in question. For example if we have a reason to believe that the underlying process is multiplicative then we can use a log function to model our data. When we do a correlation or regression of y~x we can just take the transformed variables ln(y)~ln(x) as our new data set. We are still doing a linear correlation or a linear regression but now we are doing it on the transformed variables.
Ideally we would know the form of the non-linear relationship from some theory. Absent that we could use a general functional form such as the polynomials. So our transform could be something like X^2, X^3, or X^4. Using one of these terms is usually pretty safe. But combining them in a multiple regression can be problematic. The reason is that the terms x^2 and x^3 are about 67% correlated. Using highly correlated variables to model or predict some third variable is a bad idea because you cannot trust the statistics you get.
One way around that is to use orthogonal polynomials or functions. We have previously discussed Fourier transforms and Chebychev polynomials. Both of these classes are orthogonal which also means that we can fit a few terms and add or delete terms at will. The fitted coefficients will not change if we truncate or add to the series. Each term is guaranteed to be linearly independent of the others.
Bruno Ombreux asks:
Using one of these terms is usually pretty safe. But combining them in a multiple regression can be problematic. The reason is that the terms x^2 and x^3 are about 67% correlated. Using highly correlated variables to model or predict some third variable is a bad idea because you cannot trust the statistics you get.
I have a question.
One of the reasons for adding regressors is to take into account all possible reasons behind a move in the variable we are trying to explain. However, multicollinearity being prevalent in finance, it is a source of headaches.
If we could randomize and/or design experience plans for empirical studies, as we do in biology, we could get rid of part of the problem.
Is it possible to randomize ex post? Let's say I what to study Y = aX+ b + e. If instead of taking the full history of observed (Y,X), I am taking a random sample of (Y,X), it creates some kind of post-randomization, which should reduces the impact of other factors.
Does it make sense? Of course, we would lose all the information contained in the non-sampled (Y,X). That means even less data to work with, which is not nice with ever-changing cycles.
Are there books about this type of technique? I have never heard about it so maybe it doesn't exist.
Rich Ghazarian mentions:
And of course if you want a more powerful model, you fit a Copula to your processes and now you are in a more realistic Dependence Structure. Engle has a nice paper on Dynamic Conditional Correlation that may interest Dependence modelers on the list. The use of Excel correlation, pearson correlation, linear correlation … these must be the biggest flaws in quant finance today.
Jeremy Smith adds:
With linear functions we can compute the Eigenvectors to get an orthogonal representation. One problem that gets in the way of nonlinear models is that it isn't clear what is the appropriate "distance" measurement. You need a formal metric of distance to model, compare, or optimize anything. How far apart are these points?
With linear axes, distance is determined by Pythagoras. But what is suggested for the underlying measure of distance if the axes aren't linear?
These remarks about correlation resonate with me, especially in the case of the stock market.
From Vincent Andres:
If you did replace your original axis X and Y by new axis X'=fx(X) and Y'=fy(Y) this is a transformation of the kind P=(x,y) -> P'=f(P)=(x',y')=(fx(x), fy(y)).
This transformation can be reverted without worry. P'=(x',y') -> P=(x,y) where x and y are the antecedents of x' and y' thru the reciprocal functions fx^-1 and fy^-1.
A "natural" suggested distance measure in this new universe is thus : dist(P1, P2) = dist(ant(P1), ant(P2)) ant = antecedent.
This works for all functions fx and fy being monotonous, e.g., (ln(x), x^2, etc) because there is a strict bijection between the two universes. It could even do something for a more large class of functions.
Sorry for the difficult notations, but I hope the idea is clear.
February 8, 2007 | 9 Comments
There has been entirely too little thought given to the mechanism, pathways and reasons that negative feedback works in markets. Perhaps the main reason is that the feeding web is based on a reasonable stability in what and how much is being eaten and recycled.
The people who consume and redistribute must maintain a ready and stable supply of those who produce. They develop mechanisms to keep everything going. One of them is the specialization and great efficiency in their activities. If markets deviate too much from the areas and levels within which the specialization has developed, then much waste and new effort and mechanisms will be necessary.
Aside from the grind that trend following causes (i.e. the losses in execution), and the negative feedback system of movements in the supply and demand schedules that equilibrate, which Marshall pioneered and are now standard in economics, and the numerous other reasons I've set forth (e.g. the fixed nature of the system and the flexibility to profit from it), this appears to me to be the main reason that trend following doesn't work.
Here are a few interesting articles on the subject:
Bill Rafter writes:
Dr. Bruno had posed the idea of beating an index by deleting the worst performers. This is an area in which we have done considerable work. Please note that we do not consider this trend-following. The assets are not charted, just ranked.
Let us imagine an investor who is savvy enough to identify what is strong about an economy and invest in sectors representative of those areas, while avoiding sectors representing the weaker areas of the economy. Note that we are not requiring our investor to be prescient. He does not need to see what will be strong tomorrow, just what is strong and weak now, measured by performance over a recent period.
What is a market sector? The S&P does that work for us, and breaks down the overall market (that is, the S&P 500) into 10 Sectors. They further break it down into 24 Industry Groups, and further still into 60-plus Industries and 140-plus Sub-Industries. The number of the various groups and their constituents changes from time to time as the economy evolves, but essentially the 500 stocks can be grouped in a variety of ways, depending on the degree of focus desired. Some of the groupings are so narrow that only one company represents that group.
Our investor starts out looking at the 10 Sectors and ranks them according to their performance (such as their quarterly rate of change). He then invests in those ranked first through fourth (25 percent in each), and maintains those holdings until the rankings change. How does he do? Not bad, it turns out.
From 1990 through 2006, which encompasses several types of market conditions, the overall market managed an 8 percent compound annual rate of return. Our savvy investor achieved 10.77%. A less savvy investor who had the bad fortune to pick the worst six groups would have earned 7.23%. Those results are below. (Note, for comparison purposes, all results excluded dividends.)
How can our savvy investor do better? By simply sharpening one's focus, major improvements can be achieved. If instead of ranking the top 4 of10 Sectors, our savvy investor invests in a similar number (say the top 4, 5 or 6) of the 24 Industry Groups, he achieves a 13.12% compoundedannual rate of return over the same period. Note that the same stocks are represented in the 10 Sectors and the 24 Industry Groups. At no time did he have to be prescient.
One thing you will notice from the graphs above is that the equity curves of our savvy and unlucky investors mimic the rises and declines of the market index itself. Being savvy makes money but it does not insulate one from overall bad markets because the Sectors and even the Industry Groups are not significantly diversified from the overall market.
Why not keep going further out and rank all stocks individually? That clearly results in superior returns, but the volume of trading is such that it can only be accomplished effectively in a fund structure - not by the individual. And even ranking thousands of stocks will not insulate an investor from an overall market decline, if he is only invested in equities. The answer of course is diversification.
