## Dust flux, Vostok ice core

Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

## Monday, March 3, 2014

Today we revisit a ratio I last looked at late last year--a simple comparison of the S&P500 vs gold, based on monthly closing prices, going back to the late '70s. In keeping with the theme of this blog, it has been presented in phase space. One way of studying complex systems is to attempt to illustrate the space of vectors that drive its evolution through time by observing the trajectory traced out in phase space. The time-delay phase space plot is one approach.

The S&P500-gold function is obtained by subtracting the gold price from the S&P 500 index price and dividing the result by the lesser of the gold price and the S&P 500 index. I did it in order to balance the size of the two bubblicious lobes that appear in the diagram.

The present value of the function is plotted on the vertical axis; whereas the 18-month lagged value plots on the horizontal axis. As the trajectory is placed out by the succession of points on the graph, when the trajectory is rising, the S&P 500 is outperforming gold; and when falling, gold is outperforming the S&P 500.

The downward bubble represents the rise and fall of the gold price in the late '70s to the early '80s, and lasted eight years. The upward bubble traces the rise and fall of the S&P 500 through the late '90s until 2009, and represents about 14 years. Together, the two bubbles constitute 22 years, which is more than half of the time represented by the plot.

Much of the time is spent close to the origin, meaning much of the time, gold and the S&P 500 index don't blow up with respect to one another. They still represent differences in performance of a few percentage points, and totalled over the 40 years of the graph, such differences will still be material. You might also notice that August 2011 plots just below and to the right of the origin, while December 2013 plots just above and to the left of the origin. Although not far apart on this graph, that did represent a pretty painful time for goldbugs.

Once a generation there appears to be a tremendous opportunity to make money. But the money is only made if you are able to keep it. It isn't enough to ride the bubble to the top--you need to take profits near the peak and there are opportunities during its deflation.

As we are again near the origin, there is no sign of a bubble in either of these parameters with respect to one another. If there is to be another vast bubble, we can't yet see which one is going to be inflated. But if we're taking turns, then it's gold's turn.