The following is a guest post by John Douglas, who enjoys intelligent discussions around writing and focuses on portfolio enhancement through options.

“The Shadow of a Paradox”

This series of articles attempts to create new dimensions for thinking about, and comprehending advanced investing and trading strategies. The approach differs in that perspective and philosophy are essential starting points. Our simple premise is that technical information and an unlimited source of “how to” articles has done little or nothing to assist individuals in managing their money. Given the voluminous amount of freely available information, which ranges from fundamental and technical analysis to complex option strategies, the daunting question still remains:

  • Why is it that investors sell low and buy high, just like a broken record that keeps repeating over and over?
  • Why do investors make the same mistakes time and time again?

The answer to the above questions cannot be lack of information. Indeed there may be too much information. The sheer volume of spoken and written commentary, combined with the fragmentary delivery of this information, may serve to confound and confuse-not enlighten. The market itself lurches and gyrates to a seemingly random pattern and even a highly rational mind, one that admits of the existence of chaos and disorder, finds limited confidence in broader horizons.

Yet, one has only to look back and realize that any number of optimal opportunities existed. If only these opportunities could be discovered by logical analysis-before the obvious postmortem. The annoyance is enhanced all the more when a sane, reflective mind discovers-too late-that the answer was there all along. Why was it not so obvious? The answer to this riddle requires a multi-dimensional approach.


Let us consider that a workable definition of the term “paradigm” encompasses a minimum of assumptions and a maximum of conceptual precision. And, let’s say that a shadow may be opaque, or that we know that there are shadows within shadows-as can be observed in planetary analysis-often described as a penumbra.

And, for now, let’s simply note that an option is a derivative. It ‘derives’ its characteristics from an underlying instrument. So, you might visualize an option as a shadow of something else- a silhouette, or a two dimensional representation of something.

Shadows change in dimension relative to the position of the sun on a given day, and change in relation to the rotation of the planet on its axis. There are times when an object will cast a giant shadow, and times when little or no shadow can be observed.   Sometimes, it appears that we have more than one shadow. Shadows appear a bit different in a fog. These tendencies can be described mathematically, and Greek letters have been used as an abbreviated way to communicate and depict the continuous change of these shadows, as components that describe changes in option values.  But, more on that later.

Shadows are all around us. The contemplation of shadows appears throughout art and writing. Plato’s “Allegory of the Cave” is perhaps the most famous piece of philosophical inquiry. It seeks, in part, to understand perception, where one is limited to the observation of shadows. At another level, one might suggest that the mind encounters a degree of difficulty sorting thru illusions versus reality.   Plato held that the fleeting things that constitute this world are degenerating copies of something permanent. Nonetheless, Plato embraced mathematics as the ultimate reality. In fact, posted above the door to Plato’s academy were these words: “let no one enter here who is ignorant of mathematics.”

This dichotomy between shadows and illusions, on the one hand, and reality on the other, has persisted for the duration of our species. For a more contemporary way of expressing the subject matter, we can turn to  Judy Collins, who  reveals, thru her song “Both Sides Now,”  that it’s about seeing both sides-and perhaps a bit more:

‘I’ve looked at clouds from both sides now

From up and down and still somehow

It’s cloud’s illusions I recall

I really don’t know clouds at all.’

But the introspection grows as the contemplation intensifies:

“I’ve looked at life from both sides now

From win and lose and still somehow

It’s life’s illusions I recall

I really don’t know life at all.”

Perhaps all the financial experts and money managers should go away, isolate themselves, and really contemplate these lyrics.

The point is that there is much to learn about trading by immersing ourselves in philosophy, mathematics and music. Therefore, to begin our discussion of options, as most texts do, serves no useful purpose. Our perspective is somewhat different. But, an enlightened perspective will positively impact the manner in which we begin to learn.

Ultimately, we want to approach investing and trading from a game theory dimension, and we want to embrace randomness as an enduring “shadow.” We want to look for paradox, and we adamantly seek facts that are diametrically opposed to our gut feelings.  And, we must be vigilant in ignoring the siren call of certainty. It is a dangerous distraction. Instead, we agree with Piet Hein’s simple, but elegant words:

“A bit beyond perception’s reach

I sometimes believe I see

That life is two locked boxes, each

Containing the other’s key.”

As we close out the introduction to this series, let’s take note of one more topic that receives a lot of media hype. Specifically, we are advised, if not chided, into purchasing various software packages that allow us to ‘back test’ or ‘paper trade.’ Well, despite the new age technology, we will embrace the teaching of Jesse Livermore:

“I have heard of people who amuse themselves conducting imaginary operations in the stock market to prove with imaginary dollars how right they are. Sometimes these ghost gamblers make millions. It is very easy to be a plunger that way. It is like the old story of the man who is going to fight a duel the next day.”

His second ask of him, “Are you a good shot?”

“Well,” said the duelist, “I can snap the stem of a wineglass at twenty paces,” and he looked modest.