It is possible to rank debt and alternative investment sectors alongside equities, in the hope of letting their performances dictate what the investor should own. However the debt and commodities markets have different volatilities than the equities markets. Anyone ranking them must make adjustments for their inherent differences. That is, when ranking really diverse assets, one must rank them on a risk-adjusted basis for it to be a true comparison. However if we make those adjustments and rank treasury bonds (debt) against our 24 Industry Groups (equity) we can avoid some of the overall equity declines. We refer to this as a Strategic Overlay:
Adding this Strategic Overlay increases the returns slightly, but more important, diversifies the investor away from some periods of total equity market decline. We are not talking of a policy of running for cover every time the equities markets stall. In the long run, the investor must be in equities.
Invariably in ranking diverse assets such as equities, debt and commodities, our investor will be faced with a decision that he should be completely out of equities. It is likely that will occur during a period of high volatility for equities, but one that has also experienced great returns. Thus, our investor would be abandoning equities when his recent experience would suggest otherwise. And since timing can never be perfect, it is further likely that the equities he abandons will continue to outperform for some period. On an absolute basis, equities may rank best, but on a risk-adjusted basis, they may not. It is not uncommon for investors to ignore risk in such a situation, to their subsequent regret.
Ranking is not without its problems. For example, if you are selecting the top 4 groups of whatever category, there is a fair chance that at some time the assets ranked 4 and 5 will change places back and forth on a daily basis. This "flutter" can be easily solved by providing those who make the cut with a subsequent incumbency advantage. For a newcomer to replace a list member, it then must outrank the current assets on the selected list by the incumbency advantage. This is very similar to the manner in which thermostats work. We have found adding an incumbency advantage to be a profitable improvement without considering transactions costs. When one also considers the reduced transaction costs, the benefits increase even more.
Another important consideration is the "lookback" period. Above we used the example of our savvy investor ranking assets on the basis of their quarterly growth. Not surprisingly, the choice of a lookback period can have an effect on profitability. Since markets tend to fall more abruptly than they rise, lookback periods that perform best during rising markets are markedly different from those that perform best during falling markets. Determining whether a market is rising or falling can be problematic, as it can only be done with certainty in retrospect. However, another key factor influencing the choice of a lookback period is volatility, which can be determined concurrently. Thus an optimal lookback period can be automatically determined based on volatility.
There is certainly no question that a diligent investor can outperform the market. By outperforming the market we mean that he will achieve a greater average rate of return than the market, while limiting the maximum drawdown (or percentage equity decline) to less than that experienced by the market. But the average investor is generally not up to the diligence or persistence required.
In the research work illustrated above, all transactions were executed on the close of the day following a decision being made. Thus the strategy illustrated is certainly executable. Nothing required a forecast; all that was required was for the investor to recognize concurrently which assets have performed well over a recent period. It is not difficult, but requires daily monitoring.
Charles Pennington writes:
Referring to the MathInvestor's plot:
At first glance it appears that the "Best" have been beating the "Worst" consistently.
In fact, however, all of the outperformance was from 1990 through 1995. From 1996 to present, it was approximately a tie.
Reading from the plot, I see that the "Best" portfolio was at about 2.1 at the start of 1996. It grew to about 5.5 at the end of the chart for a gain of about 160%. Over the same period, the "Worst" grew from 1.3 to 3.2, a gain of about 150%, essentially the same.
So for the past 11 years, this system had negligible outperformance.
One should also consider that the "Best" portfolio benefits in the study from stale pricing, which one could not capture in real trading. Furthermore, dividends were not included in the study. My guess is that the "Worst" portfolio would have had a higher dividend yield.
In order to improve this kind of study, I would recommend:
1.) Use instruments that can actually be traded, rather than S&P sectors, in order to eliminate the stale pricing concern.
2.) Plot the results on a semilog graph. That would have made it clear that all the outperformance happened before 1996.
3.) Finally, include dividends. The reported difference in compound annual returns (10.8% vs 8.0%) would be completely negated if the "Worst" portfolio had a yield 2.8% higher than the "Best".
Bill Rafter replies:
Gentlemen, please! The previously sent illustration of asset ranking is not a proposed "system," but simply an illustration that tilting one's portfolio away from dogs and toward previous performers can have a beneficial effect on the portfolio. The comparison between the 10 Sectors and the 24 Industry Groups illustrates the benefits of focus. That is, (1) don't buy previous dogs, and (2) sharpen your investment focus. Ignore these points and you will be leaving money on the table.
We have done this work with many different assets such as ETFs and even Fidelity funds (which require a 30-day holding period), both of which can be realistically traded. They are successful, but not overwhelmingly so. Strangely, one of the best asset groups to trade in this manner would be proprietarily-traded small-cap funds.
Unfortunately if you try trading those, your broker will disown you. I mention that example only to suggest that some assets truly do have "legs," or "tails" if you prefer. I think their success is attributed to the fact that some prop traders are better than others, and ranking them works. An asset group with which we have had no success is high-yield debt funds. I have no idea why.
A comment from Jerry Parker:
I wrote an initial comment to you via your website [can be found under the comments link by the title of this post], disputing your point of view, which a friend of mine read, and sent me the following:
I read your comment on Niederhoffer's Daily Spec in response to his arguments against trend following. Personally, I don't think it boils down to intelligence, but rather to ego. Giving up control to an ego-less computer is not an easy task for someone who believes so strongly in the ability of the human mind. I have great respect for his work and his passion for self study, but of course disagree with his thoughts on trend following. On each trade, he is only able to profit if it "trends" in a favorable direction, whether the holding period is 1 minute or 1 year. Call it what you will, but he trades trends all day.
He's right. I was wrong. Trend following is THE enemy of the 'genius'. You and your friends can't even see how stupid your website is. You are blinded by your superior intelligence and arrogance.
Victor Niederhoffer responds:
Thanks much for your contributions to the debate. I will try to improve my understanding of this subject and my performance in the future so as not to be such an easy target for your critiques.
Ronald Weber writes:
When you think about it, most players in the financial industry are nothing but trend followers (or momentum-players). This includes analysts, advisors, relationship managers, and most fund or money managers. If there is any doubt, check the EE I function on Bloomberg, or the money flow/price functions of mutual funds.
The main reason may have more to do with career risk and the clients themselves. If you're on the right side while everyone is wrong, you will be rewarded; if you're on the wrong side like most of your peers you will be ok; and if you're wrong while everyone is right then you're in trouble!
In addition, most normal human beings (daily specs not included!) don't like ideas that deviate too much from the consensus. You are considered a total heretic if you try to explain why, for example, there is no link between the weak USD and the twin deficits. This is true, too, if you would have told anyone in 2002 that the Japanese banks will experience a dramatic rebound like the Scandinavian banks in the early '90s, and so on, or if you currently express any doubt on any commodity.
