The rise and fall of US confidence

Today we look at a graph of confidence in the US system. The US confidence ratio represents the ratio of outstanding US Federal debt to the dollar value of US gold holdings (as reported*). No corrections for inflation should be necessary, as both terms are valued in the same depreciating dollars. We use the term confidence as the ability of the US to stretch this ratio to (by our thinking) absurd multiples was a reflection of the world's confidence in the United States--which differs from the ability to actually repay debts.

For post-1971 I used the assumed holdings of 250 million ounces multiplied by the average annual price (from Kitco). There are those who suggest the true holdings are substantially less than 250 million ounces. That may be so, but the picture is already bad enough if we accept the official numbers.

Confidence level sank throughout the Depression up until the beginning of WWII, after which ascendant American power was reflected in a climbing confidence ratio up to the oil crisis in the early 1970s. Confidence sank as the US withdrew from Viet Nam and inflation rose until the price of gold rose sufficiently to restore confidence in American solvency.

From 1980 to 2001 was a golden age for the US. In this time, both stock and bond markets were strong, the US currency was strong, and the only credible opposition to US hegemony disintegrated. But every bubble meets its pin, and ever since the planes hit the towers, the US power and prestige has gone into decline. This decline is marked by a rapid decline in the confidence index. How low will it go?

There is a provocative looking left shoulder and head, suggesting a drop to the neckline somewhere around 2020, after which there may be something of a resurgence in American confidence. The anticipated completion of the bankruptcy head-and-shoulders formation promises to be a hair-raising event.

Actually, though, what appears to be happening is the blowing of bubbles. A bubble is blown, but can only expand so far before confidence fails and the bubble deflates. Then another, in this case larger, bubble is blown. If the bubble is able to deflate without society collapsing, perhaps it will be possible to blow another. Or perhaps we will be wise enough to act in ways that prevent the bubble from being blown in the first place.

At the World Complex we are of the opinion that bubbles are bad--but we recognize they can be a lot of fun. Sort of like going on a bender. The US has been on a bender since 1980. Soon the weekend will be over and it will have to be back at work. Although the new boss may be of the Asian persuasion.

For the bubble to deflate, the debt must disappear, or the gold price must rise. Assuming no change in debt levels, the gold price would have to rise about ten-fold for the confidence ratio to fall to historical values. Unfortunately, a considerable rise in US debt appears to be baked into the cake at this point, so we would foresee gold to eventually reach breathtaking prices.

The 2-d reconstructed phase space of the confidence ratio appears below:

On this chart we don't dare suggest anything other than a fall towards the origin of the graph. If the ratio falls to 10, then gold has to rise to about $6,000 per ounce at today's level of debt. If the ratio falls to 5 (the last low in 1980), then gold would have to be about $12,000 per ounce (again, only at the present debt level). The numbers could be quite astronomical once the deficits in Medicare and Social Security start being realized.

NATO wrapping things up in Libya

As predicted, the NATO campaign in Libya is winding up with the massacre of civilians--albeit civilians who, in the words of this author, are "unworthy victims"--that is to say, unworthy of any of our concern. The list of unworthy victims includes the majority of civilian deaths, and foreign (mainly African) workers, who were demonized at the beginning of the conflict by the western media's insistence on calling them "African mercenaries".

Lies, War, and Empire: NATO’s “Humanitarian Imperialism” in Libya

By: Andrew Gavin Marshall

In this report I seek to examine the war against Libya in a more critical and comprehensive manner than that of the story we have been told. We hear a grand fairy tale about powerful Western nations working together to save innocent civilians in a far-off country who simply want the freedoms and rights we already have. Here we are, our nations and governments – whose officials we elect (generally) – are bombing and killing people on the other side of the world. Is it not our responsibility, as citizens of these very Western nations, to examine and critique the claims of our governments? They are, after all, killing people around the world in our name. Should we not seek to discover if they are lying?

It has been said, “In war, truth is the first casualty.” Libya is no exception. From the lies that started the war, to the rebels linked to al-Qaeda, ethnically cleansing black Libyans, killing civilians, propaganda, PR firms, intelligence agents, and possible occupation; Libya is a more complex story than the fairy tale we have been sold. Reality always is.

What Were the ‘Reasons’ for ‘Intervention’?

We were sold the case for war in Libya as a “humanitarian intervention.” We were told, of course, that we “needed” to intervene in Libya because Muammar Gaddafi was killing his own people in large numbers; those people, on the same token, were presented as peaceful protesters resisting the 40-plus year reign of a brutal dictator.

