Time Diversification

As a mathematical construct time diversification is a fallacious concept.

As a conceptually appealing rule of thumb, time diversification is intuitively appealing.

From Kritzman's Financial Analyst Journal article 1994:
Time diversification is the notion that above average returns ten to offset below average returns over long horizons. Specifically, if returns are independent from one year to the next, standard deviation of annualized returns diminishes with time, ie. the distribution of annualized returns consequently converges as the investment horizon increases.

Paul Samuelson critique: although it is true that the annualized dispersion of returns converges toward the expected return with the passage of time, the dispersion of terminal wealth also diverges from the expected terminal wealth as the investment horizon expands. This result implies that, although you are less likely to lose money over a long horizon than over a short horizon, the magnitude of your potential loss increases with the duration of your investment horizon.

According to the critics of time diversification, if you elect the riskless alternative when you are faced with a three month horizon, you should also elect the riskless investment when your horizon equals ten years, or twenty years, or any duration.

This criticism applies to cross sectional diversification (ie. 1 asset vs 10 asset portfolio) as well as to temporal diversification.

Over time the growing improbability of a loss is offset by the increasing magnitude of potential losses.

The critique is based upon the following conditions holding:
(1) Your risk aversion is invariant to changes in your wealth.
(2) You believe that risky returns are random.
(3) Your future wealth depends only on investment results.

Risk aversion implies that the satisfaction you derive from increments to your wealth is not linearly related to increases in your wealth. Rather, your satisfaction increases at a decreasing rate as your wealth increases.

Financial literature commonly assumes that the typical investor has a utility function equal to the logarithm of wealth. Based on this assumption, it can be demonstrated numerically why it is that your investment horizon is irrelevant to your choice of a riskless versus a risky asset.

Argument Mechanics - The Realm of Reason Part III (Fallacy contd)

Someone obliged to tell the whole story who tells less than the whole story while implying that all has been told, commits that form of lying called the half-truth.

“black/white thinking” - we can fall into the trap of proceeding as if every field were exhausted by a pair of opposites; black and white, A and B/
Argument environment is usually one of less than complete knowledge, the increase of knowledge being, after all, the point of arguing.

argumentum ad ignorantium - the arguer uses the other sides inability or unwillingness to prove that a thesis is false as evidence that the thesis is true.
Appeals to ignorance turned around “prove” the opposite shows the faultiness of the style of reasoning eg. since opponents can’t prove the creation account false, then Genesis must be true; but since creationists can’t prove their contention, therefore Genesis is false.
Appeals to ignorance cheat because where there is ignorance as to the exact truth, the burden of proof belongs on whoever steps off of non-committal ground.
Our “conservative” natures see no point in doing for no good reason - ie. advocating change takes on the burden of proof.
petitio principii - an argument which depends partly or wholly on its conclusion ie. begging the question.
circular reasoning - concocting a string of premises in which the string, itself insufficient to sustain the conclusion, ultimately receives support from the conclusion
when a conclusion is a theory or a deduction according to a theory, one way to stack the deck is to formulate the original problem in terms of a framework presupposed by the theory.
(ir)relevance - the issue in dispute can appear to be addressed when in fact it is not being addressed.
ignoratio elenchi - ignoring the issue or the opponents argument.
ignoring the issue - designates any argument the premise(s) of which do bear on the conclusion but which bypass the issue.
- diversion also sometimes occurs not by addressing the larger issue but by elevating a subissue.
One pervasive source of reasons not addressed to the issue is subversion of reason by the passions.

The morality of nonrational methods - we owe others control over their lives, and control is what a nonrational pitch usually denies.
Appealing to the nonrational in human nature has been a favourite form of behaviour modification eg. Eve to Adam; Klondike sales pitch “every good person gives”
nonrational methods are immoral due to (1) it denies information on which to make intelligent decision, (2) even if a good decision has been made in response to a nonrational pitch, what assurances exist that the decision will remain good? [a rational decision is flexible] ie. if and when times and circumstance invalidate old reasons, new reasons come to the fore and a new decision can be made, (3) nonrational methods can be used for the worse or for the better.

Ways to by-pass the reasoning process and jump directly to a conclusion from instinct, emotion or prejudice: Appeal to pity, appeal to vanity, appeal to gregariousness, appeal to popular prejudice, appeal to subconscious motivation.
In a relevant appeal, the issue, by its nature one which arouses emotions, will be presented with a force proportional to the issues claim to consideration.
Appeals to pity achieve irrelevance by either the type, or the degree of their appeal ie. they fail to touch the “heart strings”, or they “milk” the issue for all its worth thereby putting you off, or they “lay it on thick” by inflating an otherwise relevant factor beyond its claim to consideration.
“everybody’s doing it” tends to carry people along in a hubris or gregariousness which neglects the question or issue why this or that?