So go with the flow, and give them what they want! It makes life easier for everyone! If you can deal with your conscience of course!
The worse is that you tend to get marginalized when you express doubt on contagious thoughts. You force most people to think. You're the boring party spoiler! It's probably one reason why the most successful money managers or most creative research houses happen to be small organizations.
Jeremy Smith offers:
Not arguing one way or the other here, but for any market or any stock that is making all time highs (measured for sake of argument in years) do we properly say about such markets and stocks that there is no trend?
Vincent Andres contributes:
I would distinguish/disambiguate drift and trend.
"Drift": Plentifully discussed here. "Trend": See arcsine, law of series, etc.
Basically, our tendency is to believe that random equals equiprobability everywhere (2D) or random equals equiprobability everytime (1D), and thus that nonequiprobability everywhere/everytime equals non random
In 1D, non equiprobability everytime means that the sequence -1 +1 -1 +1 -1 +1 -1 +1 is in fact the rare and a very non random sequence, while the sequences -1 +1 +1 +1 +1 +1 -1 +1 with a "trend" are in fact the truly random ones. By the way, this arcsine effect does certainly not explain 100% of all the observed trends. There may also be true ones. Mistress would be too simple. True drift may certainly produce some true trends, but certainly far less than believed by many.
Dylan Distasio adds:
For those who don't believe trend following can be a successful strategy, how would you explain the long-term performance of the No Load Fund X newsletter? Their system consists of a fairly simple relative strength mutual fund (and increasingly ETF) model where funds are held until they weaken enough in relative strength to swap out with new ones.
The results have been audited by Hulbert and consistently outperform the S&P 500 over a relatively long time frame (1980 onwards). I think their results make a trend following approach worth investigating…
Jerry Parker comments again:
All you are saying is that you're not smart enough to develop a trend following system that works. What do you say about the billions of dollars traded by trend following CTAs and their long term track records?
Steve Leslie writes:
If the Chair is not smart enough to figure out trend following, what does that bode for the rest of us?
There is a very old yet wise statement: Do not confuse brains with a bull market.
Case in point: prior to 2000 the great tech market run was being fueled by the hysteria surrounding Y2K. Remember that term? It is not around today but it was the cause for the greatest bull market seen in stocks ever. Dot.com stocks and new issues were being bought with reckless abandon.
New issues were priced overnight and would open 40-50 points higher the next trading day. Money managers had standing orders to buy any new issues. There was no need for dog-and-pony or road shows. It was an absolute classic and chaotic case of extraordinary delusion and crowd madness.
Due diligence was put on hold, or perhaps abandoned. A colleague of mine once owned enough stock in a dot.com that had he sold it at a propitious time, he would have had enough money to purchase a small Hatteras yacht. Today, like many contemporary dot.coms, that stock is essentially worthless. It would not buy a Mad magazine.
Corporations once had a virtual open-ended budget to upgrade their hardware and software to prepare for the upcoming potential disaster. This liquidity allowed service companies to cash in by charging exorbitant fees. Quarter to quarter earnings comparisons were beyond belief and companies did not just meet the numbers, they blew by them like rocket ships. What made it so easy to make money was that when one sold a stock, all they had to do was purchase another similar stock that also was accelerating. The thought processes where so limited. Forget value investing; nobody on the planet wanted to talk to those guys. The value managers had to scrape by for years while they saw their redemptions flow into tech, momentum, and micro cap funds. It became a Ponzi scheme, a game of musical chairs. The problem was timing.
The music stopped in March of 2000 when CIO's need for new technology dried up coincident with the free money, and the stock market went into the greatest decline since the great depression. The NASDAQ peaked around 5000. Today it hovers around 2500, roughly half what it was 7 years ago.
It was not as if there were no warning signs. Beginning in late 1999, the tech market began to thin out and leadership became concentrated in a few issues. Chief among the group were Cisco, Oracle, Qwest, and a handful of others. Every tech, momentum, and growth fund had those stocks in their portfolio. This was coincident with the smart money selling into the sectors. The money managers were showing their hands if only one could read between the lines. Their remarks were "these stocks are being priced to perfection." They could not find compelling reasons not to own any of these stocks. And so on and on it went.
After 9/11 markets and industries began to collapse. The travel industry became almost nonexistent. Even Las Vegas went on life support. People absolutely refused to fly. Furthermore, business in and around New York City was in deep peril. This forced the Fed to begin dramatically reducing interest rates to reignite the economy. It worked, as corporations began to refinance their debt and restructure loans, etc.
The coincident effect began to show up in the housing industry. Homeowners refinanced their mortgages (yours truly included) and took equity out of their homes. Home-buyers were thirsty for real estate and bought homes as if they would disappear off the earth. For $2000 one could buy an option on a new construction home that would not be finished for a year. "Flipping" became the term du jour. Buy a home in a hot market such as Florida for nothing down and sell it six months later at a much higher price. Real estate was white hot. Closing on real estate was set back weeks and weeks. Sellers had multiple offers on their homes many times in the same day. This came to a screeching halt recently with the gradual rise in interest rates and the mass overbuilding of homes, and the housing industry has slowed dramatically.
Houses for sale now sit on the blocks for nine months or more. Builders such as Toll, KB, and Centex have commented that this is the worst real estate market they have seen in decades. Expansion plans have all but stopped and individuals are walking away from their deposits rather than be upside down in their new home.
Now we have an ebullient stock market that has gone nearly 1000 days without so much as a 2% correction in a day. The longest such stretch in history. What does this portend? Time will tell. Margin debt is now at near all-time highs and confidence indicators are skewed. Yet we hear about trend followers and momentum traders and their success. I find this more than curious. One thing that they ever fail to mention is that momentum trading and trend following does not work very well in a trendless market. I never heard much about trend followers from June 2000 to October 2002. I am certain that this game of musical chairs will end, or at least be temporarily interrupted.
As always, it is the diligent speculator who will be prepared for the inevitable and capitalize upon this event. Santayana once said, "Those who cannot remember the past are condemned to repeat it."
From "A Student:"
Capitalism is the most successful economic system in the history of the world. Too often we put technology up as the main driving force behind capitalism. Although it is true that it has much to offer, there is another overlooked hero of capitalism. The cornerstone of capitalism is good marketing.
The trend following (TF) group of fund managers is a perfect example of good marketing. As most know, the group as a whole has managed to amass billions of investor money. The fund operators have managed to become wealthy through high fees. The key to this success is good marketing not performance. It is a tribute to capitalism.
The sports loving fund manger is a perfect example. All of his funds were negative for 2006 and all but one was negative over the last 3 years! So whether one looks at it from a short-term one year stand point or a three year perspective his investors have not made money. Despite this the manager still made money by the truckload during this period. Chalk it up to good marketing, it certainly was not performance.