In early March of 2011, news headlines in Western nations reported that Gaddafi would kill half a million people.[1] On March 18, as the UN agreed to launch air strikes on Libya, it was reported that Gaddafi had begun an assault against the rebel-held town of Benghazi. The Daily Mail reported that Gaddafi had threatened to send in his African mercenaries to crush the rebellion.[2] Reports of Libyan government tanks sitting outside Benghazi poised for an invasion were propagated in the Western media.[3] In the lead-up to the United Nations imposing a no-fly zone, reports spread rapidly through the media of Libyan government jets bombing the rebels.[4] Even in February, the New York Times – the sacred temple for the ‘stenographers of power’ we call “journalists” – reported that Gaddafi was amassing “thousands of mercenaries” to defend Tripoli and crush the rebels.[5] Italy’s Foreign Minister declared that over 1,000 people were killed in the fighting in February, citing the number as “credible.”[6] Even a top official with Human Rights Watch declared the rebels to be “peaceful protesters” who “are nice, sincere people who want a better future for Libya.”[7] The UN High Commissioner for Human Rights declared that “thousands” of people were likely killed by Gaddafi, “and called for international intervention to protect civilians.”[8] In April, reports spread near and far at lightning speed of Gaddafi’s forces using rape as a weapon of war, with the first sentence in a Daily Mail article declaring, “Children as young as eight are being raped in front of their families by Gaddafi’s forces in Libya,” with Gaddafi handing out Viagra to his troops in a planned and organized effort to promote rape.[9]

As it turned out, these claims – as posterity notes – turned out to be largely false and contrived. Doctors Without Borders and Amnesty International both investigated the claims of rape, and “have found no first-hand evidence in Libya that rapes are systematic and being used as part of war strategy,” and their investigations in Eastern Libya “have not turned up significant hard evidence supporting allegations of rapes by Qaddafi’s forces.” Yet, just as these reports came out, Hillary Clinton declared that the U.S. is “deeply concerned by reports of wide-scale rape” in Libya.[10] Even U.S. military and intelligence officials had to admit that, “there is no evidence that Libyan military forces are being given Viagra and engaging in systematic rape against women in rebel areas”; at the same time Susan Rice, U.S. Ambassador to the United Nations, “told a closed-door meeting of officials at the UN that the Libyan military is using rape as a weapon in the war with the rebels and some had been issued the anti-impotency drug. She reportedly offered no evidence to backup the claim.”[11]

An investigation by Amnesty International, released in June, attempted to assess the on-the-ground (as opposed to ‘in-the-newspapers’) reality of the claims made which led to Western “intervention” in Libya. Among the stories of mass rapes were the use, by Gaddafi, of “foreign mercenaries” and using helicopters and jets to attack rebel forces and protesters. As the Independent reported in June:

An investigation by Amnesty International has failed to find evidence for these human rights violations and in many cases has discredited or cast doubt on them. It also found indications that on several occasions the rebels in Benghazi appeared to have knowingly made false claims or manufactured evidence.[12]

Article continues here 

Americans diss Cote d'Ivoire again

Check it out. In the third column, which shows the per capita GDP in 2010 as estimated by the CIA--Cote d'Ivoire ranks last. Last. It seems that both the IMF and the World Bank both disagree.

Never mind that the IMF estimates per capita GDP for Cote d'Ivoire to be nearly ten times that of Burundi. What does the IMF know about economics anyway?

This is what happens when Americans don't like you.

Historic gold production: a review of Müller and Frimmel (2010) - updated

In a recent paper, authors J. Müller and H. E. Frimmel discuss cycles in historic gold production and implications for the future of the monetary metal. The World Complex applauds such studies, especially when they are backed up by data. Even better that this is one is published on an open source, so anyone can view it.


The analyses used by the authors are reflective of Hubbert's (1982) approach to estimating future production on the basis of past production, however as we will see I take exception to some of the authors' conclusions. Let's go!

The authors' observations can be summarized as follows:

1) Gold production has grown at a rate of about 2% per year since about 1850.

2) Historic gold production has been strongly influenced by four cycles of discovery and exploitation

Exponential curve fitted to gold production--four cycles highlighted. 

No doubt the first hiccup at about 1850 is California, and the little peak

before the first cycle is the Yukon. From Müller and Frimmel (2010).

