Looking for Leverage
I would like to make explicit a few points that Zelotes (a.k.a. Adam Hamilton) and I touched on in the recent essay entitled "Mining the XAU for Gold". In order to do this I must first emphasize a trend determined from the examination of about 18 years of XAU and spot gold data.
Consider the graph shown below. The first data point in the graph below was generated as follows. Any price of gold greater than or equal to 250 and strictly less than 255 was added to the total and then the total was normalized by the number of data points. The XAU values associated with these spot prices were also added and normalized. Thus, we have effectively looked at a "$5 bin" of gold prices to generate one (POG, XAU) data point. Note that individual contributions to this single data point may be separated by years in the overall data set. This procedure was repeated for increasing $5 intervals until the data was exhausted. Also plotted on the graph is the linear trend line (LTL) for the XAU vs. POG, and a line that represents one fourth of the POG. Notice that the XAU = ¼ POG is a very good approximation to the linear trend line of the entire XAU vs. POG data set. For simplicity, we will use the "¼ rule" rather than the trend line itself in the remaining text. I will not reiterate the approximations inherent in the utility of a linear trend line, as I am sure we are all intimately aware of their strengths and weaknesses.
Now that we have established that XAU = ¼ POG is a good approximation in the sense of averages, we may go on to make the following observations.
First, when someone says that the historical spread = POG – XAU is 220, what are they really saying? Implicit in this statement is some type of averaging. Thus, it is reasonable to apply the rule that we have previously established. So substituting, ¼ POG for XAU above gives the spread = POG – ¼ POG = ¾ POG. Solving for the POG with a value of 220 for the spread gives a POG of about $293. Thus, all they were really saying was that the average POG has been about $293! More generally, when anyone uses the spread in an averaging sense, they are doing nothing more than looking at a scaled POG, as the spread in an average sense is simply ¾ POG. That is, the XAU and the POG are not independent variables in the "average sense" introduced in this discussion.
Why is this important? Because the "220 rule" for the spread as often utilized is misleading. Consider the POG at $273.30 and the XAU at 58.78, which happen to be Friday's closing numbers. If we compute the spread = 273.3 – 58.78 or about 214.5, one might mistakenly presume that this meant that the XAU was overvalued with the 220 rule (values less than 220 would imply XAU overvalued and values of the spread over 220 would mean the XAU was undervalued). But using the "¼ rule", we find that ¼ POG is about 68.3 so that since the XAU is at 58.78 (considerably less than 68.3), the XAU is currently undervalued on an historical basis.
The other point to notice about the average historical (and approximate) relationship between the XAU and the POG given by XAU = ¼ POG is illustrated by the answer to the following question. What happens to the XAU if the POG doubles? The XAU doubles! So what happened to the leverage (i.e. majors outperforming the spot by 2 to 3 and juniors outperforming 5 to 7, etc.)? Barring a thorough examination of the individual issues in the XAU, the answer seems obvious. While stocks like NEM, HM and AEM will significantly outperform the spot, some stocks in the XAU must necessarily under perform the spot if 18 years of historical trend is to be followed. Could these under performers be the highly hedged companies such as ABX and AU? Will PD (Phelps Dodge) also stand out as a significant under performer? Last week's performance of these shares adds weight to this consideration. We will see. But, if historical trend holds and gold is going up from here, one DOES NOT want to emulate the performance of the XAU in his mining portfolio if he is "looking for leverage". One might well consider some combination of the unhedged XAU shares such as NEM, AEM and HM together with some South African shares such as DROOY, GOLD, and HGMCY.
In closing, I would like to make a clarification about the synthetic data series given by (XAU-IXAU)/IXAU introduced in the referenced paper. Substituting as in that paper, IXAU = ¼ POG, in the above statement, we have (4 XAU/POG –1). Thus, the series introduced was simply a scaled and translated XAU/POG ratio. Its value was in being able to quantify easily how the XAU was currently valued in percentage terms, relative to historical norms. As in the referenced paper, we emphasize that due credit must be given to past authors who have analyzed this XAU/POG ratio.
Finally in the referenced paper … I saw Adam's words about sending PMtrader some love at the same time the rest of you did … you gotta love Adam …
"PMtrader"
PMtrader@yahoo.com
11 June 2001
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