Guest Post: Gold-Silver Ratio In Phase Space

Tyler Durden's picture

Submitted by The World Complex

Gold-Silver Ratio In Phase Space

The reconstructed phase space portrait is one tool that can be used to gain insight into the dynamics of complex systems, whether these systems be natural or man-made.

Today we will use these tools to look at precious metals.


The near-constant slope over long stretches of this plot tells us that gold is already increasing in price exponentially. So don't say that gold price will increase exponentially during a financial crisis. It is already doing so, and has been since early 2001 (notwithstanding the recent turmoil).

The break in slope in late 2005 tells us that the gold price suddenly began to increase more rapidly. I don't know if anything unusual happened in late 2005, but there was a bland warning by the ECB issued in December 2005 about growing global financial imbalances.

Reconstructing phase space portraits normally requires two or more time series, sampled at equivalent intervals. You can simply plot one series against the other (a scatter plot). If you are using excel or a similar program, this is remarkably easy.

Looks impressive--the gold line represents a gold:silver ratio of about 60. Deviations from that line represent deviations in this ratio. Silver's rise to nearly $50 in 2011 causes the funny looking nose on the graph at upper right. The curve represents the time evolution of the system, which moved in herky-jerky fashion from the lower left (in January 2000) towards the upper right of the graph (a little while ago). Each plotted point represents the state at the end of each month until roughly the present.

For graphs covering at least an order of magnitude, it may be worth using logarithmic axes.

The problem with these graphs is the presence of the US dollar. Most of the action in the plot is due to the declining value of the US dollar. To remove it, let us consider only the gold:silver ratio itself.

There are a number of long-accepted methods for projecting a single data series into a state space of more than one dimension. The intuitively obvious approach is to plot the data against its first (and higher, if desired) time derivatives. The approach I have used most commonly in these pages is a time delay plot, in which the respective observations are plotted against another, older observation. The lag is the number of time steps between the two observations, and there are prescribed methods for establishing an ideal lag.

Taking the month-end ratio of the gold price to the silver price, plotting it against a lagged copy of itself (delayed by one year), we see the following.

We are presently near where we started (just before the last financial crisis, and currently following a trajectory similar to that which we followed in the summer of 2008 (the yellow dot represents where we would be if April ends at today's prices). Given what we've recently experienced in the metals markets and stocks, it is extremely worrisome to consider we are only at the equivalent of mid-summer 2008!

There is more to the story--plotting phase space in only two dimensions can be a little risky because the third dimension may convey a lot of information. To create the third dimension, we apply a second lag equal to the first--so that the third axis represents an observation two lag periods behind the observation plotted on the first axis.

In the above graph, the red curve represents the 2-d projection shown above plotted on a reference plane (z=55)--and the green curve represents the 3-dimensional phase space portrait shown relative to the reference. Where there are green dashed lines between the 3-d and 2-d plots, the 3-d plot is above the reference plane, and where there are red dashed lines, the 3-d plot lies below the reference plane.

In the 3-d plot, we see that the current trajectory (near the bottom of the graph) is quite a bit below the trajectory during the crisis of 2008. It may be that the 2008 financial crisis was one of financial institution solvency, whereas our current crisis is starting to look like one of financial system failure. If this is the explanation for the differing trajectories then my projection is that we are going to see something we haven't seen before.

The gold-silver ratio has the potential to rise to heights never before seen. The reason is that major crises encourage hoarding and flight; and it is much easier to flee with a million dollars in gold than a million dollars in silver.

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IridiumRebel's picture

Roughly 60 to 1 ratio now from gold to silver? Fuckin bull shit. Thanks for the sale I guess you motherfuckers.

nope-1004's picture

Although this statement is true in theory:  it is much easier to flee with a million dollars in gold than a million dollars in silver

Would like some insight as to what percentage of the global pop has a million dollars, LIQUID!  Sure there are those who have high net worth (on paper), but who has the ability to take or transform their wealth into 1 million dollars of gold right now?  I bet a very small fraction of the population.

And why is the assumption that some "fleeing" must be done as it relates to owing silver or gold?  This article is a bit MSM-ish.  It plants a supposition or two, then draws a conclusion that is not necessarily true.

Sounds to me like buddy is on the hunt for some physical silver on the cheap - Gold already out of his reach.


ratso's picture

The World Complex rocks.

