Dust flux, Vostok ice core

Dust flux, Vostok ice core

Wednesday, April 24, 2013

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.

Sunday, April 21, 2013

Size distribution of global deposits redux

Same idea as last time, but working from an updated database of 439 gold deposits of one million ounces or more.

Size distribution of global gold deposits on log-log scale. Data from NRH.

The chart is a graph of the number of gold deposits larger than a certain size, with both axes plotted on a logarithmic scale. The point at the upper right tells us that there is one deposit (in this case, the Pebble Deposit) larger than 88.1 M oz (which is the size of the number 2 deposit, Grasberg). The point at the far left tells us there are 438 deposits larger than 1 M oz.

In an ideal scale-invariant system, the points would line up on a straight line. We don't expect to see this completely here for two reasons: 1) not all gold deposits have been discovered; and 2) we don't really have a consistent definition for a deposit. Some deposits are so large that in settings where concessions would be smaller, they might count as several separate deposits. One might argue that all of the gold deposited in a geological province during one ore-forming event should count as a single deposit. If so, then the number of deposits on our chart above would be much smaller, and their average size would potentially be larger.

There is a noticeable break in the slope at about the 2,000,000 ounce size--the number of smaller deposits falls off more rapidly than would be expected given the number of deposits greater than 2 M oz. This may be a reflection of a bias towards larger deposits. In financing discussions over the past few years it has been made clear to me that there is not a lot of interest in deposits smaller than 2 M oz.

We are grateful to Natural Resource Holdings for taking the time and effort to put this list together.
The line in the above plot would suggest that there are still at least 500 deposits of 1 million oz or more still to be discovered. This would suggest that we have discovered only about half of the total gold deposits > 1 M oz in size that there are to be discovered. I would contend that we have a lot more to discover.

As above, with last year's reported distribution in blue.

In the last year, NRH added 200 deposits to their list. These were not all newly discovered or bumped up to this level--clearly, the majority of these additions had been missed the first time. It is reasonable to assume that there are still some deposits in this category that have been missed in the 2012 report, so that the 2013 report will have more deposits, but probably not 200 more. What I don't think will change significantly is the above estimate--that our present discoveries are less than half of what gold remains to be discovered.

Monday, April 15, 2013

You can stop now, thank you