Numbers don’t answer the question, “Why this or why that?”
Advertising testimonials, lacking usually even the pretence of authority or expertise, fall more neatly under the present heading, the irrelevant subrational appeal.
Many products don’t meet actual needs, they meet potential needs which are then created by advertising.
Playing on culturally induced fears, likes and aversions has won many an election, provided support for many a war, etc. Techniques that go under various guises such as “grandstanding” “playing to the gallery”.
For the political scoundrel, shallow patriotism, far from being a last refuge, becomes a vanguard.
Humor is used for the avoidance of argument confrontation.
Humorous ads seem especially effective at avoiding discussion of the product or issue.

Argument Mechanics - The Realm of Reason Part II (Fallacy)

Fallacy - Argument Evaluation
“to study the abnormal is the best way of understanding the normal” William James.
non sequitur - “it does not follow”
A fallacy is a bad way of arguing.

oversimplify - distorting the facts by making them simpler than they actually are.
smoke-screen - incapacitating thought by diversion.
- to neglect significant or potentially significant facts is to oversimplify
when in doubt, suspect the question (improper questions)

Any question expresses what could be called assumptions.
“complex question” = “many questions”, i.e. Have you stopped beating your wife?
- provided that the false assumptions poked into them (complex questions) are recognised, complex questions are easy to counter: Attack the question by dividing the question, and then deny the false assumption.
false dilemma = the phony either - or. As people tend to answer a question before examining the question itself, so they tend to choose either the “either” or the “or” option w/out examining the pair of options itself.
Ways to cope with a false dilemma (1) reject both options, (2) choose a new option (“going between the horns” of the dilemma)

“poisoning the wells”- an opponent gets the “choice” of drinking at one of two or more wells, all but one of which the arguer has unfairly tainted, usually by name calling or caricature.
When attacking a general position there can be no excuse for not attacking the position’s strongest version.

A “straw man” argument attacks what may look like the position, but what is really only a simple version, or part of the position or a ridiculous exaggeration.
- there is a difference between exaggerating a position and carrying a position to its logical conclusion.
To show a position to be self-refuting, or to lead to untenable consequences, is to create a reductio ad adsurdum: accept the argument (temporarily) and show that on its own grounds the argument is reduced to absurdity.
- the careful thinker weighs generalities not only against fact, but also against themselves.
“There are no absolutes; everything is relative” Ans. “Are you absolutely sure”

infinite regress - a manoeuvre which undercuts an attempted explanation by showing that it systematically must leave something else unexplained.
Instead of confronting opponents as individuals, the stereotyper gives them labels, types them, puts them in pigeon holes, thus making use of the various association which the labels evoke.
In general our malevolent side exercises itself less with individuals and specific proposals than with groups and ideologues.
“projecting an image” - forget what the product is, and project a simple fantasy picture instead.
To overcome stereotyping, emphasise the variety which the oversimplification ignores.

Psychological Foibles

You think the market has risen too far too fast and is due a pullback.

The conundrum.

How and when do you decide to get back in?

The Psychological Challenge
The market starts breaking a little. Hope rises. It is moving your direction. You don't want to jump in too soon. After all you have been short and patiently waiting for this for quite a while. You don't want to waste those missed opportunities (now sunk opportunity cost) by blowing your powder too soon and seeing it pan out in the fashion you envisioned all along. On the other hand, you have been in this position before on the run-up, failed to cover or buy the dip, and seen it tear off again, only to have to chase (or worse fight a losing cause).

There is no good answer to the question. Doing your due diligence. Setting price levels and being disciplined. Having a system, a process, and a philosophy. You're not going to win them all. But you do want to have a system or process in place where you put the odds on your side when you go to bat.

I Guess We're Not In Kansas Anymore

The central banks have fled the coop and are in Oz. The markets are a bedlam of optimism.

As if unlimited monetary easing was not enough (I guess the zero bound puts a kink in a few models). Yesterday the Bank of Japan's adopted a 2% inflation target (nothing sensational, except the country has been stuck in the mire for two decades...an asset/debt bubble will do that to you) and unlimited asset purchases, joining its compatriots (in monetary crime) at the Fed and the ECB.

The potential for negative unknown and unintended consequences increases. The margin for error has decreased.

The cost of post-GFC bailing is accumulating in the system and at some point will hit a tipping point. The effectiveness of monetary policy is diminishing with each cast of the die.

Until then, party on Garth.