3) Exploited ore grades have declined steadily through time

4) The dollar value of gold discovered per dollar spent on exploration has fallen catastrophically since the 1960s.

Discovered gold per dollar of exploration expenditure. From Müller and Frimmel (2010).

Just to interject some comments on these observations--other authors have noted that this last exploration cycle has yielded less "bang for the buck" than others. But the data source is unclear--what do we mean by gold in the ground? Are these inferred resources? Defined reserves? Or gold actually mined? It may be that the poor performance of the last decade has to do with the regulatory expense of defining resources. And if the numbers above relate to mining, there are a lot of potential mines discovered in the past decade that are not yet in production.

Additionally, although gold production has been falling, according to USGS figures, world production increased in 2009 over 2008, although it is still short of 2001 production.

From these observations, the authors conclude:

1) Gold production will continue to decline, possibly until 2026.

2) Peak gold production may have been in 2001.

3) The total mineable gold in the earth's crust is estimated to be about 300,000 tonnes, approximately double the total mined historically.

Hubbert linearization graph projecting total production of gold to be between 

230,000 and 280,000 tonnes of gold. Chartists might want to try 

drawing your own lines. From Müller and Frimmel (2010).

Although it is true that you cannot produce what you have not discovered--we should be sure we understand why we haven't discovered it yet.

The authors point out that there are rather large errors at the historical beginning of the above graph (that would be at the left). Yet they use that segment of the graph to project total historical production (the "optimistic assessment".

Alternatively, they use a projection of the falling production of the last decade to estimate total production (the "pessimistic assessment"). However, when we go back to the top figure, we see that historical production has driven by major cycles. During these cycles there are periods of sharply rising production followed by declining production. Yet long-term production has increased. Therefore using the decline of the latest cycle ignores the possibility of future cycles (perhaps driven by the current re-exploration of previously mined out areas now possible due to improved recovery) and possible reversion to the historical mean rate of production growth--not indefinitely, but for some period of time.

One factor that seems to be missing in the authors' reasoning on gold production cycles is the cycle of investment. Although they correctly recognize a significant lag between peaks of production and peaks in price, reflecting the time required to prove up and build a mine. I would argue that the peak in mining production in 2001 is the lagged response to the price peak in 1979; and that the peak in production as a consequence of the ongoing rise in the price of gold will not be seen for some years.

That lag has increased of late, largely due to increased costs. Many of these costs are forecast to increase. But a large part of those costs are regulatory--and as the economy shifts from a financial basis back to real production of real things--we may find those regulatory costs falling.

I think that Hubbert's approach was driven by his familiarity with the oil market. I agree that like oil, there is only a finite amount of gold on earth; however the geological differences are sufficient that gold (and the other metals) may not lend themselves so easily to his method of analysis. I have written on this topic before: the appearance of peak production in metals may be simply due to lack of investment driven by the low prices of the last two decades.

It is true that mined gold grades are declining, and costs per ounce of gold mined are increasing. But this is true of all other metals mined through history. Human ingenuity ensures that gold will continue to be mined at lower and lower grades--although how low we can go over what timeframe cannot be foreseen.

Energy costs, in particular are expected to increase. But lack of energy by itself will not cause gold production to cease. Gold has the highest marginal utility. Production of gold will cease as we near the point where it requires more energy and materials to mine than can be paid for by an equivalent amount of gold.

It is nice to see an article of this type in a formal setting because in my experiences at both academic (AGU, GAC) and industry (PDAC) conferences, few geologists understand why anyone would wish to mine gold. It is interesting to ponder deep questions of the market.

For instance, if we take the USGS data and plot the apparent consumption (within the US) against price since 1900, we get the following:

How do we reconcile the above with classical ideas of supply and demand?

Normal demand varies inversely with price (red curves).

There are actually two separate hyperbolae in our demand-price graph.

The smaller hyperbola at left reflects price and demand prior to the expansion of the South African production (gold production cycle 3). The greater hyperbola reflects the ability of the American public to own gold.

An interesting feature is highlighted by the green ellipse--demand increasing along with price in years 2008 and 2009. Since the economic crisis which came into focus in 2008, it appears that gold may be acting as a Giffen good. It has been hypothesized that safe financial assets act as such during bad economic times, as evidenced by the recent price rises in both gold and bonds.

