From: John Conover <john@email.johncon.com>
Subject: Re: Poll on market efficiency
Date: 4 Aug 2000 04:46:01 -0000
Hi Jim. Yea, in the sense of the EMH, a fair and efficient market has
infinite entropy, (entropy being measured in the time series of a
stock's price, or index value, or market cap of an exchange, etc.) A
lower value means that there is some predictability, which is
exploitable to those that know how, so the system is not fair, or
efficient.
There are several different spins on EMH, (the strong, weak, etc.,)
but all depend on the characteristics of a stock's price being a
Brownian motion fractal, (its actually a mathematical model of stock
price fluctuations,) which has infinite entropy.
One of the problems with using entropic terminology in finance is that
we really don't, (as you kind of point out,) have a good definition of
what randomness means-there are currently nine definitions floating
around in the literature, (unpredictability and disorder are two often
sited.)
I guess your question is why is entropy related to efficiency? The EMH
states, (depending on who is telling the story, of course,) that the
driving force behind price changes for any commodity is new
information coming into the market from the outside world, and, (in
the EMH model,) traders process this information so efficiently that
prices adjust instantaneously, i.e., it is 100% efficient Brownian
motion fractal, (and probably should be seen as a first order
approximation to the process.)
If there was some time delay, there would be lower entropy, and thus
some predictability, which could be exploited by the nimble, (with the
best computer equipment, best analytical software, fastest access to
posting transactions, etc.)
John
BTW, it is fairly easy to disprove by exception the premise of the
EMH. If everyone watches the news, then prices have already adjusted
to accommodate the news, so no one should-and if no one does, everyone
should because they would have a unique advantage; a self referential
trap in the paradigm's foundation. (Not that the EMH is not useful,
though-it is; Black-Scholes was/is based on it, and there is more
trades executed on B-S than any other paradigm.)
In a Brownian fractal, there is a 50/50 chance that what happened
today, (to a stock's price,) will happen again tomorrow. A more
sophisticated approach is to allow the EMH model to have some
inefficiency i.e., some persistence; based on entropic measurements of
all stocks in the US exchanges for the last century, there is about a
55% chance of what happened today happening again tomorrow, (and there
are other implications of the inefficiencies-like leptokurtosis in the
distribution of the fluctuations, where a Brownian process has a
strict Normal/Gaussian distribution, an increase in the fractal
dimension, etc.)
jim blair writes:
>
> <conover@rahul.net> wrote in message news:so6fdp78o0b94@corp.supernews.com...
> > FWIW, efficiency in the sense of the EMH, (depending on who is telling
> > the story, of course,) gets larger as the system's entropy gets
> > larger, (the EMH assumes infinite entropy, i.e., 100% efficiency, as a
> > first order approximation; .....etc.
>
> Hi,
>
> I have thought over your clam of a relationship between "efficiency" and
> entropy (=disorder), but fail to see any connection. If anything, I would
> expect a reverse relationship (if any). Greater order connected to greater
> efficiency?
>
> At any rate, one problem with entropy is the need to define a "zero level".
> That is, only changes in entropy can be measured.
>
> In chemistry, the 3rd Law establishes (defines) the zero level of entropy.
> But what is it in economics/market/or whatever it is we are trying to relate
> to?
>
--
John Conover, john@email.johncon.com, http://www.johncon.com/