## Thursday, March 26, 2009

### FX Scaling Laws

This article by Glattfelder, Dupuis and Olsen, brought to my attention by a reader, proposes an empirical set of scaling laws that apply to FX markets.
After considering them, in view of devising an interesting indicator for trading, the problem appears to be that these laws mostly concerns averages taken over 5 years, that is a serious limitation for their applicability on a short period of time.
Nonetheless, I identified one, the law (12) that may be of interest, provided some more work:

$\Delta x_{cum}^{*}=\sum_{i=1}^{n}\left |\Delta x_{i}^{*} \right |=\left (\frac{\Delta x_{dc}}{C_{cum,*}} \right )^{E_{cum,*}}$

This law(applied to the total move, *=tm) gives the length of the coastline for a given pair for a year of activity (250 days) as a percentage, relatively to a resolution defined as the directional-change threshold (cf chapter 2.3 in the article).
Considering the case without the transaction costs (an assumption, I think, justified by the small scale considered), I then look at Table A19 to know the parameters of the Law relative to the currency pair I am interested in. For the following I will consider EUR/USD, which is the pair I trade most often, the law therefore becomes :

$\Delta x_{cum}^{tm}=\left (\frac{\Delta x_{dc}}{200.9} \right )^{-0.937}$

As I am interested in moves around 10 PIPs, I shall then consider a resolution of 0.001 for EUR/USD, so:

$\Delta x_{dc}=0.001$

Which gives me a resolution between 12 and 14 PIPs (for the current value of the EUR/USD) since 0.001 is a percentage.
As a result, I get:

$\Delta x_{cum}^{tm}=93087.68$

This is the annualised length of the coastline, I am more interested in this length for 15 minutes, I therefore have to divide it by 250*24*4, for a result of:

$\Delta x_{cum}^{tm}=93087.68/(250*24*4)=3.88$

Which is equal to about 520 PIPs (taking 1.35 for EUR/USD) as the length of the coastline for 15 minutes.

This information is the best I can get so far from the scaling laws described in the article. It may be used to determine the width of a channel (volatility), though, even for this, it needs to be included in further calculations (that will likely used the Graph Dimension, or the Hurst exponent). I am currently thinking of ways to do that, and will publish any success I may have with this line of thought in the future.

## Friday, March 6, 2009

### Is bargaining anti-capitalistic ?

Let me indulge a bit more in some economic ranting while I am still on holiday.

It is easy to verify the fact that bargaining is most popular in those places the less developed in terms of capitalism, and the more a country will "progress" in accepting the principles of modern capitalism, the more the activity of bargaining will disappear. It may almost seem like paradox, but is it really one?
I come to think of a possible explanation for this phenomenon, whether it accounts totally for it or only partially can certainly be a matter of debate.

Bargaining is properly a confrontation between one offer and one demand, it is a highly individualistic process. Despite that the offerer can back his side of the exchange by a direct reference to the overall demand for the specific product, and on this ground he will argue for a higher price than the customer is ready to pay. On the other hand, the customer can argue that this overall demand is merely virtual, projected, but ultimately unrealized in the very short term, while his present buying of the goods means immediate, actual money for the seller.

That's how it used to be in traditional societies, in those areas where the exchange of goods was falling beyond the reach of the despotic rulers. It seems odd then to think that an extension of the domain of free exchange(Capitalism) has entailed a quasi disparition of bargaining.
Bargaining assumes that the price of a commodity is open to debate, it is not a static given of the transaction, on the contrary, it is a dynamic component of it. Opposite to this, obviously lies the principle that any given commodity has a fair ("natural") price. If nowadays, a customer intend to bargain, the selling person(who is likely to work for a salary, not even indexed on his selling performance) can simply reply, that the price displayed is already the optimal price, and that there is nothing better to hope for.

One may then say that the almost disappearance of bargaining is simply an effect of the mass-consumption and the bureaucratization of the modern world, and that it has nothing to do with Capitalism, I believe Schumpeter[1] may disagree with that with regard to the origins of modern bureaucracy, that he saw as a manifestation of the rationalization of the economic and social life (the latter being largely conditioned by the former in a capitalist system).
So, even if bargaining could have survived the rational theory of commodities exchange that has developed after Ricardo, and evolved into the neo-classical theory, and its widespread acceptation by our societies, it seems difficult to imagine that it could have survived its multifarious pervasive effects.