Update:

After corresponding with the lead author of the paper, he sent me a copy of a newer paper which contains a more favourable estimate of the global endowment of gold which may be eventually recovered by mining. In the new paper (Müller and Frimmel, 2011), the total mineable gold is estimated to be as high as 390,000 t; although with the caveat that the estimate is sensitive to the estimate of the amount of gold mined prior to 1900. 


I still believe there are two points of contention.


1) It is easy to underestimate the amount of gold produced in Graeco-Roman times (and, indeed, by the Incas), but the amount may have been substantial. As support I offer the following:

Atmospheric lead in Greenland ice. Time runs right to left--note log scale. 

The red ellipse shows the influence of Roman industry and mining, peaking 

2,000 years ago, at levels which were not surpassed until the late 13th century. 

The peak 20,000 years ago relates to glaciation. From Delmas and Legrand (1998).

Gold has been of considerable significance for thousands of years. Apart from the busy-ness of Mediterranean cultures, a great deal of gold migrated from West Africa to Europe in historical times.

As for the peak in lead in the above chart, that is due to the removal of tetraethyl lead from gasoline in the 1970s. One last bit of deliciousness from the mid-20th century:

I love the wholesome imagery. Lead--it's just like vitamins! Ladies Home Journal says so!

2) There is still another very large untapped frontier in gold exploration and mining--the seafloor. In addition to placer deposits on continental shelves, the work attempted by Nautilus Minerals Inc. near Papua New Guinea and Diamond Fields International in the Red Sea may prove ultimately to be game-changers. Last time I checked there was more sea than land, and if rift margins turn out to be the principal prospects for hydrothermal reasons, there are about five million square kilometres of highly prospective turf out there.

For disclosure--I do not work for and never have worked for either of the above companies, nor do I hold any position in shares, long or short, in either of them.


References:


Delmas, R. J. and Legrand, M., 1998. Trends recorded in Greenland in relation with Northern Hemisphere anthropogenic pollution. IGACtivities, Issue 14.

Hubbert, M. K., 1982. Techniques of prediction as applied to oil and gas. U.S. Department of Commerce. NBS Special Publication 631, pp. 16-141.

Müller, J. and Frimmel, H. E., 2010. Numerical analysis of historic gold production cycles and implications for future subcycles. Open Geology Journal, v. 4, pp. 35-40.


Müller, J. and Frimmel, H. E., 2011. Abscissa-transforming second-order polynomial functions to approximate the unknown historic production of non-renewable resources. Mathematical Geosciences, doi: 10.1007/s11004-011-9351-8.

Another explanation for recent market volatility

All the noobs.



I think this video shows one of the younger hedge fund traders discovering the wonders of HFT.

Can HFT hold up the market?

Now here's a funny thought. Market volatility has been unpleasant, to say the least just lately. Liquidity has vanished, thanks to HFT. Arguably, the S&P 500 should be a good deal lower than it is.

Suppose you are an institutional holder of shares, and your models are telling you to sell; but every time you try, liquidity vanishes and you end up completing your sale at a much lower price than anticipated. Your boss yells at you. Worse, your year-end bonus suffers. So what do you do?

What can you do? Any attempt to sell in size collapses the price of the security in which you are trading. You have to come up with a strategy to minimize your losses in selling. Either you limit your orders, which means under the HFT regime they never fill (except for a handful of shares), or you don't sell at all. It's possible that some of these institutions are locked into positions they can't get out of (except at desperately lower prices).

There could be a whole country full of institutions that want to sell but dare not for fear to the scalping they'll receive from the algo traders.

Here is another "gift" HFT has given us. Liquidity on the buy side has already vanished; now liquidity on the sell side is going too. The likelihood of a fair price discovery through the market has taken another beating. Although arguably this allows the market to levitate at far above reasonable value, it also means long years of pain for "investors" as every tick up is desperately sold.

Chile tries to boost the price of copper

If this doesn't work, nothing will.



Chile's contestant for Miss Universe this year will attend in a dress made of copper.

Update (4:30 p.m. EDT) - so it doesn't seem to have worked, but give it time. These advertising campaigns can take awhile. Just ask DeBeers.

The once and future strategic metal

News from Venezuela has Chavez nationalizing the gold industry and calling in its gold reserves stored in foreign banks. It may be that the nationalization fear is overblown, but bringing Venezuela's gold back into the country may be a shrewd move, particularly in light of recent statements that the US could sieze the gold reserves of other countries which are stored in New York. Possession, in this case, is ten tenths of the law.

