The Adjusted Gold/XAU Ratio as an Indicator of Forward Returns for Gold Stocks

Trend of the gold/XAU ratio from 1973 to 2011

Several articles have recently argued that, relative to gold bullion, gold mining shares are undervalued, based on the observation that the recent high level of the gold/XAU ratio (which I will refer to simply as “R”) has occurred only twice since 1973, namely in 1980 and 2008, and that soon after both of those peaks gold stocks gained significant value.

My analysis uses the daily XAU data from December 19, 1983 to September 8, 2011. Prior to this, the weekly Barron’s Gold Mining Index (BGMI) was used to derive a hypothetical value for XAU, assuming that the BGMI-to-XAU ratio was 7.0.

Figure 2 shows, from 1973 to 2011, the gold price, XAU, the gold/XAU ratio, and the best fit trendline of the ratio. The current value of R cannot be compared directly with a historic value of R, because R is trending itself. The trend observed reduces the value of gold stocks relative to the price of gold bullion over time, which thus increases R. In order for previous values of R to reflect gold stocks at the current value, one has to adjust for the trend of R by increasing the historic values of R. 

I adjusted R based on its trendline, with the most recent value of R remaining unchanged. See Appendix B for the equations of the trendline and the adjusted Gold/XAU ratio, R’.

The adjusted gold/XAU ratio (R’) is shown in figure 3. The linear regression line for R’ is a horizontal line and has the equation R’ = 6.054. Gold stocks are undervalued relative to gold when R’ is above and overvalued when R’ is below this line.

One can now directly compare the current value of the gold/XAU ratio with the adjusted values of the ratio in the past. 

Investment criteria and constraints for positive forward returns for gold stocks

A comprehensive analysis of the role of the gold/XAU ratio relative to returns for gold stocks was presented in 1999 by John Hussman in Going for the Gold. In this article, he presented the following criteria for positive forward returns:  

1. The rate of inflation must be higher than six months earlier.
2. Treasury bond yields must be lower than six months earlier.
3. The NAPM Purchasing Managers Index (PMI) must be below 50.
4. The gold/XAU ratio has to be above 4.0.

Hussman did not stipulate a required minimum change for the inflation rate, required change of the bond yields or minimum length of an investment period.

My analysis showed that XAU, as a proxy for gold stocks, produced good returns without any major losses after a minimum investment period of 240 days following a date when:

1. The adjusted gold/XAU ratio R’ was equal to or above 6.20.
2. The 10-year Treasury yield was lower by at least 0.50% than six months earlier.
3. The six-month rate of inflation was at least 0.50% higher than six months earlier.

I found that including the Purchasing Managers Index as an additional constraint provided no benefit; it merely reduced the number of investment periods with positive returns.

The criteria values and constraints that have historically produced very good returns for XAU at the end of the indicated minimum investment period are listed in table 1 below. Investments in XAU were initiated when the value of the adjusted gold/XAU ratio was at least equal to one of the criteria values listed, provided that all applicable constraints that go with it were also satisfied at the time.

An investment in XAU never lost money when R’ was equal to or higher than 7.5 and the minimum investment period was 150 days.

As R’ increases, the constraints become less onerous, and the minimum length of the investment period shortens. Criteria values of R’ will be higher in the future when the model has to be re-calibrated because of the rising trend of the gold/XAU ratio.

The minimum length of the investment period does not become shorter even if the specified criterion value and applicable constraints are no longer present later in this period. The minimum length of an investment period may become longer than the stipulated minimum length. For example, for the criterion R' ≥ 7.5 the minimum specified length of the investment period is 150 days. This period is extended if R’ is greater than 7.5 at the end of 150 days until R’ becomes less than 7.50. Also, if during the initial 150 days R’ becomes less than 7.50 and subsequently within the initial 150-day period becomes greater than 7.50, a new investment period of 150 days is initiated from the time that R’ exceeded 7.50. This period may be extended again in the same way as the initial investment period was, and so on. The effect of this is that investment periods may become considerably longer than the minimum stipulated length.

The historical returns for the criteria values of table 1 are summarized in table 2.

Total gain is the sum of the gains and losses for all investment periods. Gain or loss is the difference of the value of XAU at the end and beginning of each investment period.

The recent gold/XAU ratio and historic returns for XAU

Since the end of June 2011, the gold/XAU ratio has been higher than 7.50.

At that time Bob Kargenian, in his article Investing with a View of Significant Inflation, wrote, “A long-term BUY signal for gold stocks took place June 24, 2011, for only the 14th time since 1976. This signal is based on our version of a variation of the Gold/XAU Ratio, known as the K-Ratio, which uses the Barron’s Gold Mining Index. Relative to physical gold, as represented by the ratio, gold stocks are at the second-cheapest level in nearly 35 years.”

As discussed earlier, the current gold/XAU and gold/BGMI ratios do not reflect the same value for gold stocks in the past as they do now. Using the adjusted gold/XAU ratio, one finds seven previous periods since 1973 when gold stocks were as cheap relative to gold as they were at the end of June 2011. The average return for an investment in XAU over those periods was about 4.7% per month, and one would have been invested intermittently for a total of 82 months from February 1979 to September 2011, or 21.1% of the total time. These figures are also listed in table 2.

The present gold/XAU ratio and historic returns for XAU

Over the last month, the average value of the gold/XAU ratio was 8.37.

In the last 39 years, there have been only four instances when an adjusted ratio of 8.30 with no yield or inflation constraint has occurred (September 1979, June 1982, October 2008, and the beginning of August 2011). Below is a list of returns for the various investment periods following the first three dates.

It is interesting that the average returns for the various investment periods were similar and did not increase for longer minimum investment periods as one might have expected.

If history repeats itself, then gold stocks should grow by about 50% over the next eight months, but one should not hold on to those stocks afterwards, as the likelihood of significant increases at a later date is low.

Appendix A

The adjusted gold/BGMI ratio from 1940 to 2011

Figure 4 shows the trend-adjusted gold/BGMI ratio. The adjustment was made similar to what I described earlier for the gold/XAU ratio but using the trendlines shown in figure 1. Note that the trendline of the adjusted ratio has the same value as the trendline line shown in figure 3.  One can now directly compare the current ratio with the adjusted ratios back to 1940.

There were numerous instances from 1940 to 1965 when the ratio was as high as it is now.  Table A1 summarizes the returns and other investment details for the criteria values listed in table 1. No constraints were applied, but the minimum investment periods applicable were used. No negative returns were observed.

Appendix B

The trendline which fits the gold/XAU ratio best is a power curve having the equation
 
R = 6.83E-12 x^2.8869 + 3.6413

where x is the number of trading days from January 3, 1973 onwards.

The equation for the adjusted Gold/XAU ratio, R’, is

R’ = R + 6.83E-12 (n^2.8869 – x^2.8869)

where,

R = un-adjusted Gold/XAU ratio,  
n = total number of trading days from January 3, 1973 to September 8, 2011 and
x = the number of trading days from January 3, 1973 onwards to the date where R is to be adjusted.

Read more articles by Georg Vrba, P.E.