The secret to this marketing success is intriguing. Normally hedge funds and CTAs cannot solicit investors nor even publicly tout their wares on an Internet site. The TF funds have found a way around this. There may be a web site which openly markets the 'concept' of TF but ostensibly not the funds. On this site the names of the high priests of TF are repeatedly uttered with near religious reverence. Thus this concept site surreptitiously drives the investors to the TF funds.
One of the brilliant marketing tactics used on the site is the continuous repetition of the open question, "Why are they (TF managers) so rich?" The question is offered as a sophist's response to the real world question as to whether TF makes money. The marketing brilliance lies in the fact that there is never a need to provide factual support or performance records. Thus the inconvenient poor performance of the TF funds over the last few years is swept under the carpet.
Also swept under the rug are the performance figures for once-great trend followers who no longer are among the great, i.e., those who didn't survive. Ditto for the non-surviving funds in this or that market from the surviving trend followers.
Another smart technique is how the group drives investor traffic to its concept site. Every few years a hagiographic book is written which idolizes the TF high priests. It ostensibly offers to reveal the hidden secrets of TF.
Yet after reading the book the investor is left with no usable information, merely a constant repetition of the marketing slogan: How come these guys are so rich? Obviously the answer is good marketing but the the book is moot on the subject. Presumably, the books are meant to be helpful and the authors are true believers without a tie-in in mind. But the invisible hand of self-interest often works in mysterious ways.
In the latest incarnation of the TF book the author is presented as an independent researcher and observer. Yet a few days after publication he assumes the role of Director of Marketing for the concept site. Even the least savvy observer must admit that it is extraordinary marketing when one can persuade the prospect to pay $30 to buy a copy of the marketing literature.
Jason Ruspini adds:
"I attribute much of the success of the selected bigs to being net long leveraged in fixed income and stocks during the relevant periods."
I humbly corroborate this point. If one eliminates long equity, long fixed income (and fx carry) positions, most trend-following returns evaporate.
Metals and energies have helped recently, after years of paying floor traders.
I don't agree with all the points above. For example, the beauty of capitalism is not its puffery, but the efficiency of its marketing and distribution system as well as the information and incentives that the prices provide so as to fulfill the pitiless desires of the consumers. Also beautiful is in the mechanism that it provides for those with savings making low returns to invest in the projects of entrepreneurs with much higher returns in fields that are urgently desired by customers.
I have been the butt of abuse and scorn from the trend followers for many years. One such abusive letter apparently sparked the writer's note. Aside from my other limitations, the trend following followers apparently find my refusal to believe in the value of any fixed systems a negative. They also apparently don't like the serial correlation coefficients I periodically report that test the basic tenets of the trend following canon.
I believe that if there are trends, then the standard statistical methods for detecting same, i.e., correlograms, regressions, runs and turning point tests, arima estimates, variance ratio tests, and non-linear extensions of same will show them.
Such tests as I have run do not reveal any systematic departures from randomness. Nor if they did would I believe they were predictive, especially in the light of the principle of ever changing cycles about which I have written extensively.
Doubtless there is a drift in the overall level of stock prices. And certain fund managers who are biased in that direction should certainly be able to capture some of that drift to the extent that the times they are short or out of the market don't override it. However, this is not supportive of trend following in my book.
Similarly, there certainly has been over the last 30 years a strong upward movement in fixed income prices. To the extent that a person was long during this period, especially if on leverage, there is very good reason to believe that they would have made money, especially if they limited their shorts to a moiete.
Many of the criticisms of my views on trend following point to the great big boys who say they follow trends. To the extent that those big boys are not counterbalanced by others bigs who have lost, I attribute much of the success of the selected bigs to being net long leveraged in fixed income and stocks during the relevant periods.
I have no firm belief as to whether such things as trends in individual stocks exist. The statistical problem is too complex for me because of a paucity of independent data points, and the difficulties of maintaining an operational prospective file.
Neither do I have much conviction as to whether trends exist in commodities or foreign exchange. The overall negative returns to the public in such fields seem to be of so vast a magnitude that it would not be a fruitful line of inquiry.
If I found such trends through the normal statistical methods, I would suspect them as a lure of the invisible evil hand to bring in big money to follow trends after a little money has been made by following them, the same way human imposters work in other fields. I believe that such a tendency for trend followers to lose with relatively big money after making with smaller amounts is a feature of all fixed systems. And it's guaranteed to happen by the law of ever-changing cycles.
The main substantive objection to my views that I have found in the past, other than that trend followers know many people who make money following trends (a view which is self-reported and selective and non-systematic, and thus open to some of the objections of those of the letter-writer), is that they themselves follow trends and charts and make much money doing it. What is not seen by these in my views is what they would have made with their natural instincts if they did not use trend following as one of their planks. This is a difficult argument for them to understand or to confirm or deny.
My views on trend following are always open to new evidence, and new ways of looking at the subject. I solicit and will publish all views on this subject in the spirit of free inquiry and mutual education.
Jeff Sasmor writes:
Would you really call what FUNDX does trend following? Well, whatever they do works.
I used their system successfully in my retirement accounts and my kids' college UTMA's and am happy enough with it that I dumped about 25% of that money in their company's Mutual Funds which do the same process as the newsletter. The MFs are like an FOF approach. The added expense charges are worth it. IMO, anyway. Their fund universe is quite small compared to the totality of funds that exist, and they create classes of funds based on their measure of risk.
This is what they say is their process. When friends ask me what to buy I tell them to buy the FUNDX mutual fund if their time scale is long. No one has complained yet!
It ain't perfect (And what is? unless your aim is to prove that you're right) but it's better than me fumfering around trying to pick MFs from recommendations in Money Magazine, Forbes, or Morningstar.
I'm really not convinced that what they do is trend following though.
Dylan Distasio Adds:
For those who don't believe trend following can be a successful strategy, how would you explain the long-term performance of the No Load Fund X newsletter?
Michael Marchese writes:
In a recent post, Mr. Leslie finished his essay with, "I never heard much about trend followers from June 2000 to October 2002." This link shows the month-to-month performance of 13 trend followers during that period of time. It seems they did OK.
Hanny Saad writes:
Not only is trend following invalid statistically but, looking at the bigger picture, it has to be invalid logically without even running your unusual tests.
If wealth distribution is to remain in the range of 20 to 80, trend following cannot exist. In other words, if the majority followed the trend (hence the concept of trends), and if trend following is in fact profitable, the majority will become rich and the 20-80 distribution will collapse. This defeats logic and history. That said, there is the well-covered (by the Chair) general market upward drift that should also come as no surprise to the macro thinkers. The increase in the general population, wealth, and the entrepreneurial spirit over the long term will inevitably contribute to the upward drift of the general market indices as is very well demonstrated by the triumphal trio.
