Yes, that's the model. So, tell me. Would any profit be possible in an ideally functioning market? If so, how is any item worth more than the total cost of all inputs including externalities? If not, how is such a dynamic system attracted to an ideal state, given that those who would make the market ideally functional are best placed to gain from market inefficiency and dysfunction? Given an answer, do you have a sound game theory explanation for this?
Additionally, what is the nyquist limit for such an ideally realised market, if it is indeed to be modelled as a recursive sampled approximator and how is this derived? Given an infinitely recursive network of arbitrarily connected market agents, is any such calculation convergent? If so, why? If not, how does the market ever converge to any appropriate price - a price which accurately reflects the market conditions excluding pricing operations and market costs which aren't directly related to the production of the instrument in question?
Keep in mind that, if the market is functioning ideally no market participant will exceed the nyquist rate as all participants knowledge of market conditions converges to zero. How is any sampling rate, excluding zero, convergent? If not, how is any such market realisable? If so, what is the loss function between ideal model and realisable, perfectly imperfect real world implementation? What is the minimum profit, if not zero, and why?
However, it does seem that arbitrage opportunities decrease when such high-speed trading is occurring and, does so even more quickly the faster trading speed and market sampling are increased. How can we account for this, if not by increased market efficiency?
I conjecture that, by ever increasing the sampling rate and the speed at which transactions complete, markets are not being made more efficient. Instead, I hypothesise that, as markets directly effect the price of the instrument reflexively, the feedback latency produced creates relative local pockets of perceived value - which are only profitable trades in relation to local information asymmetry. As the vast majority of high-speed trading holds market positions on extremely short time scales, shifting exposure constantly, this profit is immediately realised locally resulting in the gradual diffuision of this inefficiency as the increase in price of all instruments. This is a direct result of the cost of trading being factored directly into the agent's local acceptable sale price of held instruments. Every local agent trading action is ideal, but the global market is a divergently inefficient one. Indeed, it is a market in which its pricing inefficiency is maximally concealed from all market participants.
In a sense, I conjecture that the estimator is not functioning to increase market efficiency but is, instead amplifying local inefficiency globally, in effect, much like a charge pump would operate in a voltage multiplier circuit. In essence such a scheme acts to conceal increased market cost and overhead (including the profit of market participants) into market instrument pricing. However, it does so in an extremely small and diffuse way so as to make the rise in price of a single instrument, as a result of this activity, extremely difficult to detect as all instruments increase similarly on the same time scale.
This behaviour appears to be similar in nature to 'salami slicing', an often effective embezzlement technique - except that, instead of exploiting an information asymmetry created by lack of interest in small quantities in the part of auditing accountants, it exploits the information asymmetry created by the speed of light itself.
Of course, the faster the sampling rate, the more efficient the described amplification process would take place. Does this effect correlate between markets with differing but estimable information asymmetry? If there is no correlation, this hypothesis is invalid. It would seem to be an area ripe for research and analysis of market data.
Do you see any technical issue with this conjecture by which we may discount it immediately?
A perfect market where all participants get information at the same time does not exist.
>This profit is immediately realised by the increase in price of all commodities globally.
This would only hold if there weren’t profitable short trades. The profit can also be realized by the decrease in global commodities that would have been slower before.
I'm sorry for the confusion, I should've reviewed my post before submitting - I have edited that section extensively for, hopefully, greater clarity of thought.
No worries at all. I know it's an extremely long comment on a comment on an article - thanks for reading it.
On further thought, the conjecture's behavioural outcome is actually not quite so analogous to 'salami slicing' as it is analogous to monetary policy caused inflation. In effect, the amplification effect would serve to create profit by creating an apparent valuable trade where none actually exists - such trades essentially print money. This activity would function much like the "profit" realised by a central bank when it chooses to print additional currency for redistribution at government prerogative.
However, monetary policy induced inflation is merely limited in effect to those exposed to any one central bank's monetary policy domain - and generally only occurs when the money supply is permitted to rise for all participants. The type of inflation produced by the activity outlined by the conjecture is inherently global - and would exert a pressure on all existing markets which permit this type of trading; and it is not governments, which are ideally responsible to those they represent, which benefit from this inflation - it is private market participants, in the profit they realise from each trade.