Of course they will be reimbursed for it. The money is probably being printed right now.

Gold and oil operations have been nationalized before. It is a significant, albeit understated risk facing investors in mining companies. When gold prices languish, governments care not for the yellow metal; but a rapidly rising price makes gold a strategic metal.

Ghana once nationalized its mining industry; resulting in a dramatic reduction to annual production. After speaking with government officials in Ghana over the past few years, I am confident there will be no nationalization there as they seem to still understand that siezing the mines is killing the golden goose. But I can't say the same about other governments, especially in developing countries.

Ghanaian officials are worried about the growing scale of artisanal mining, and the friction between illegal miners, landowners, and legitimate mining companies. The rise in gold prices is changing the economics of small villages, where many have been lured away from family farming or fishing interests by the high price of gold. Apparently, it is illegal artisanal mining behind Chavez' move as well. 

Fifty times in forty years

That's the performance of gold. From $35/oz on August 15, 1971 to a close of $1766.20 at close on August 15, 2010.

Sounds impressive until you realize that that is only about 10.4% compounded annually.

Gold rated AAAA, now two steps above US treasuries

Bank of America has rated given gold its first-ever AAAA investment rating. Take that, Buffet!

Gold AAAA

Remember that this is a sovereign debt crisis and not a company debt crisis. Moats, pitchforks, farmland, silver, companies that produce real products that don't depend on government--also pretty good investments. Companies based on debt, government contracts, many other forms of paper--bad.

Machines without memory

The Masters of the Market stay
In darkened rooms where 'lectrons play
And talking heads cannot convey
The new idea's birth

For they hunger in their secret dreams
For the trading highs of cruel machines
Projected on a million screens
Without a sense of worth.

At last the HFT algo show!
The crash nobody could foresee!
Your neck inside the rope!
Indices wihout hope!
The looters that ignore the SEC!

Perfumed fingers through the till
The asks all grow but never fill
The red ink has begun to spill
The market starts to tank!

The regulators and the traders too
Are uncertain if the plunge is through
And consult their charts to find a clue
But the frozen screens go blank!

At last the HFT algo show!
High VIX grown of a fractal seed!
A bubbilicious time!
A dark and dirty crime!
The bulging eyes of traders strangled by their greed!

(apologies to Alan Moore)

A paper by W. S. Rea and co-authors reminds me of why the methods of analysis I used in this article failed to provide any useful insight despite appearing to work on longer term charts here, here, here, and here.

The time series outputs of some dynamic systems possess long memory--meaning that the present beharviour is influenced by the entire past history of the system. It may be that recent events have a larger statistical impact on the present, but the characteristic of a long memory requires that even events in the distant past are reflected in the present behaviour.

How memory is "stored" in the system varies. For instance, in the days when HFT was a distant dream, the response of a stock's price to a good quarter would depend at least in part to the company's past behaviour. One which disappointed quarter after quarter would not benefit as much from a good quarter as one which had a history of meeting or exceeding expectations--the market might exhibit some skepticism. Where is this memory stored?

In climate systems, the memory may be "stored" in slow-response variables, which may yet influence the reactions of fast-response variables to various forcings. The geological system is extremely complicated, because local climatic factors, which are driven by such things as ocean currents and the distribution of continental land masses are strongly influenced over the long-term by tectonic activity; and over shorter timescales by the distribution of fresh water bodies, themselves being altered in response to isostatic uplift. Slow variations occasionally lead to catastrophic events, meaning sudden irreversible changes can occur in what had been a slowly evolving system.

Many economic systems appear to have long memory. The activities of today are influenced by events of the past. Nixon striking down the last vestige of the gold standard, Volcker raising interest rates, the "strong dollar" policy of Summers, the wars of Bush the Elder and Bush the Younger, Obama's lates raise of the debt ceiling--all of these have had impacts that have rippled through the USD gold price from then until today.

Dynamic systems analysis--at least the type used on this blog--work best on systems that have this kind of memory. The lessons of the past must echo, at least in some form, through the system for analysis to give us some interpretable results, as they do for unemployment and the gold-silver ratio.

HFT algos are different. They have no memory and only dream of a concept of value. Arguably, they estimate a value on the basis of variability in observed parameters; but their means of acquiring or disposing of a stock subverts the normal method of price discovery. Each trade during a flash crash has no identifiable connection with previous trades, but represents that maximizing of an unpredictable opportunity. When the flash is done, normal trading between human resumes as if nothing had happened.