While all world markets did well over the last 100 yrs, you notice upon closer examination that the markets that outperformed were the US, Canada, Australia, and New Zealand. The one common denominator that these countries have is that they are all immigration countries. They attract people.
Contrary to what one hears about the negative effects of immigration, and how immigrants cause recessions, the people who leave their homelands looking for a better life generally have quite developed entrepreneurial spirits. As a result, they contribute to the steeper upward curve of the markets of these countries. When immigrants are allowed into these countries, with their life savings, home purchases, land development, saving and borrowing, immigration becomes a rudder against recession, or at least helps with soft landings. Immigration countries have that extra weapon called LAND.
So in brief, no - trends do not exists and can not exist either statistically or logically, with the exception of the forever upward drift of population and general markets with some curves steeper than others, those of the countries with the extra weapon called land and immigration.
A rereading of The Wealth And Poverty Of Nations, by Landes, and the triumph of the optimist may be in order.
Steve Ellison adds:
So Mr. Parker's real objective was simply to insult the Chair, not to provide any evidence of the merits of trend following that would enlighten us (anecdotes and tautologies that all traders can only profit from favorable trends prove nothing). I too lack the intelligence to develop a trend following system that works. When I test conditions that I naively believe to be indicative of trends, such as crossovers of moving averages, X-day highs and lows, and the direction of the most recent Y percent move, I usually find negative returns going forward.
Bacon summarized his entire book in a single sentence: "Always copper the public play!" My more detailed summary was, "When the public embraces a particular betting strategy, payoffs fall, and incentives (for favored horsemen) to win are diminished."
Trend Following — Cause, from James Sogi:
Generate a Brownian motion time series with drift in R
MU<-.15*DELTAT;SIG<-.2*sqrt(DELTAT);TIME<-(1:1024)/252 stock<-exp(SIG*RW+MU*TIME) ts.plot(stock)
Run it a few times. Shows lots of trends. Pick one. You might get lucky.
Trend Following v. Buy and Hold, from Yishen Kuik
The real price of pork bellies and wheat should fall over time as innovation drives down costs of production. Theoretically, however, the nominal price might still show drift if the inflation is high enough to overcome the falling real costs of production.
I've looked at the number of oranges, bacon, and tea a blue collar worker's weekly wages could have purchased in New York in 2000 versus London in the 1700s. All quantities showed a significant increase (i.e., become relatively cheaper), lending support to the idea that real costs of production for most basic foodstuffs fall over time.
Then again, according to Keynes, one should be able to earn a risk premium from speculating in commodity futures by normal backwardation, since one is providing an insurance service to commercial hedgers. So one doesn't necessarily need rising spot prices to earn this premium, according to Keynes.
Not All Deer are Five-Pointers, from Larry Williams
What's frustrating to me about trading is having a view, as I sometimes do, that a market should be close to a short term sell, yet I have no entry. This betwixt and between is frustrating, wanting to sell but not seeing the precise entry point, and knowing I may miss the entry and then see the market decline.
So I wait. It's hard to learn not to pull the trigger at every deer you see. Not all are five-pointers… and some will be bagged by better hunters than I.
From Gregory van Kipnis:
Back in the 70s a long-term study was done by the economic consulting firm of Townsend Greenspan (yes, Alan's firm) on a variety of raw material price indexes. It included the Journal of Commerce index, a government index of the geometric mean of raw materials and a few others. The study concluded that despite population growth and rapid industrialization since the Revolutionary War era, that supply, with a lag, kept up with demand, or substitutions (kerosene for whale blubber) would emerge, which net-net led to raw material prices being a zero sum game. Periods of specific commodity price rises were followed by periods of offsetting declining prices. That is, raw materials were not a systematic source of inflation independent of monetary phenomena.
It was important to the study to construct the indexes correctly and broadly, because there were always some commodities that had longer-term rising trends and would bias an index that gave them too much weight. Other commodities went into long-term decline and would get dropped by the commodity exchanges or the popular press. Just as in indexes of fund performance there can be survivor bias, so too with government measures of economic activity and inflation.
However, this is not to say there are no trends at the individual commodity level of detail. Trends are set up by changes in the supply/demand balance. If the supply/demand balance changes for a stock or a commodity, its price will break out. If it is a highly efficient market, the breakout will be swift and leave little opportunity for mechanical methods of exploitation. If it is not an efficient market (for example, you have a lock on information, the new reality is not fully understood, the spread of awareness is slow, or there is heavy disagreement, someone big has to protect a position against an adverse move) the adjustment may be slower to unfold and look like a classic trend. This more often is the case in commodities.
Conversely, if you find a breakout, look for supporting reasons in the supply/demand data before jumping in. But, you need to be fast. In today's more highly efficient markets the problem is best summarized by the paradox: "look before you leap; but he who hesitates is lost!"
Larry Williams adds:
I would posit there is no long-term drift to commodities and thus we have a huge difference in these vehicles.
The commodity index basket guys have a mantra that commodities will go higher - drift - but I can find no evidence that this is anything but a dream, piquant words of promotion that ring true but are not.
I anxiously stand to be corrected.
Marlowe Cassetti writes:
"Along a similar vein, why would anybody pay Powershares to do this kind of work when the tools to do it yourself are so readily available?"
The simple answer is if someone wishes to prescribe to P&F methodology investing, then an ETF is a convenient investment vehicle.
With that said, this would be an interesting experiment. Will the DWA ETF be another Value Line Mutual Fund that routinely fails to beat the market while their newsletter routinely scores high marks? There are other such examples, such as IBD's William O'Neal's aborted mutual fund that was suppose to beat the market with the fabulous CANSLIM system. We have talked about the great track record of No-Load Fund-X newsletter, and their mutual fund, FUNDX, has done quite well in both up and down markets (an exception to the above mentioned cases).
For full disclosure I have recently added three of their mutual funds to my portfolio FUNDX, HOTFX, and RELAX. Hey, I'm retired and have better things to do than do-it-yourself mutual fund building. With 35 acres, I have a lot of dead wood to convert into firewood. Did you know that on old, dead juniper tree turns into cast iron that dulls a chain saw in minutes? But it will splinter like glass when whacked with a sledgehammer.
Kim Zussman writes:
…about the great track record of No-Load Fund-X newsletter and their mutual fund FUNDX has done quite well in both up and down markets… (MC)
Curious about FUNDX, checked its daily returns against ETF SPY (essentially large stock benchmark).