This would certainly seem to account for the new behaviour of central banks having to cut their interest rates to near or at zero to compensate for this asymmetric inflation to drive slowing market activity outside of the financial sector... if the conjecture holds - they appear to have entirely lost control of monetary policy to the global market - and those who are best placed to capture value in those markets as a gestalt - via this mechanism.
If the conjecture holds - and central banks and regulators are unable to reign in the behaviour globally - the economy will experience hyperinflation of Weimarian proportions. Unfortunately, such inflation will have vastly asymmetric effect - benefiting only those best positioned to participate in and drive the amplification behaviour itself.
Indeed, it appears to be a naturally occurring divergent state in a market permitting ever higher sampling and clearing rates. Such behaviours are increasingly profitable - seemingly without end - and so it will attract a geometrically accelerating amount of market activity until such activity is no longer profitable due to market collapse.
The analogy is a fascinating, and scary, thing. It's a bit like considering someone nucleating the economic equivalent of a false-vacuum collapse - or someone already having done so. I need to think about it more and find some way of formally stating and ideally disproving the conjecture.
We might disprove the conjecture by looking for anti-correlations in the growth, availability and capacity of high-speed trading and clearing in markets controlling for the returns of financial institutions instruments and portfolios and the changing monetary policies of various central banks under whose jurisdiction they fall. Simulation of economic systems with and without these elements might also yield some insights, when compared to market conditions at large.
Is anyone aware of any other similar research, work, and/or thought in regards to this concept?
I'm an Econ grad student currently not paying attention in a Maths class (something about the Implicit Function Theorem) and I'm absolutely intrigued by your two comments. Kudos.
Also, to sidetrack a little bit, may I ask how long it took you to gather these thoughts and post them? I'm trying to get a sense of how far along I am about gaining a holistic understanding of markets and trading.
While I don't think any time taken is necessarily a great indicator of general understanding, I was struck by a great feeling of unease while reading 1e-9's comment. Initially I sought to understand the apparent contradiction in the measurable reduction in arbitrage opportunity as a generally accepted proxy measure for increasing market efficiencies with my general understanding that HFT generally massively increases volatility and does not generally appear to result in the reduction of instrument pricing due to lower trading overheads and losses. I also sought to explain the seemingly unending profit stream made possible by such strategies - when, paradoxically the more efficient the market becomes, the less profitable all HFT stratigies should become globally - and yet, it does not seem they do.
All in all, about 10 minutes or so of consideration, followed by about an half an hour of editing.
That said, I'll likely spend much more time looking for existing models of financial markets under the information relativistic conditions created by HFT activity - it occurs to me that as trading moves closer to speed of causality in the market the models underlying market understanding may need to be adapted, perhaps using relativity as a prototype. With any luck they already have and I can elaborate from those to solve for conditions of such markets with information asymmetry and agents capturing value. If such markets are inherently volatile and that volatility increases geometrically nearing the speed of causality - presumably, the speed of light, then this may provide the mechanism for the apparent global inflation of instrument prices via distributed profitable high-speed trading activity while preserving lessened arbitrage opportunity and other visible market behaviours.
I really must formalise this so that it may be thoroughly and logically evaluated - both symbolically and under simulation. However, I'm at a disadvantage in that I am merely a dabbler in the field of economics and game theory. I also have no formal background in stochastic finance or physics. I am but a Systems Engineer. So, fun challenges ahead.
Of course, I welcome any contribution, furtherance of the analysis of this idea, or criticism of any reasonable kind.
I don't know, I see many problems with this comment (akin to the writing of postmodern continental philosophers). Maybe you can restate your conjecture again?
> In effect, the amplification effect would serve to create profit by creating an apparent valuable trade where none actually exists - such trades essentially print money.
Trading is a zero sum game (notwithstanding the allocative function enabled by proper price signals), so I don't see how it would engender inflation.
> the new behaviour of central banks having to cut their interest rates to near or at zero to compensate for this asymmetric inflation
There are many theories about the persistent low rates ("secular stagnation") etc., but I've _never_ heard that particular problem linked to HFT.
> I conjecture that, by ever increasing the sampling rate and the speed at which transactions complete, markets are not being made more efficient.
That's fairly clear, and I can agree with that.