Pinto Currency's picture


There are probably ~ 250 million to 500 million oz. of physical gold (net of leased gold) held by central banks and about another 4.5 billion oz. held outside c.b.'s.

Of silver, there are ~ 1 billion oz. of visible inventory - far, far less than gold in dollar value.

Gold may well be remonetized by govs/c.b.s which would give it a big lurch in price.

The market (ctiizens) will remonetize silver for day-to-day purchases so it may lag somewhat if gold is remonetized by central planners - but there are much smaller inventories of silver available to market in the meantime.  And there are critical industrial applications for silver - much less for gold.

A mugs game to predict with certainty what will happen.  Citizens are certainly voting with their feet in grabbing silver right now.

Jam Akin's picture

Since the article makes little sense, here's a distriction.  From Yahoo comes word of a feminine counterpart to the attire of India's answer to Mr. T.  On the link modeled by another fine BRIC product, Caroline Correa.


“Zac Posen has indeed designed an entire gown made out of gold. Not gold fabric, but actual 24-karat paillettes. Okay, truth be told - paillettes covered in 24-karat gold leaf. But, still! An entire dress with $1.5 million worth of material!”


Herd Redirection Committee's picture

He doesn't address the suppression.  So which one has been suppressed more?  If currency becomes gold-backed again within the next couple years then maybe its gold, but if things kind of meander along like they have been, with no single catalyzing event, just the continuing process of the world's populace losing faith in fiat and government.

Manthong's picture

Duh..   banks ain't got no silver

just wait till all the paper fries to see what flies..

TwoShortPlanks's picture

Those tracks are dope. I love F1.

SafelyGraze's picture

the prices of gold and silver are highly correlated

mainly because of gold's use in photography and silverware, which perfectly tracks silver's

the price of gold and the size of the money supply and the size of the national debt are highly correlated for the same reasons

francis_sawyer's picture

@nope [And why is the assumption that some "fleeing" must be done as it relates to owing silver or gold?]


I agree 100% & that was my very first thought... Though I liked all the charts, the conclusions were irrelevant... Worse ~ Why go to all that trouble to make a case, then practically pin the whole argument on the final decision being made to FLEE an area?...

Sounds Simon Black-ish to me...

Deo vindice's picture

Silly me. I always thought the purpose of graphing was to clarify something to one's mind. Not to confuse.

When you use an illustration in a speech to make a point, and then have to explain the illustration ... you've lost the audience.


Wile-E-Coyote's picture

No this is what happens when you let your four year old play in your office. Crayon-paper they just can't help themselves, moth to a flame.

Manthong's picture

There is nothing about those plots that do not supremely correlate with the mind of a statist / politician.

1000 splendid suns's picture

With rigged markets, do any of these doodles matter? Like playing idiot poker. Just get out of paper related assets.

malikai's picture

Here's a simple graph. In summary, we're on the razor's edge.

Captain Kink's picture

I never really understood the term, "mental masturbation"... until now.  

El Oregonian's picture

" voting with their feet in grabbing silver right now"


You mean beat'in feet to grab it with BOTH HANDS...


Dewey Cheatum Howe's picture

Yeah and if we go back to a gold backed standard, coinage is not going to be in gold but most likely silver. Way I see it you save gold you spend silver. It is easier to create smaller denominations in silver than gold if the money is to be actually worth something and not be a debt note like the US dollar,

DoChenRollingBearing's picture

I want to think about this article some more.  There may be some great insights, or perhaps not.  Sorry!  But, any further comments I would have RIGHT NOW would not be worth much.

Nonetheless, new ideas and new ways of looking things (FOFOA is a great example) sometimes come right out of the blue like this.

Thank you, Tyler, for putting up a thought-provoking piece!

macholatte's picture

I want to think about this article some more.

So this might come under the heading of some guy got stoned and screwed around with excel and made some funny looking graphs and then decided to write up a rational for it before he sobered up ..... or not. 

Question is:  Does it matter?

If I was going to flee and didn't want to get caught with a ton of PM's I'd just sell them and wire the money some place else or trade for diamonds.  Remember that guy trying to get out of Cyprus with the trunk full of gold? So maybe that scenario is not relevant. Maybe the charts are. I don't care.

A squirrel dying in front of your house may be more relevant to your interests right now than people dying in Africa.