Regression Analysis of FUNDX versus SPY since inception, 6/02 (the regression equation is FUNDX = 0.00039 + 0.158 SPY):
Predictor Coef SE Coef T P
Constant 0.00039 0.000264 1.48 0.14
SPY 0.15780 0.026720 5.91 0.00
S = 0.00901468 R-Sq = 2.9% R-Sq (adj) = 2.8%
The constant (alpha) is not quite significant, but it is positive, so FUNDX did out-perform SPY. Slope is significant and the coefficient is about 0.16, which means FUNDX was less volatile than SPY.
This is also shown by F-test for variance:
Test for Equal Variances: SPY, FUNDX
F-Test (normal distribution) Test statistic = 1.17, p-value = 0.009 (FUNDX<SPY)
But t-test for difference between daily returns shows no difference:
Two-sample T for SPY vs FUNDX
N Mean St Dev SE Mean
SPY 1169 0.00041 0.0099 0.00029
FUNDX 1169 0.00045 0.0091 0.00027 T=0.12
So it looks like FUNDX has been giving slight/insignificant out-performance with significantly less volatility; which makes sense since it is a fund of mutual funds and ETFs.
Even better is Dr Bruno's idea of beating the index by deleting the worst (or few worst) stocks (new additions?).
How about an equal-weighted SP500 (which out-performs when small stocks do), without the worst 50 and double-weighting the best 50.
Call it FUN-EX, in honor of the fun you had with your X that was all mooted in the end.
Alex Castaldo writes:
The results provided by Dr. Zussman are fascinating:
The fund has a Beta of only 0.157, incredibly low for a stock fund (unless they hold a lot of cash). Yet the standard deviation of 0.91468% per day is broadly consistent with stock investing (S&P has a standard deviation of 1%). How can we reconcile this? What would Scholes-Williams, Dimson, and Andy Lo think when they see such a low beta? Must be some kind of bias.
I regressed the FUNDX returns on current and lagged S&P returns a la Dimson (1979) with the following results:
Multiple R 0.6816
R Square 0.4646
Adjusted R Square 0.4627
Standard Error 0.0066
df SS MS F Significance F
Regression 4 0.0444 0.0111 251.89 8.2E-156
Residual 1161 0.0511 4.4E-05
Total 1165 0.0955
Coefficients Standard Error t-Stat P-value
Intercept 8.17E-05 0.000194 0.4194 0.6749
SPX 0.18122 0.019696 9.2007 1.6E-19
SPX[-1] 0.60257 0.019719 30.5566 6E-151 SPX[-2] 0.08519 0.019692 4.3260 1.648E-05 SPX[-3] 0.04524 0.019656 2.3017 0.0215
Note the following:
(1) All four S&P coefficients are highly significant.
(2) The Dimson Beta is 0.914 (the sum of the 4 SPX coefficients). The mystery of the low beta has been solved.
(3) The evidence of price staleness, price smoothing, non-trading, whatever you want to call it is clear. Prof. Pennington touched on this the other day; an "efficiently priced" asset should not respond to past S&P price moves. Apparently though, FUNDX holds plenty of such assets (or else the prices of FUNDX itself, which I got from Yahoo, are stale).
S. Les writes:
Have to investigate the Fund X phenomenon. And look to see how it has done in last several years since it was post selected as good. Someone has to win a contest, but the beaten favorites are always my a priori choice except when so many others use that as a system the way they do in sports eye at the harness races, in which case waiting for two races or two days seems more apt a priori. VN
I went to the Fund X website to read up, and the information is quite sparse. It is a very attenuated website. I called the toll free number and chatted with the person on the other line. Information was OK, but, in my view, I had to ask the proper questions. One has several options here. One is to purchase the service and do the fund switching themselves based on the advice of their experts. The advisory service tracks funds that have the best relative strength performance and makes their recommendations from there, www.fundx.com.
Another is to purchase one of four funds available. They have varying levels of aggressiveness. Fund 3 appears to be the recommended one.
If one purchases the style 3 one will get a very broad based fund of funds. I went to yahoo to look up the holdings at www.finance.yahoo.com/q/hl?s=FUNDX.
Top ten holdings are 47.5% of the portfolio, apparently concentrated in emerging markets and international funds at this time.
In summary, if money were to be placed into the Fund X 3 portfolio, I believe it would be so broad based and diversified that returns would be very watered down. Along with risk you would certainly be getting a lot of funds. You won't set the world on fire with this concept, but you won't get blown up, either.
Larry Williams adds:
My 2002 book, Right Stock at the Right Time, explains such an approach in the Dow 30. The losers were the overvalued stocks in the Dow.It is a simple and elegant idea…forget looking for winners…just don't buy overvalued stocks and you beat the idex.
This notion was developed in 1997, when i began actually doing it, and written about in the book. This approach has continued to outperform the Dow, it is fully revealed.
Craig Cuyler writes:
Larry's comment on right stock right time is correct and can be used to shed a little bit of light on trend following. This argument is at the heart of fundamental indexation, which amongst other points argues that cap weighting systematically over-weights overvalued stocks and under-weights undervalued stocks in a portfolio.
Only 29% of the top 10 stocks outperformed the market average over a 10yr period (1964-2004) according to Research Affiliates (this is another subject). The concept of "right stock right time" might be expressed another way, as "right market right time." The point is that constant analysis needs to take place for insuring investment in the products that are most likely to give one a return.
The big error that the trend followers make, in my mind, is they apply a homogeneous methodology to a number of markets and these are usually the ones that are "hot" at the time that the funds are applied. The system is then left to its own devices and inevitably breaks down. Most funds will be invested at exactly the time when the commodity, currencies, etc., are at their most overvalued.
Some worthwhile questions are: How does one identify a trend? Why is it important that one identifies a trend? How is it that security trends allow me to make money? In what time frame must the trend take place and why? What exactly is a trend and how long must it last to be so labeled?
I think it is important to differentiate between speculation using leverage and investing in equities because, as Vic (and most specs on the list) point out, there is a drift factor in equities which, when using sound valuation principles, can make it easier to identify equities that have a high probability of trending. Trend followers don't wait for a security to be overvalued before taking profits. They wait for the trend to change before then trying to profit from the reversal.
Jeff Sasmor adds:
As a user of both the newsletter and the FUNDX mutual fund I'd like to comment that using the mutual fund removes the emotional component of me reading the newsletter and having to make the buys and sells. Perhaps not an issue for others, but I found myself not really able to follow the recommendations exactly - I tend to have an itchy trigger finger to sell things. This is not surprising since I do mostly short-term and day trades. That's my bias; I'm risk averse. So the mutual fund puts that all on autopilot. It more closely matches the performance of their model portfolio.
I don't know how to comment on the comparisons to Value Line Arithmetic Index (VAY). Does anyone follow that exactly as a portfolio?
My aim is to achieve reasonable returns and not perfection. I assume I don't know what's going to happen and that most likely any market opinion that I have is going to be wrong. Like Mentor of Arisia, I know that complete knowledge requires infinite time. That and beta blockers helps to remove the shame aspect of being wrong. But there's always an emotional component.