Flash crash: business model or indicator?

After the series on deconstructing algos, a few things become clear:

1) HFT, by and large, does not increase liquidity. On the contrary, it works by reducing liquidity at key intervals (during periods of determined buying or selling), resulting in larger price moves than would otherwise be the case.

2) We can distinguish between the brief episodes when an algo clears out those pesky human bids from those when two algos are going toe-to-toe in a stat arb war, as well as those intervals when an algo is taking some hapless mutual or pension fund to the cleaners.

Examples below are accessible through here, except for the first one which was posted here.

Eliminating human bids before the fun begins--2 s.

Scalping the fund by removing liquidity in the face of determined buying. Note the sudden

 rapid rise in stock price while the fund buys, and the price returns to normal afterward.

Two algos slugging it out. Notice a lot of activity in the bid/ask but very few trades actually occur.

Two algos duel. Then, at 10:25, a committed buyer shows up for a scalping.

A committed seller experiences HFT (note the rapid decline in price).

The flash crashes occur because somebody needs to sell a quantity of shares. The algos "perceive" the orders coming to market and choke off liquidity, and the seller gets a poor price.

The flash "rises" occur because somebody needs to buy. In response to demand, the algos again remove liquidity.

In neither case is liquidity being offered when it is needed. In fact, the exact opposite is occurring. By systematically removing liquidity when it is needed most, HFT algos destabilize the system. This destabilization is merely a side effect--the algos increase the profits of the companies that operate them. But this is very much like the Enron method of doing business--shut down plants at a time of soaring electricity demand to line your own pockets while possibly bringing down the electrical network.

Days with a lot of flash crashes, as on Friday (August 5), are days where there is a lot of institutional selling. It is possible that the focussed withdrawal of liquidity by these service providers contributed to the rather steep decline of the indices on that day.

Deconstructing algos part 5: Are there any humans in the market?

In the past few days, some unusual behaviour has been occurring in after-hours trading of Earthlink shares.

Are there any humans in this market? Hello?

After hours pricing on ELNK, August 2, 2011. Lots of action. Image from Nanex.

Details of the above image. Same source.

And here's the trading action. Not much considering all the bidding activity.

I think what we are seeing is the elimination of humans from the market. Two algos, using their own stat-arb approaches have a differing opinion about ELNK. One thinks it is a buy at any price below, say, $8--the other thinks it a sell at any price better than, say, $7.95. It is normal for such differences of opinion to exist--indeed, they have to exist for the market to exist. When two humans meet in the market, with just such a difference in opinion, they would soon come to an agreement, the price being dependent on which participant gives away his opinion first.

The algos each try to maximize its own gain. And they do this by showing only a small offering at the best price that doesn't attract any attention. As soon as some interest is shown in their bid, it is cancelled and moved to a much more favourable price. It would be as if one of the human traders had opined "I might be interested in selling some ELNK at $7.95", and then when anyone expresses an interest, suddenly changes his mind, and say, "actually, I meant $8.15." Then the other trader says, "well, if you came down to $8.10, I might be interested," and just as the first trader goes to agree, the other suddenly says, "actually I mean $7.75." After this goes back and forth for awhile until the inevitable fistfight breaks out. 

No trading would occur. This approach provides no liquidity.

It is a contest, like the game where you try to step on your opponents foot. One favoured tactic is to dangle your foot in front, luring your opponent into an attack, pulling it out of the way as he does so, and then quickly counterattacking your opponent's extended foot. Every so often one of the opponents manages to touch the other and a trade goes through. Otherwise, the bids and offers just go up and down furiously.

*  *  *  *  *  *  *  *  *  *  *

In the last "Deconstructing algos" article we looked at two-dimensional reconstructed phase space portraits of busted trade data for CNTY; original data acquired from the Nanex site here.

As described earlier, one approach to creating a geometric representation of a phase space from a time series is to generate a time-delay plot, in which the values of our time series are plotted against lagged values of the same series. We use a constant lag for reasons described here.

Now, in the CNTY data (and in the data series in today's articles) the time control isn't as fine as we would like. In particular, even though the trades are presented in order, the time stamps only extend to the second. We may have 250 transactions in order in that second, but we don't actually know the length of time between any of them. How do we come up with a constant lag?