Mark Zuckerberg

Doña K's picture

In my opinion, his statement of fleeing is metaphoric. The portabilty of gold v. silver is and will always be an advantage. Silver's advantage is its utility as a commodity, affordabilty to those with lesser means and ease in frequent transactions.

One argument on the transactions, is the 1/10 oz. gold coin, but the commission % on the smaller gold pieces are not as attractive as silver coins.

IMHO, the ratio will hover around 60/1 until the archaic proverbial "when the shoeshine boy and the elevator operator are starting to talk about PM's instead of the ponys". In which case, silver will break its bounds and lower the ratio.  

sunaJ's picture

The author is f*cking insane.  I love it.  I'm not fleeing anywhere.  I'm here to fight, bitchez.

Ignatius's picture

My thinking has been that gold would out-perform for the fact that gold is a reserve asset.  Joe six-pack seems to see it otherwise:  gold available while silver is SOLD OUT locally.

sunaJ's picture

Let's extrapolate a few things.  First of all, this author does nothing to address what we all know is the crisis right now: physical vs. paper, so a lot of this pricing is irrelevant.  We have entered a new phase, alright, but it is one where paper has been used to manipulate the price and that ever-so-trusty tool is breaking before our eyes.  People recognize this and smart people with big money surely recognize this.  Western governments are late to the game, of course, because they are most dependent upon and enraptured with the fantasy of fiat.


If we live in an oligarchical society now, you can believe that at least in the United States, it will be the 1% that ends up with the vast majority of the gold.  Do you want to play by their rules?  People will seek alternatives to theft and tyranny.  They will trade chickens for light bulbs if they have to, but they will jump to silver without even batting an eye at what the government tells them to "use."  So this author presupposes a lot of things, but he thinks that the ratio of silver to gold can be infinitely large, when anyone that can read the simple datum of mined silver to mined gold would tell you otherwise. 


The author has said "we are going to see something we haven't seen before."  He should have left it at that.

Ralph Spoilsport's picture

But, these graphs are in 3-D!

Doña K's picture

That's also a metaphor. He is telling us that prices have the potential to go extragalactic in a space-time continuum. Thus, you do need a 3 and a 4 dimensional graph modeling.




bernorange's picture

Yes.  That's one more D than normal - for when you want that extra edge. /Nigel Tufnel


So, the more interesting question is this:  How much gold has been extracted from the people by all of the cash for gold outfits?  who owns these outfits? who is getting the bars of gold after all this jewelery is melted down?

This has happened before, when commies needed precious metals to buy stuff abroad, they engineered a famine (well, they didn't kill the crops, they simply sold all the grains for foreign currency) and offered to give a cup of grain for silver/gold.  At least today they are exchanging for paper money... I wonder for how long?

Dewey Cheatum Howe's picture

Gold vs silver for Joe six-pack is fairly straightfoward, Joe six-pack doesn't have lots of excess dollars to spend on gold based on the price, it is a little too far out of most joe six-packs discretionary budgets except for 1/10 ounce coins (a joe six-pack sized denomination) which there is a shortage of btw so silver is the next best thing from a price standpoint. Small money chases the smaller metal based on price and there is a lot more of it than there is big money. Either way we can all agree on one thing he who is not holding debt and something tangible will be the last men standing when this shit show finally blows up.

I still say silver will recover above $30 and gold above $1500. Wait until Obamacare kicks in that is going to be the death knell of the US economy. That is going to push people over the edge when the find out the old bait and switch routine was pulled on them and they were sold a bill of goods. The panic stampede is going to start then when the matrix wakes up and starts running for every safe haven they can possibly find.

I personally believe anyone sitting on silver now if they can hold it long enough is going to get a better deal on gold later flipping it back as far as price per ounce than the current sale goes when it does go back to or above premuim being asked now as a buy price from a dealer directly for resale.


"If this is the explanation for the differing trajectories then my projection is that we are going to see something we haven't seen before."

We are cursed: We live in interesting times indeed...

You know, lots of people think that there's going to be some huge, climactic and migratory end to all of this...  There won't be any fireworks to signal The event...

Those who are paper rich or wealthy will wake up with nothing one morning.  The rest of the world already has nothting.

So, do you expect to see the 1% occupy the Wallstreet or something? I don't think so.  I do expect to see Huge celebrations when Eartlings can put this nighmare behind us...  I suspect there won't be any pity for anyone who gets wiped out.