“That’s all very well,” said the unimpressed second. “But can you snap the stem of the wineglass while the wineglass is pointing a loaded pistol straight at your heart?”

You might want to keep this in mind, as you rack up the easy money in the “virtual” world.


As indicated, the purpose of this paper is to set forth a different perspective by which to understand a rather complex subject. To some extent, it’s not that the subject is so complicated, but fuzzy definitions and colloquialisms probably do more to deter understanding, than to facilitate useful information. In short, it is critical that our paradigm reflect appropriate usage of Occam’s razor- entities should not be multiplied beyond necessity. To the extent possible, we seek to determine if what appears to be complicated flows from surprisingly simple underlying programs.

Recall that Lewis Carroll’s White Queen would have defended everyone’s right to believe six impossible things before breakfast. Know, then, that the market can believe all sorts of improbable, if not impossible things, as you plan for your trading day or horizon. The process by which we form a belief or opinion has been studied at great length, over a long period of time, and it’s a topic that requires a great deal of thought.


There are several billion neurons in the circuits of one human brain. The number of synapses formed among those neurons is at least 10 trillion, and the length of the axon cables forming neuron circuits totals something on the order of several hundred thousand miles. Within one second in the life of our minds, the brain produces millions of firing patterns over a large variety of circuits distributed over various brain regions.  The elementary secrets of mind reside with the interaction of firing patterns generated by many neuron circuits, locally and globally, moment by moment, within the brain of a living organism.

So, our “wiring” is both intricate and amazing-yet, the issue of decision-making is a baffling subject. As the work of Amos Tversky and Daniel Kahneman demonstrate, the objective reasoning we employ in day-to-day decisions is far less effective than it ought to be.  Antonio R. Damasio (M.D., Ph.D., and M.W. Allen Professor of Neurology at the University Of Iowa College Of Medicine) indicates: “To put it simply our reasoning strategies are defective…the fragile instruments of rationality need special assistance.”

It is worthwhile-no, it is mandatory- to study the works of Tversky and Kahneman. But first, a notable quote from G.K. Chesterton:

“The real trouble with this world of ours is not that it is an unreasonable world, nor even that it is a reasonable one. The commonest kind of trouble is that it is nearly reasonable, but not quite. Life is not illogicality; yet it is a trap for logicians. It looks just a little more mathematical and regular than it is; its exactitude is obvious, but its inexactitude is hidden; its wildness lies in wait.”


Consider this mental exercise, which was first reported in 1979. Subjects were asked to choose between an 80% chance of winning $4,000 and a 20% chance of winning nothing versus a 100% chance of receiving $3,000. Even though the risky choice has a higher mathematical expectation-$3,200-80% of the subjects chose the $3,000 certain. This represents a risk-averse perspective.

Kahneman and Tversky then offered a choice between taking the risk of an 80% chance of losing $4,000 and a 20% chance of breaking even versus a 100% chance of losing $3,000. Now, 92% of the respondents chose the gamble, even though its mathematical expectation of a loss of $3,200 was once again larger than the certain loss of $3,000. This asymmetrical pattern appears consistently in a wide variety of experiments.

Consider the following experiment, which was conducted some time later:

“Imagine that a rare disease is breaking out in some community and is expected to kill 600 people. Two different programs are available to deal with the threat. If program A is adopted, 200 people will be saved; if program B is adopted, there is a 33% probability that everyone will be saved and a 67% probability that no one will be saved. Which program would you choose?”


The risk averse person will prefer Plan A’s certainty of saving 200 hundred lives over Plan B’s gamble, which has the same mathematical expectancy but involves the risk of a 67% chance that everyone will die. The results of the tests reflected that 72% of the subjects went with Program A. But, suppose the same problem is posed differently. If Program C is adopted, 400 of the 600 people will die, while Program D entails a 33% probability that nobody will die and a 67% probability that 600 people will die. (Note that the first of the two choices is now expressed in terms of 400 deaths rather than 200 survivors, while the second program offers a 33% chance that no one will die. When presented this way, Kahneman and Tversky found that 78% of their subjects were risk-takers and opted for the gamble-they could not tolerate the prospect of the sure loss of 400 lives).

The important thing to note is that this behavior is inconsistent with “rational” decision-making. The major driving force is loss-aversion. Note the words of Tversky as he sought to explain this curious behavior:

“Probably the most significant and pervasive characteristic of the human pleasure machine is that people are much more sensitive to negative than to positive stimuli…Think about how well you feel today, and then try to imagine how much better  you  could feel… There are a few things that would make you feel better, but the number of things that would make you feel worse is unbounded.”


2 Responses to “New Reflections on Understanding Options”

  1. John Maroney Says:

    penses sur options

  2. Tips to stock trading » Blog Archive » Seeing Options From Both Sides Says:

    […] following is an email response by Christopher Ebert to the article “New Reflections on Understanding Options“. Christopher will be joining as an options contributor. Options certainly are […]

Leave a Reply

You must be logged in to post a comment.