As someone who is not a financial professional, but who is asked what to buy by friends and acquaintances who know I trade daily (in my small and parasitical fashion), I have found that this whole subject of investing is opaque to most people. Sort of like how in the early days of computing almost no one knew anything about computers. Those who did were the gatekeepers, the high priests of the temple in a way. Most people nowadays still don't know what goes on inside the computer that they use every day. It's a black box - opaque. They rely on the Geek Squad and other professionals to help them out. It makes sense. Can't really expect most people to take the time to learn the subject or even want to. Should they care whether their SW runs on C++ or Python, or what the internal object-oriented class structure of Microsoft Excel is, or whether the website they are looking at is XHTML compliant? Heck no!
Similarly, most people don't know anything about markets; don't want to learn, don't want to take the time, don't have the interest. And maybe they shouldn't. But they are told they need to invest for retirement. As so-called retail investors they depend on financial consultants, fee-based planners, and such to tell them what to do. Often they get self-serving or become too loaded with fees (spec-listers who provide these services excepted).
So I think that the simple advice that I give, of buying broad-based index ETFs like SPY and IWM and something like FUNDX, while certainly less than perfect, and certainly less profitable than managing your own investments full-time, is really suitable for many people who don't really have the inclination, time, or ability to investigate the significant issues for themselves or sort out the multitudes of conflicting opinions put forth by the financial media.
You may not achieve the theoretical maximum returns (no one does), but you will benefit from the upward drift in prices and your blended costs will be reasonable. And it's better than the cash and CDs that a lot of people still have in their retirement accounts.
BTW: FOMA = Foma are harmless untruths, intended to comfort simple souls.
An example : "Prosperity is just around the corner."
I'm not out to defend FUNDX, I have nothing to do with them. I'm just happy with it.
Steve Ellison writes:
One might ask what the purpose of trends is in the market ecosystem. In the old days, trends occurred because information disseminated slowly from insiders to Wall Streeters to the general public, thus ensuring that the public lost more than it had a right to. Memes that capture the public imagination, such as Nasdaq in the 1990s, take years to work through the population, and introduce many opportunities for selling new investment products to the public.
Perhaps some amount of trending is needed from time to time in every market to keep the public interested and tossing chips into the market. I saw this statement at the FX Money Trends website on September 21, 2005: "[T]he head of institutional sales at one of the largest FX dealing rooms in the US … lamented that for the past 2 months trading volume had dried up for his firm dramatically because of the 'lack of trend' and that many 'system traders' had simply shut down to preserve capital."
I saw a similar dynamic recently at a craps table when shooters lost four or five consecutive points, triggering my stop loss so that I quit playing. About half the other players left the table at the same time. "The table's cold," said one.
To test whether a market might trend out of necessity to attract money, I used point and figure methodology with 1% boxes and one-box reversals on the S&P 500 futures. I found five instances in the past 18 months in which four consecutive reversals had occurred and tabulated the next four points after each of these instances (the last of which has only had three subsequent points so far). The results were highly non-predictive.
Starting Next 4 points
Date Continuations Reversals
01/03/06 3 1
05/23/06 1 3
06/29/06 2 2
08/15/06 2 2
01/12/07 1 2
Anthony Tadlock writes:
I had intended to write a post or two on my recent two week trip to Cairo, Aswan, and Alexandria. There is nothing salient to trading but Egypt seems to have more Tourist Police and other guards armed with machine guns than tourists. It is a service economy with very few tourists or middle/upper classes to service. Virtually no westerners walk on the streets of Cairo or Alexandria. I did my best to ignore my investments and had closed all my highly speculative short-term trades before leaving for the trip.
While preparing for taxes I was looking over some of my trades for last year. Absolute worst trade was going long CVS and WAG too soon after WalMart announced $2 generic pricing. I had friends in town and wasn't able to spend my usual time watching and studying the market. I just watched them fall for two days and without looking at a chart, studying historical prices and determining how far they might fall, decided the market was being stupid and went long. Couldn't wait to tell my visitors how "smart" a trader I was and my expected profit. It was fun, until announcement after announcement by WalMart kept causing the stocks to keep falling. The result was panic selling near the bottom, even though I had told myself before the trade that I could happily buy and hold both. Basically, I followed all of Vic's rules on "How to Lose."
Trends: If only following a trend meant being able to draw a straight line or buy a system and buy green and sell red. The trend I wrote about several months ago about more babies being born of affluent parents still seems to be intact. I have recently seen pregnant moms pushing strollers again. Planes to Europe have been at capacity my last two trips and on both trips several crying toddlers made sleep difficult, in both directions. Are people with young children using their home as an ATM to fund a European trip? Are they racking up credit card debt that they can't afford? Depleting their savings? (Oh wait - Americans don't save anything.) If they are, then something fundamental has changed about how humans behave.
From James Sogi:
My daughter the PhD candidate at Berkeley in bio-chem is involved in some mind-boggling work. It's all very confidential, but she tried to explain to me some of her undergrad research in words less than 29 letters long. Molecules have shapes and fit together like keys. The right shape needs to fit in for a lock. Double helices of the DNA strand are a popular example, but it works with different shapes. There is competition to fit the missing piece. They talk to each other somehow. One of her favorite stories as a child was Shel Silverstein's Missing Piece. Maybe that's where her chemical background arose. Silverstein's imagery is how I picture it at my low level.
Looking at this past few months chart patterns it is impossible not to see the similarity in how the strands might try fit together missing pieces in Wykoffian functionality. The math and methods must be complicated, but might supply some ideas for how the ranges and strands in the market might fit together, and provide some predictive methods along the lines of biochemical probability theory. I'll need some assistance from the bio-chem section of the Spec-list to articulate this better.
From Kim Zussman:
Doing same as Alex Castaldo, using SPY daily change (cl-cl) as independent and FUNDX as dependent gave different resluts:
Regression Analysis: FUNDX versus SPY ret, SPY-1, SPY-2
The regression equation is FUNDX = 0.000383 + 0.188 SPY ret - 0.0502 SPY-1 - 0.0313 SPY-2
Predictor Coef SE Coef T P
Constant 0.000383 0.00029 1.35 0.179
SPY ret 0.187620 0.03120 6.01 0.000* SPY-1 -0.050180 0.03136 -1.60 0.110 SPY-2 -0.031250 0.03121 -1.00 0.317 *(contemporaneous)
S = 0.00970927 R-Sq = 3.2% R-Sq (adj) = 3.0%
Perhaps FUNDX vs a tradeable index is the explanation.