We all start fresh.  A clean slate.

ebworthen's picture

I was going to say/ask the same thing; if I'm hunkering down which is the better value/price point?

Looks like Silver at the moment, though I'd buy Gold too, of course.

disabledvet's picture

This looks more like fun with an etch a sketch than anything that exists "rationally." It is fun to add fun to an equation..."children playing without inhibition." We all know the equation with silver and gold though and that is in times of stress it is highly "ineleastic" or "price sensitive" with very little inputs. This makes for some truly extraordinary moves which...when overlaid with "fun" causes "various monetary authorities to scurry about to gather their little children" (margin rates) and tell them "play time is over, dinner is ready." Should be yet another fascinating week for a substance everyone says they should but no one knows why they need it. I feel as well like we've been here before...can't explain why though.

spine001's picture

Forget about the explanations all explanations are bullshit. The phase diagram is showing signs of instability and the exploration of new phase space indicates danger level lack of stability in the system suggesting that we are about to jump to another attractor in the world economy. That means lost control for the CBs. Again impossible to know when we are getting there.

Until next time,,


Kirk2NCC1701's picture

My Chief Engineer flagged the subspace for these PM ratios, when Earthlings finally get Transparent Aluminum. ;-)

jeebus's picture

The US has by far the most millionaires with over 5 million. Next closest are a bunch of countries that all have a million millionaires. So, there are literally tens of millions of people whom have at least $1,000,000 of liquidity.

samcontrol's picture

How many do you know with a million in paper silver?

mickeyman's picture

Actually, you're right. I am looking for some cheap physical silver. Gold too. And both are cheaper now than they were a few weeks ago.

beaker's picture

This is like cloud watching.   I see a dolphin riding a horse in that one chart....  no, maybe thats an airplane smoking a cigarette.

TraderTimm's picture

Wow, n-dimensional plot and you know where it is going to go? Someone call in Doctor Who to square up your tesseract.

I don't see how you can even make the simplest prediction doing this:

Original series: 1,2,3,4,5,6

ColA, ColB, ColC


2         1

3         2       1

4         3       2

5         4       3

6         5       4


And plotting them on a three-dimensional graph. Its an interesting manipulation of data, but fuckall for predicting jack squat.


Aeternus's picture

Translation for the chartmentally impaired.



And for the acronympaired.

Buy The Fuckin' Dip!

prains's picture


that concept needs more exploration;

is said fleeing going to be orderly? no

is the act of fleeing a form of panic? yes

if panic is to ensue, will it be orderly?no

if not orderly, then how disorderly? very fucking disorderly


the entire narrative of the article comes down to this premise;


 it is much easier to flee with a million dollars in gold than a million dollars in silver.


true but irrelevant if you're not willing to explore the concept of "fleeing". Where are you going to flee? after your third tank of gas runs out will there be anyone left to sell you a fourh tank of gas? will you have to kill for that tank of gas? THEN WHAT ARE YOU TALKING ABOUT?

If you are incapable of extrapolating the many different facets of the act of "fleeing" then who cares if it's easier to carry a million in gold over silver 'cause at some point if you can't run for four hours at 180 bpm in the dark over rough terrain carrying your last child your fucked anyway.


DoChenRollingBearing's picture

Fleeing to Peru by plane with, say, $100,000 worth of gold would be easy...  It's the timing that's a bitch.

GlobalCtzn's picture

The timing question IMO is answered with "While you still can." Better to be a couple years early than a day too late. I cannot imagine getting stuck in the U.S. when it all really goes down. Me, I am already gone............

Jorgen's picture

Easy if you do it right - see #3509181 However, you should rather take a direct flight from the U.S. to Peru. Here is a story of an American guy who was flying with his 150 gold coins to Panama via Mexico. He must have done it correctly with the U.S. Customs but well... their Mexican counterpart was a different experience.

samcontrol's picture

my father timed it in 1978 PARIS , France. He said ...i will never pay these fuckers taxes! or any fucker!

Seer's picture

Yeah, ain't it a bit funny that the author can spout 3-D yet fails to THINK in three dimensions!

What's the logic in fleeing with a bunch of gold when the REASON that you're likely fleeing is because someone wants that gold- is there a place where there are no others who would also want that gold?  The greatest visibility is in the running.

If you have what looks like excess then EXPECT that you'll have to fight to keep/maintain it.  And in the future there won't be any "safe zones" where you can flee.