Does Heisenberg's uncertainty
principle shed light on "manipulation" of the London Gold Fix? Or
is it the other way around?
WHEN Werner Heisenberg looked at his brand new quantum formulae in
1927, writes Paul Tustain, founder and CEO of BullionVault, he noticed
something weird.
The world of very small spaces and
particles is ruled by matrix mechanics, but as you may remember from your
school mathematics, in matrix multiplication A*B is not the same as B*A. What
Heisenberg saw was that because of the difference in the two matrix products
there would always be uncertainty as to key physical properties of a
particle. His discovery forbids a particle from having both precisely defined
motion and precisely defined position at the same time.
Spotting this earned Heisenberg a Nobel
prize, and a lifetime of being widely misunderstood.
The rest of us have a very deep seated
'common-sense' view of spacetime and particles, and almost all of us reject
the subtle complexity of the 'Uncertainty Principle'. Indeed I am prepared to
bet that if you are here reading about it for the first time you are mentally
rejecting it. "Of course", you will be thinking, "whether we
can measure it or not, a particle obviously has a particular position and a
particular speed."
Alas you would be wrong. But don't beat
yourself up about it because you are in good company. Even Albert Einstein
was on your side for a while.
In physics you can pin down individual
quantities very precisely, but by knowing one quantity exactly you will
automatically give the particle freedom to be uncertain in another. Woe
betide any physicist who interpolates between observations to state as fact
something he didn't specifically measure, because physical particles do not
do predictable things when they are unmeasured; they appear to spend their
unobserved lives weighing up the choices of where physics allows them to be
found next, and then pressing the hyperspace button to get there whenever
somebody looks.
If you took to examining particle paths
between observations the best route map you could draw to describe the motion
of an unmeasured particle would look something like this :-
The diagram shows how we located the
particle precisely at point A, and again at point B. But in being so precise
about its location at an instant of time we made its motion uncertain.
At time A, it might have been going up,
or down, there is no answer. In making our precise measurement of position at
instant A (and B) we actually denied the particle a definitive up/down
motion. It's weird, but that is how particles work in spacetime – it really
is.
Nevertheless a good physicist will be
able to perform certain quantum calculations, and she will be able to give us
a sense of where our particle might have been found, if we had looked. She
will be able to calculate that if we were to set everything up the same way
and make hundreds of additional measurements at Time T, then the particle
would be found in the various ranges shown on the blue dotted line on the
picture, with the various probabilities shown.
Even many physicists find it
unsatisfactory that the most nature allows us to say about where the particle
was when we weren't looking is basically "probably about here". But
there it is. Without an observation there was no single explicit position at
Time T, because the phenomenon of unmeasured position did not properly exist
except in our own mental models. Unmeasured position is smoothed out into a
fuzzy realm of possibilities.
The Gold Fix
The situation of a particle's motion and
position bears a striking similarity to price. Let's have a look at
another picture.
The blue dots are 'quotes' from a market.
Someone from Bloomberg has tracked bankers' gold price quotes, each of which
is here represented as a blue spot.
Bloomberg decided to be helpful to the
rest of us, and they filled in the gaps between the points with a solid line.
Then they sold it to us as a gold price chart – a track of the position of
price, through time.
A few years ago, before derivatives were
invented, the rest of us would have taken that plotted line with a pinch of
salt. We always knew it was an approximation, and not a very good one either,
because when we waited to see the price reporting at the end of the day we
could see a whole load of real gold deals (here the green dots) obstinately
refusing to position themselves on Bloomberg's line.
We did not care much, because none of us
who worked in real markets ever thought for one moment that anyone would
start to treat the lines interpolated by Bloomberg as something real. They
were a useful visualisation – that was all.
It was only later, when financial
engineers started building products that were valued by reference to that
line, and when people started making profits, or losing, depending on where
Bloomberg drew their line, that investors started attaching significantly
more weight to the line itself than to the reality of the reported deal
prices.
Is the gold price uncertain too?
Okay, so I am clearly drawing a parallel.
Price charts and particle route maps are doing something quite similar. But
let's take it a stage further. Let's try doing what Heisenberg did, and make
the bold assertion that there is no price between the data points of trades,
just a realm of possibilities.
The derivatives engineers, and even a few
of the gold bugs are going to go nuts with this, but it stands up to some
pretty detailed scrutiny.
For a start the price that gets printed
by Bloomberg is without size. If the bullion banker were to be asked a real
price, by a real trader, the banker's first question would be "what is
the size?" He has to know if he is quoting for a $200 deal or a $200
million dollar deal, because the prices are completely different!
This gives a third dimension to the
price, one which any spot price chart always ignores. At any given point in
time the price of anything is a function of the amount of it you want to buy
or sell.
Unlike quantum particles this is not difficult
concept to grasp. If I were a greengrocer, and you asked me for one banana,
I'd probably charge you 20 pence. If you asked me for 10, I might give you a
discount, and sell for £1.90 (19p each). If you asked me for 500 I might
charge you a premium, because I'd have to get in the van and go and purchase
a lot more bananas – so maybe £110 (22p each). But if you asked me for
1,000,000 there is no price. I don't want to sell you 1,000,000 bananas
because I wouldn't know where to get them, and I certainly don't want to
spend my week in the van hunting them down and paying ever larger prices for
the diminishing stock! As you can see the price varies according to size.
