Of Parabolas and the Markets

I have been noticing (and you may too) more discussions about the possibility that the S&P 500 has gone parabolic, implying that a severe correction is in the offing. Additionally, the same line of reasoning has been applied (more so in the blogosphere) to the price of gold, supporting extremely bearish calls on the yellow metal. I am here to say that both views are wrong, and that neither market has been or is in a 'parabolic' ascent.

Before I get into the why, let me take a step back and provide some details into what a parabolic price move is. If you remember from high school calculus, a parabola is a two-dimensional curve that approximately looks like the letter 'U'. Mathematically, the parabola can be expressed in one of its simplest forms by the function Y= x^2. A typical parabola looks similar to the shape below.

Parabola's essentially represent a system that change at a geometric rate.

Turning back to investments, when an analyst, market pundit, etc. say that a stock or some investment has gone parabolic, they are usually describing a severe upward move where not only the slope is strongly positive but the rate of change in the rate of change is or has been accelerating. Usually, a parabolic move is a sign of top and can be a precursor to a severe correction. In essence, a parabolic move is an exhaustive move in a stock that is characterized by a swarm of buyers that overwhelms sellers. 

This last point does not characterized either the price move of the S&P 500 or that of gold. What many are missing is that a true unstable parabolic move is time dependent. Unsustainable parabolic moves that are followed by severe corrections should occur within a short time frame. Given enough time, a great deal of investments and stock prices will approximate parabolas, and can look unsustainable. Why? Well, stock prices will generally (or at least should) represent the compounding of the underlying earnings over time. Given enough time, the compounding will become more parabolic. As for gold, which does not have any earnings, gold has been following the compounding growth in the supply of money since Fed embarked on its easy money policy since the crash of 2000. Parabolas on long-term charts are the normative, not the exception.

One way I adjust for the compounding effects of time is by examining the chart on a log scale, or by my preference the natural log. By making this adjustment, what once appeared as an unsustainable parabola will be shown as the result of compounding over time. This adjustment will also confirm true parabolic moves in investments. For instance, I present three examples below. 

Stocks with parabolic moves
Dell


Qualcomm


Excel Maritime


Notice in the three above chart, the log price of the three stocks turned significantly upward and in some cases went vertical just before collapsing. Compares these charts to that of the S&P 500 and gold charts  shown below.

S&P 500


Gold


Neither the trend in the S&P 500 nor the price of gold is showing any signs of an unsustainable parabolic move on the log scale. For another illustration, I thought it would be interesting to look at a longer-term chart on gold. The below chart shows the price of gold since 1968 and compares the log price of gold versus the actual price.

Gold Since 1968






The illustrative point here is that the upward move in the price gold from late-1979 to 1980 can be described an unsustainable parabolic move, as the price and the log-scale price both were accelerating. Compare this to any period since 2000. We just have not seen any vertical move on the log scale at point in the price of gold since then.