The debate on the relative merits of classical predictive statistical analysis and the application of Bayesian analysis when applied to markets when you have a prior probability computed for a given time frame is whether it is better to exit at the optimal time given at the time of entry of the trade or to alter your probabilities and trade based on the arrival of new information, new ticks and new changes in price, news, or announcements while the trade is pending. The classical statistical theory asserts that you have to trade the probabilities and to alter course creates the danger of Bacon's "switches" and diminishing the favorable edge. The prior distribution has ups and downs in the returns but overall the sum probabilities will be positive over the long run and to try short run this distribution reduces the overall return. The application of the Bayesian theory argues that adjusting the position during the trade to the arrival of the new information and can increase the probabilities and returns and avoid the "switches". In practice the former seems to be beating the latter but this may be due to lurking variables in execution. This could be tested easily enough on historical data. The problem in testing is which parameters to use for the posterior criteria.
Thomas Leonard and John Hsu's book Bayesian Methods, from the Cambridge Series in Statistical and Probabilistic Mathematics, has understandable definitions of the concepts for the practitioner and the theoretician. The Bayesian paradigm investigates the inductive modeling process where inductive thought and data analysis are needed to develop and check plausible models. Indeed, one of the the main reason for the spec list is inductive thought to develop models and their testing. Mathematics and deductive reasoning are then used to test those models. Too much concentration on deduction can reduce insight, and too much concentration on induction can reduce focus. An iterative inductive/deductive modeling process has been suggested. Bayes' Theorem states generally that Posterior information equals prior information plus sampling information.
The Expected Utility Hypothesis (EUH) microeconomic procedure helps make rational decisions about money and might be used as a model to quantify decision making and risk as an addition or alternative to Dr. McDonnell's risk formula by considering the choices of the trader or client relative to the statistics to determine whether the amount at risk and the decision frame work being used is rational or will lead to losses or lower return for given probabilities. This work parallels the work of Tversky and Kahneman, but is quantified in Bayesian terms. The basic idea is that people place a premium on certainty which leads to irrational decisions about risk and leads to more losses than is right. This is a good quantification of the gambler vs speculator distinction just discussed, as the gambler's probability expectation is negative while the speculator's probability expectation is positive. Using as examples such as the St. Petersburg Paradox, Allais' Paradox, and the risk aversion paradox, the EUH can be used to make better decisions. Some seek the premium for certainty and fall into the trap known as the "Dutch Book" resulting in certain losses over a series of iterations. This is the distinction between a gambler and a speculator. Formally, does your choice satisfy the utility function U(r) such that for any P1 and P2 P1 <= P2 if and only if:
E(U(X) | P1) < = E(U(X) | P2)
The EUH measures whether you choose a positive but more random expectation over more certain but lesser return. The St. Petersburg paradox is a good example. A fair coin is tossed repeatedly until a head is obtained for the first time. If the first head is obtained after n tosses, you receive a reward of 2^n dollars. What certain reward reward would you accept as an equivalent to the random reward? The paradox occurs because the expected winnings are infinite, but most people would accept 6 or 8 dollars. The EUH can quantify an individual's utility function. This might be a good way to allocate money among funds or risk profiles using an elicitation process and creating utility curve for allocating either clients or moneys among funds or accounts with varying risk profiles and expectations or leverage.
Back to the original point. Let's say you are in a trade that says the optimum expectation is tomorrow. What if the market goes up big today in a big rush all of a sudden. Do you wait it out because the system says so or do you take the gift. The odds have changed on the expectation due to today's rise. What if the twin towers are bombed. Do you bail or ride the original trade? The answer to these is simple, but as shades go, it is not so clear. The criteria for judging the posterior probability seems to be the crux of the issue, but should follow a rational method.
Dr. Phil McDonnell responds:
The origins of Expected Utility Theory go back to The Theory of Games and Economic Behavior by Morgenstern and Von Neumann (1944). They asserted that the expected utility is given by:
E(u(x)) = sum( p(i) * u( x(i) ) summed over all outcomes i
where: p(i) is the probability of outcome x(i) occurring. u(x) is presumed to be an unknown but monotonic increasing utility function which may be unique to each individual. Note that the expectation is a sum over all outcomes.
In their paper Kahneman and Tversky (KT) on Prospect Theory a prospect is essentially a set of outcomes as above, in which the sum of the probabilities is 1. The latter constraint simply means that all outcomes are included. In the first page of KT they say "To simplify notation, we omit null outcomes". Null outcomes comes from two sources. One is a probability of zero which is innocuous because the zeros would not be included in the sum of all the probabilities adding to 1 in any case. KT makes the unsupported assumption about the nature of the utility function in the following two cryptic remarks from p.266.
,with u(0)=0, (p.266)
In both cases they are making an assumption about the utility function which neither supported nor even explained. In addition the paper is using what may be the wrong zero point.
Daniel Bernoulli made a very insightful analysis of the St. Petersburg Paradox mentioned by Jim Sogi. His key understanding was that the utility of money is logarithmic with the natural log ln() being the convenient choice. The compounded value of a dollar is given by (1+r)^t where r is the rate and t is time. This is simply a series of multiplications of (1+r) by itself t times. We know that multiplication can be replaced by sums of logarithms. After which we take the anti log to restore the final answer. So if our goal in a sequence of investments or even prospects (bets) is to maximize our long term compounded net worth we should look to the ln() function as our rational utility of a given outcome with respect to our current wealth level w. In particular, for a risk indifferent investor, a given outcome x would be worth:
u(x) = ln( (1+r) * w )
This thinking is the basis for the optimal money management formulas and for what could be called a Rational Theory of Utility. Note that the formula only depends on wealth. It is non linear and concave.
Thus it is reasonable to ask what was the average net worth of the individuals in the Israeli, Swedish, Allais and KT studies. For the most part they were students with some faculty. The average net worth of a student was probably about $100. A little beer and pizza night out was considered living high for most.
Using questions with numbers reduced in size from Allais, KT asked subjects to choose between:
A: 2500 with p= .33 B: 2400 with certainty 2400 with p= .66 0 with p= .01 For N=72 [18%] [82% chose this]
The expected log utility for these choices under rational utility is: E( u(x) ) = 3.1996 E( u(x) ) = 3.2189
Clearly the 3.2189 value chosen by 82% of the subjects was the better choice.
Looking at Problems 3 and 4, Choices A, B, C and D we find that the rational utility function agreed with the test subjects every time without exception. KT disagreed with both the rational utility function proposed herein and their test subjects. Based on this metric it would appear that the subjects are quite rational in their utility choices.
One can find the KT paper here.
Here is some R code to calculate the expected log utility for a rational investor for each of the referenced KT problems:
Jeremy Smith responds:
Note that there are at least 2 ways the distribution can change. It might change unpredictably, e.g. due to arrival of new information or it might change for example because of the approaching expiration of options. Even if Bayesian methods and Markov Models aren't good at the first kind of change, they ought to be useful for the 2nd kind.
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