I would therefore say that bargaining is NOT anticapitalistic, I believe it is on the contrary, the most genuinely capitalistic activity one can think of: It is the epitome of individual freedom at the level of the most elementary economic transaction, the freedom of agreeing on a price.
Clearly this freedom is not denied in the direct sense of fixing the prices of goods by laws as what may be thought of in marxist-inspired societies, but an indirect influence is just as powerful and much more difficult to identify. Prices are also fixed in modern Capitalism, by sophisticated economic theories about which Georgy Lukacs once said that a statue should be erected for their authors in front of every ministry of economy in the communist countries, because they are the main contributors to the practice of state socialism (I think it is Lukacs, but if someone wants to correct me and can cite the exact quote, I will be happy to correct this post in the sense necessary).

What bargaining is clearly incompatible with, is the ideology that affirms the existence of an objective natural price, in a sense not far from the existence of a natural law. It is that ideology that takes away from the individual negotiation the freedom of fixing the price for an individual transaction.

On a side-note, the sociological dimension of bargaining could also be an interesting topic of discussion. I mean by that the way such an activity exceeds the merely utilitarian aspect of commodity exchanges and may be a strong basis for building or consolidating a network of social human relationships, with diplomacy and common understanding as a basis. Maybe somebody can point me towards some authors who investigate these aspects.

References:
[1]: Capitalism, Socialism and Democracy

## Thursday, March 5, 2009

### For a deontological code in Finance

I came through the following article[1], that provides with an analysis of the responsibility of Finance and Economics Academia with regard to the current crisis, and one of their conclusion is as follows:
A second, more likely explanation, is that they did not consider it their job to warn the public. If that is the cause of their failure, we believe that it involves a misunderstanding of the role of the economist, and involves an ethical breakdown. In our view, economists, as with all scientists, have an ethical responsibility to communicate the limitations of their models and the potential misuses of their research. Currently, there is no ethical code for professional economic scientists. There should be one.

I certainly agree with that, but for such warnings about the models to be heard in the capitalist world we are living in, they must be broadcasted quite loudly, and even enforced by some sort of regulations. Some people just don't want to hear certain truths, especially when these ones are liable to jeopardize their multi-millions bonuses. Let's keep in mind that most financial researchers are funded by these people (directly or indirectly), and that they therefore are cordially invited to present results that are pleasing to their benevolence.
If speculators pay for the financial researches done in academia, is it such a big surprise to find that these researches tend to show the harmlessness of speculation?

While the overall article is interesting, I'd like to comment a bit on the following:
Of course, considerable progress has been made by moving to more refined models with, e.g., ‘fat-tailed’ Levy processes as their driving factors. However, while such models better capture the intrinsic volatility of markets, their improved performance, taken at face value, might again contribute to enhancing the control illusion of the naïve user.

The user who thinks that Levy processes may somehow enhance his control, is not naïve, he is ignorant of what a Levy process is all about. Levy process is exactly telling us that we have less control about what's going on, and particularly, it invalidates the dynamic hedging strategy inspired by Black, Merton and Scholes work. Furthermore, this invalidation is not a matter of opinion, it is a matter of mathematical correctness, as Haug and Taleb have shown in the previously cited article (Haug and Taleb, November 2007), a Levy distribution entails such a weakening of the Central Limit Theorem that the hypothesis(finite variance) making possible dynamic hedging becomes false.

And last but not least, it would be unfair not to mention the existence of the Truncated Levy Process(TLF) that seemingly resolved the "inconvenience" of the Levy Process with regard to the infinite variance, and therefore bring it back to the scope of validity of the Central Limit Theorem, making Dynamic Hedging again possible. It is indeed what Andrew Matacz in this article[2] aims at achieving.
While I don't question the value of the mathematical parts in the article, I wonder about their applicability from an investment point of view, and there's indeed a profound ethical problem at play here, and it is rooted in the belief of the possibility of a riskless strategy (which is at the core of Dynamic Hedging). There can't be such a strategy, because if there was one, its implementation would invalidate it (the statistical model of a market is always historical, the market can perfectly shift from one model to another, it is not causally determined to stay within the limits of one precise model).
A riskless strategy is potentially the equivalent of the perpetual motion machine in mechanics, to use it may well lead to its destruction (and also create a speculative bubble in the process).
On the other hand, the study of TLF is interesting and should be pursued, but it is necessary to separate this study from the sole motivation of creating an investing edge in the market (again the problem of deontology and financing creeps back). In this sense, the approach of Cont, Potters and Bouchaud in this article[3] from May 1997, displaying as its primary concern the fitting with existing data, appears more promising.

References:
[1]: The Financial Crisis and the Systemic Failure of Academic Economics
[2]: Financial Modeling and Option Theory with the Truncated Levy Process
[3]: Scaling in stockmarket data: Stable laws and beyond