We can't. What I did in the last episode was assume that all trades were evenly spaced. In reality, this was unlikely. The result is that my phase space portraits were distorted somewhat from reality. How much distortion depends on how far from evenly spaced the samples are. In practice, with lots of points, the distortion isn't really going to be bad unless you have more than 80% of the trades compressed into an interval comprising less than 20% of the time investigated. This seems unlikely, but it would be nice to be able to check. Intuitively, it seems likely that the many trades at similar values occur close together in time.

A geological time series may be a representation of midsummer temperature, captured at thousand-year intervals. We don't know what the temperature does in between each of our observations, but it would be reasonable to assume that it varies, probably in quasiperiodic fashion. Worse, our control over the timing of our samples is nowhere near as nice as we like to pretend. Ask a geologist if his samples really are separated by thousand-year intervals and he will smile and have a distant look in his eye. In reality, the samples are at uncertain intervals, and the time series is fitted to some sort of time scale, and the geological parameters of interest have been interpolated (usually in a linear fashion).

Pricing series are different. Each of our observations is one sale. There is no doubt what the price is between sales. By convention the price between sales is that price of the last sale. So there is no need to interpolate data.

Let's look at a simple example. Brown-Forman Corp. (BF.A) had some interesting gyrations on July 12, 2011, as detailed on the Nanex strange days page.

We observe 46 trades time-stamped 09:30:01. Notice the stock trades from $68 down to $23 during this second. The trades are not quite evenly spaced, but I have created the time-delay pseudo phase space plot by assuming they are, and plotting the price of one of the trades with this time stamp against the fifth trade prior (with the same time stamp). Hence we have 42 paired trades to put on a scatter plot. By convention we draw a trajectory through them in sequence. Here is what the resulting pseudo phase space plot looks like.

A masterpiece of flash impressionism! Look at the elegant lines. It looks ready to take flight, free at last from human meddling with the stock price! The initial trades are near the upper right, the final trades took place at the left lower tip.

Now we can add some trading density to the graph. We know the location of each of the paired trades. We choose select the volume--either that of the original trade or that of the lagged trade--it doesn't matter which, but be consistent! I have chosen the lagged volume and contoured using various bin sizes. In these graphs, the bins are 2x2 squares, centred in the midpoint of the four squares.

The above plot used fairly large bins. Each bin has a $20 trading range. I had to use such large bins because there weren't very many trades. The contours are at 10% intervals, meaning that all bins (2x2 boxes) centred within the first shaded contour contain at least 10% of all trades during the one second interval represented in the plot. Most trades occur in the $60-$70 range. The trading density thins out at the lower price intervals.

Here is the same plot with smaller bins.

Smaller binning gives a better image of what's going on. Here we see the greatest trading density was actually in the $50 range. There are five disjoint basins (six disjoint areas, maybe). Other than that I don't know how to interpret this. I'm not sure whether there is any point in trying to tease out any more information from it.

Let us look at trades for ASIA on July 14, 2011.

The stock began trading near $16 and within 1 s had retreated to $14.

Trading density plot.

Here I've used an absolute trading density (i.e. number of shares traded). The most shares traded in one bin was in excess of 50,000 (labelled on diagram). Instead of contouring, I shaded the bins in accordance with the legend. The labelled dot is the first state at 9:30:01.

This exercise is really about displaying the data in a different form in the hopes that we can make some kind of interpretation of it. It is always possible that no interpretation is possible. This has made me dizzy. I am posting these (and will post a few more shortly) in the hopes that someone sees something of note.

Or perhaps this is the correct interpretation.

Gold-silver ratio breakout looks to last longer than the "Buffet hammer" of 1998

Today we present a simpler version of a chart we have seen before--a reconstructed state space diagram of the gold-silver ratio over the past twelve or so years. The differences are that instead of reconstructing the phase space from the gold-silver ratio, I have used a three point moving average of the gold-silver ratio to reduce some of the noise.

Three features of interest are the "Buffet hammer" of 1998 (so-called because its trajectory looks like a hammer), which resulted in a brief, sharp rise in the price of silver; the silver crash of 2009, and our current apparent breakout. The current breakout is about one month short of the duration of the Buffet hammer. If the gold-silver ratio remains at about its current value, the trajectory will curve towards the lower left corner of the graph--however this movement will take at least a year, before the lagged values (vertical axis) fall to where they are at present.

The fierce correction in the price of silver since early May is reflected in the little loop on the tail of the current breakout.