> Instead, I hypothesise that, as markets directly effect the price of the instrument reflexively, the feedback latency produced creates relative local pockets of perceived value - which are only profitable trades in relation to local information asymmetry.
What?
> As the vast majority of high-speed trading holds market positions on extremely short time scales, shifting exposure constantly, this profit is immediately realised locally resulting in the gradual diffuision of this inefficiency as the increase in price of all instruments.
Not sure what you're saying there, but of course the idea is that traders with superior information can realise trading profits, and via such trading, information spreads through the market, until no such trading opportunities persist. However, HFT does not necessarily follow this kind of Hayekian vision, but is maybe more insightfully analysed in a game-theoretic framework.
> This is a direct result of the cost of trading being factored directly into the agent's local acceptable sale price of held instruments. Every local agent trading action is ideal, but the global market is a divergently inefficient one.
> Indeed, it is a market in which its pricing inefficiency is maximally concealed from all market participants.
What?
> In a sense, I conjecture that the estimator is not functioning to increase market efficiency ...
Possibly, yes.
> ... but is, instead amplifying local inefficiency globally, in effect, much like a charge pump would operate in a voltage multiplier circuit.
How is it amplifying it? Yes, we have seen flash crashes, sure, resulting in some transfer of wealth. But this does not explain or predict inflation, geometrically accelerating market activity, nucleated false-vacuum collapse, or any such things.
All excellent points and questions. I'll consider appropriate answers and restatements and respond soon. I'm rarely satisfied with my ability to communicate ideas like these. I really must express this conjecture formally - in the language of mathematics - so that it may be unambiguously communicated in the appropriate contexts.
Additionally, what is the nyquist limit for such an ideally realised market, if it is indeed to be modelled as a recursive sampled approximator and how is this derived? Given an infinitely recursive network of arbitrarily connected market agents, is any such calculation convergent? If so, why? If not, how does the market ever converge to any appropriate price - a price which accurately reflects the market conditions excluding pricing operations and market costs which aren't directly related to the production of the instrument in question?
Keep in mind that, if the market is functioning ideally no market participant will exceed the nyquist rate as all participants knowledge of market conditions converges to zero. How is any sampling rate, excluding zero, convergent? If not, how is any such market realisable? If so, what is the loss function between ideal model and realisable, perfectly imperfect real world implementation? What is the minimum profit, if not zero, and why?
However, it does seem that arbitrage opportunities decrease when such high-speed trading is occurring and, does so even more quickly the faster trading speed and market sampling are increased. How can we account for this, if not by increased market efficiency?
I conjecture that, by ever increasing the sampling rate and the speed at which transactions complete, markets are not being made more efficient. Instead, I hypothesise that, as markets directly effect the price of the instrument reflexively, the feedback latency produced creates relative local pockets of perceived value - which are only profitable trades in relation to local information asymmetry. As the vast majority of high-speed trading holds market positions on extremely short time scales, shifting exposure constantly, this profit is immediately realised locally resulting in the gradual diffuision of this inefficiency as the increase in price of all instruments. This is a direct result of the cost of trading being factored directly into the agent's local acceptable sale price of held instruments. Every local agent trading action is ideal, but the global market is a divergently inefficient one. Indeed, it is a market in which its pricing inefficiency is maximally concealed from all market participants.
In a sense, I conjecture that the estimator is not functioning to increase market efficiency but is, instead amplifying local inefficiency globally, in effect, much like a charge pump would operate in a voltage multiplier circuit. In essence such a scheme acts to conceal increased market cost and overhead (including the profit of market participants) into market instrument pricing. However, it does so in an extremely small and diffuse way so as to make the rise in price of a single instrument, as a result of this activity, extremely difficult to detect as all instruments increase similarly on the same time scale.
This behaviour appears to be similar in nature to 'salami slicing', an often effective embezzlement technique - except that, instead of exploiting an information asymmetry created by lack of interest in small quantities in the part of auditing accountants, it exploits the information asymmetry created by the speed of light itself.
Of course, the faster the sampling rate, the more efficient the described amplification process would take place. Does this effect correlate between markets with differing but estimable information asymmetry? If there is no correlation, this hypothesis is invalid. It would seem to be an area ripe for research and analysis of market data.
Do you see any technical issue with this conjecture by which we may discount it immediately?