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I agree. I would love to hear your comments on the following:
The more you have information, the more you are confident about the
outcome. Now the problem: by how much? Common statistical method is
based on the steady augmentation of the confidence level, in
nonlinear proportion to the number of observations. That is, for an n
times increase in the sample size, we increase our knowledge by the
square root of n. Suppose I am drawing from an urn containing red and
black balls. My confidence level about the relative proportion of red
and black balls, after 20 drawings is not twice the one I have after
10 drawings; it is merely multiplied by the square root of 2 (that
is, 1.41).
Where statistics becomes complicated, and fails us, is when we have
distributions that are not symmetric, like the urn above. If there is
a very small probability of finding a red ball in an urn dominated by
black ones, then our knowledge about the absence of red balls will
increase very slowly – more slowly than at the expected square root
of n rate. On the other hand our knowledge of the presence of red
balls will dramatically improve once one of them is found. This
asymmetry in knowledge is not trivial--it is a central philophical
problem for such people as Hume and Karl Popper. I can confirm that
an investor trader is a bad investor (if he blows up); but I can
never rule out that he may be one.
To assess an investor's performance, we either need more astute, and
less intuitive, techniques, or we may have to limit our assessments
to situations where our judgment is independent of the frequency of
these events.
But there is even worse news. In some cases, if the incidence of red
balls is itself randomly distributed, we will never get to know the
composition of the urn. This is called the problem of stationarity.
Think of an urn that is hollow at the bottom. As I am sampling from
it, and without my being aware of it, some vicious child is adding
balls of one color or another. My inference becomes thus
insignificant. I may infer that the red balls represent 50% of the
urn while the vicious child, hearing me, would swiftly replace all
the red balls with black ones. This makes much of our knowledge
derived through statistics quite shaky.
The very same effect takes place in the market. We take past history
as a single homogeneous sample and believe that we have considerably
increased our knowledge of the future from the observation of the
sample of the past. What if vicious children were changing the
composition of the urn? In other words, what if things have changed?
The "science" of econometrics consists of the application of
statistics to samples taken at different periods of time, which we
called times series. It is based on studying the times series of
economic variables, data, and other matters.
Studying the European markets of the 1990s will certainly be of great
help to a historian; but what kind of inference can we make now that
the structure of the institutions and the markets has changed so much?
Stanford economist Mordecai Kurz puts it as follows:
The process of structural change (i.e. non-stationarity) in our
society is the central building block of its complexity and the root
cause of the diversity of beliefs about it. In such a system, the
past is not an entirely satisfactory basis for assessment of risks in
the future.
Practitioners of the "financial engineering" methods measure risks (I
just use stops), using the tool of past history as an indication of
the future. We will just say that the mere possibility of the
distributions not being stationary makes the entire concept seem like
a costly (perhaps very costly) mistake. This leads us to a more
fundamental question: the problem of induction which is a different
subject.
rgds, Pal
--- In amibroker@xxxxxxxxxxxxxxx, "Gary A. Serkhoshian"
<serkhoshian777@xxxx> wrote:
> Ahh-hah ! You see this is where watching the equity curve would
tell you that you are bouncing off trees rather than moving through
the forest unimpeeded. Also, if you recorded your journey through a
large forest rather through a simple patch of trees you would have a
better gague on growth patterns of trees and hence your path.
>
> Taking this a step farther, pine trees grow differently than
redwoods. So, you would run into trouble if you took a recording of
a journey through a redwood forest, and used it to guide you through
a pine forest.
>
> What people fail to understand is by virtue of picking some set of
parameters we are optimizing. I see people with smug looks on their
face when they say they don't believe in optimizing, but are hell-
bent on making decisions with a 12,26,9 MACD.
>
> It's like a social drinker berating an alcoholic. They both drink
alcohol, it's just that the social drinker ensures he doesn't wake up
in the gutter. Over optimizing is a disease just like over drinking.
>
> Regards,
> Gary
>
> Joseph Platt <jplatt@xxxx> wrote:
>
> Lots of talk lately about Optimization, Overoptimization,
> Robustivity, Randomness, etc. Regarding optimization here is a copy
> of an email I sent to a FastTrack friend of mine recently....don't
> know if it makes any sense or not.
>
**********************************************************************
> ******************
> You know, most all systems depend on optimization at some level but
> one day when I was in a dreamy mood, (perhaps muscatel induced),
this
> analogy with regards to optimization popped into my head. Takes a
> little imagination....
>
> Suppose a person decided to take a one mile walk through a well
treed
> area of woods. He would have no trouble negotiating the path since
> the trees are quite visible and he could navigate a path right
around
> them.
>
> Suppose further that he had been carrying some kind of an
electronic
> recorder with him (this is the part that takes a little
imagination)
> and every step along the one mile stretch was recorded.
>
> Still feeling energetic he decides to pick up where he left off and
> try another one mile hike through the next stretch of woods. He
> reasons that it's not necessary to look for an unobstructed path,
at
> least not as carefully as he did on the first stretch, because
after
> all he has a recording of the whole journey and all he has to do is
> put it in the "play it again Sam" mode.
>
> The analogy doesn't have a very happy ending....he got through the
> second mile alive but just barely....you would hardly recognize him.
>
> But to be fair there is a difference between trees that, as far as
we
> know, grow randomly and the stock market which arguably isn't
totally
> random as many claim.
>
**********************************************************************
> ******************
> I guess my friend got the email OK but his only response was "watch
> out for the trees".
>
> .....Joe Platt
>
>
>
>
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