Once you introduce this extra dimension
to the price chart, so as to get the real feel for where the trading price
is, the single line of Bloomberg starts to look like a gross
over-simplification. Because not only is there uncertainty in the vertical
momentum of the price between two measured points (trades) but also there is
a completely different answer depending on the size.
So instead of a line progressing from
last quote to next quote the reality is that there is a very large volume of
three dimensional economic space between the points, and, with different
probabilities, the next trading price could be any point within that volume.
All in all it seems to me that there is a
very good case for saying that in the absence of a trade there is no such
thing as price. Anyone who seeks to know a price without the hard experiment
of executing a trade is deluding themselves into creating a phenomenon which
does not really exist. Price is an attribute of a specific trade. It occurs
meaningfully only at points in the economic continuum where an exchange
happens, and it depends on the individual circumstances, reasons and
emotional states of two experimenters (sorry, traders) who each foresee the
price subsequently moving in opposite directions.
So price is not smoothly variable, but
point-like, quantised, and a generator of uncertainty; and everything between
real trades is probabilistic guesswork.
Is Gold fixed?
If I were to criticise the Gold Fix I
would certainly concede that it is rather stupidly named. Also in the era of
Chinese walls – rules which insist colleagues do not tell each other what
their common clients are doing – there is something unusual in allowing bank
principals to know their own internal customer order book.
However in my opinion this oddity is
rather elegantly offset by the fact that the Gold Fix allows another bank
principal to steal those orders simply by offering a better price during the
auction. I believe this system is much more robust than Chinese walls,
because it relies on natural competition rather than self-imposed discipline.
Also two other powerful points jump out
for comment:-
- The Gold Fix is a real trading price.
It is not a survey, like LIBOR, and it is not a chart of quotes, like
the Bloomberg spot gold ticker. It is a price at which a very large
number of buyers and sellers chose to deal, and this makes it
real.
-
- It was dealt in open competition in
very large size, positively swamping the sizes of the individual bullion
bank quotes on the Bloomberg ticker. As I explained above this size
gives it a right to be different.
-
Besides, if the sellers thought they were
getting a bad deal day after day wouldn't they simply deal on the spot
market? Or on Comex? There is nothing stopping them, because the Gold
Fix publishes the auction prices while it is happening, and lets clients
remove their orders during the process, so as to place them instead in
alternative (if usually smaller) sources of liquidity.
Forgive me, but I don't really care much
in any case. There remains quite a large number of people who are wedded to
gold price conspiracy theories. Many of them buy paper gold (gold futures)
and then grumble that sellers of paper gold exist. In my opinion they
perfectly match each other's requirement!
Meanwhile not one person who has bought
gold, to take delivery, has only got paper. All the sellers were able to
deliver real gold. That makes a concerted price suppression story – through
shorting – very difficult to swallow.
More interesting than the Gold Fix
But there is still unfinished business
here, because the physics element of this story is far more interesting than
the gold element. Could it be that a run-of-the-mill financial spat begins to
show us a route to solving the central riddle of quantum physics? Now that
really would be something.
Since quantum physics first arrived 87
years ago its application has been stupendously successful, but no-one has
been able to explain its results in a way we can grasp and call 'reality'.
Physicists remain stumped when it comes to describing the weird world they
see through their simplest experiments.
In the absence of anything better we all
fall back, a bit lazily, into the default human mental model of thinking of
particles as being somewhere and moving somewhere smoothly, rather than in
jerks from point to point. We have taken to thinking – much as conspiracy
theorists do when they look at price charts – that unmeasured particles have
real position and real motion, even when they are isolated from the rest of
our universe and no-one is looking.
But this perfectly natural, common sense
interpretation leaves science at an impasse. Our mental model and the
experimental facts are in fundamental disagreement with each other about how
stuff really is.
Physicists have been wringing their hands
trying to solve this. They want to explain a reality under quantum physics in
a way which does not make the act of measurement special. They want reality
to be permanent, whether or not they are looking, and they have come up with
some truly zany models ranging from 'there is no reality' to 'there are
countless zillions of realities, and entire universes are created every
nano-second to cope with all the quantum possibilities'. I am not kidding.
These are both pretty standard models of quantum reality which physicists are
clinging to.
Yet – and this is the amazing thing –
through analysing price at the Gold Fix we can actually see a workable
metaphor for quantum experiments, and that really excites me. It's as if the
quantum world is an incredibly fast moving market, heaving with tiny trades,
where each exchange produces an instant of perfect precision in some physical
attribute or other, enabling the countless trillions of particle events in
the observable universe to map themselves, with respect to each other, into
the unambiguous history of our spacetime.
I have read lots of physics books, and
not understood many of them, but by sitting in my office and thinking about
gold prices I can for the first time start to see how something which appears
to be deeply real and continuous is in fact point-like, and fuzzy between the
points. I can explain, and in an understandable way to anyone who knows
markets, that between one trade and the next price is undefined, uncertain
and unreal. We don't know exactly where it is, or if it's moving up or down.
All we can do is copy the quantum physicists and make probabilistic guesses
until the next trade.
Is there something here the physicists
could learn from us? After all, so many physics laboratories have lost their
brightest research stars to the quant funds. Perhaps it's time the
London bullion market offered the labs some of our Gold Fix dealers, on
sabbatical, of course.