Friday, December 08, 2006


warning: technical mumbo jumbo ahead. that I don't fully comprehend. for those only interested in montevideo info, skip this post

G. Soros focuses his finance book on the concept of "reflexivity" I listened to his book on tape while enduring the daily drudgery of early morning commutes from east bay to silicon valley a couple of years ago.

While I understood the words he was saying, I wasn't really "getting it" until recently when some other thoughts tied the idea together for me.

Buy low, Sell high

This is perhaps one of the oldest mantras heard in retail investing, however, in practice a deceptively difficult thing to accomplish.


Well, traditional thinking and economic theory would lead one to believe that there is some "correct" price for a given asset. Since "markets will fluctuate" (JP Morgan), this traditional approach to investment would drive a trader, to buy when he perceived assets as relatively cheap by some historical measure, and attempting to sell when "expensive".

Traditionally, I've thought of the "natural price" or "right price" as being like a "magnet" drawing the price towards its magical point of balance any time it strays too far....

Traditional economic theory tells us that according to the "efficient markets" theory, that things should be priced about right given an equal number of motivated and informed sellers and buyers (or something like that! :) ). Pricing anomolies are short term in nature and usually do not exist for long if ever and the market tends to revert naturally and quickly back to its "true" and "fair" price.

As you'll see later (maybe) I believe the theory is out of line (slightly) with reality. This might (partially) explain why having an econ PhD doesn't necessarily enhance ones trading results.

Probabilities & Reversion to the "mean"

When pricing assets (like stocks, eg), while present values are important, what really gets people interested is the *future* value of a given asset or security (house or stock option, e.g.)

"yeah, like, um....'duh', fubarrio. so what?"

This is where probabilities come into play and eggheads start scribbling down random greek letters and arcane symbols in an attempt to bewilder the lesser minded canines amongst us, like yours truly.

Now, if fuBarrio hadn't been so slothenly his Junior year at the University, had the class been a *little bit* later in the day, had his professor's Chinese accent been even remotely understandable, fuBarrio might have a firmer grasp of statistics. Alas, we'll have to make due with my simpleton explanation.

Eggheads like to predict that a stocks future price will fall somewhere within a "distribution" of potential future prices. In a perfect world, this would be a standard distribution around some expected future price, with the probability curve being fattest where the future price would most likely come out ---shortest at the outlying extremes -- your standard bell curve.

The idea is that each "tick" has some probability of being up, and some probability of being down. After some X number of ticks, the price will most likely fall within some standard distribution type pattern.

ok, clearly I'm out of my depth in a parking lot puddle when it comes to statistics, and yet I press on with this tasty bit -- just in case you were in danger of acquiring any real knowledge:
(to make things more complicated and keep us under the dinner table just in case our forepaws ever develop oppposible thumbs, the eggheads often instead use a "lognormal" curve...a curve with a non-symetrical shape. Lognormal curves are skewed, and don't look like standard bell curves.


Well, best I can make out is because a 50$ gain, followed by a 50% loss (or vica versa) leaves one with a 25% loss, not breakeven (-- as a casual observation by a card carrying member of the mathematics illiterati, like myself might at first assume).

"Uh...ok...have we strayed far enough from the point yet?"

I think so, but in some vain attempt to bring it back, I will point out that the "crux" of all this probability talk though is the concept of "reversion to the mean".

"Reversion to the mean" as I understand it means that given a large enough sample size, things will tend to average out....A classic example (I guess) is flipping a coin. Even though you may have a string of dozen or so "heads" in a row, after enough flips, one would expect the number of heads to be roughly 50%. (If you aren't a lazy dog like fuBarrio you can google any of these terms and have a deeper more meaningful understanding in 30 seconds).

So, people will insist that markets will tend to "revert to the mean" of historical precedents in either pricing or fundamentals which will eventually drive pricing. As it so happens, this is effectively at the crux of some of fuBarrio's "US residential housing or the dollar or both must go down" arguments....for instance when he points out in exasperation that median incomes to median prices (or some other historical measure is completely out of whack!) does that mean he is/was wrong?

No, but the theory of reflexivity helps explain why while he he was right, he sold two years too early.

So, fuBarrio, armed with your doggie wit and C minus in elementary statistics, why aren't you a trading superstar bazillionaire like George Soros, and furthermore, why do so many economists suck at trading?

"Trending" markets and reflexivity's role

Reflexivity, in this context, means an asset (or security) price's ability to effect its own price.


Reflexivity is a bit like a computer programmer's recursive function call. The function, in effect, calls itself until some preset condition is met (or the open loop hogs all the cycles and available memory) :)

In the interest of brevity (yeah right) I'll only use two examples to make my point.


I'm using housing as an example of a reflexive market on the way down. However, the same principles work in reverse on the way up.

If we accept the fact that a certain number of homes around the world were being bought with:
1.) equity withdrawals from previously "purchased" real estate.
2.) money earned from sales, construction, financing, etc of houses during the boom

Then, it is perhaps not difficult to imagine that once affordability exhausts itself, real estate will enter into a "self reinforcing" downward spiral....or a "reflexive" relationship where its future price movement is strongly influenced by its immediately preceding price movement.

As rate resets, unemployment, overbuilding, unaffordability start to slow sales, builders and home owners with lots of equity will be the first to lower prices to raise cash. These lower prices will affect comparable sales, used in appraising the value of other homes in the neighborhood, for the purposes of sales or home equity withdrawals. As more people who represent buyers at the fringe have trouble staying liquid, credit standards will eventually have to get tougher.

It doesn't take much of an imagination to see that once the "cracks" start in a market driven by speculative excesses, the bottom won't likely be reached until it is as cheap as or cheaper to buy than to rent.

Reflexivity in an up market:

Where reflexivity in a down market is characterized by liquidity constriction and fear, the opposite is true for reflexivity in an up market. It is driven by greed and liquidity expansion.

Well how does that work?

Let's suppose that fuBarrio (or someone who is actually respected) starts touting Uranium as an investment (as an example). If there is no positive price movement, or negative price movement, it is quickly dismissed and you say, "well, duh....a bald dog with bad teeth and empty grey eyes can't spot a trend" and that is that.

If however, the prediction proves correct in the short term, people start to think that fuBarrio's hair must've fallen out after extensive radiation poisoning during research in underground U3O8 mines.

You think, "He must know something. That balding, spotted mutt fubarrio is rakin it in on Junior Uraniums and he only got a C minus in stats at that crappy school of Huskies! If I have to put up with all his meglomaniacal rants, I'm going to benifit a little too. I'm gonna follow his lead...."

If your make a little money, you tell friends about your astute stock picking, and they want a taste, new miners are able to raise money in IPO's, private placements, and secondary offerings. Winners from the sector cash in winnings and put them on new stocks (often in the same sector)....until the quality of investments and the prices being paid for speculation are so out of wack that the world runs out of "greater fools".

So, reflexivity is an attempt to explain part of the rationale behind, "the trend is your friend" and "The markets can stay irrational longer than you can stay liquid." Rather than be pulled by an invisible hand to some "correct" price, greed, fear, and the power of reflexivity will create markets that oscillate, constantly pushed away from our concept of "neutral" or "correct" pricing.


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