The Adjusted Gold/XAU Ratio as an Indicator of Forward Returns for Gold Stocks
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While the recent bull market took gold prices to new highs, the prices of goldmining companies lagged. Some claim those companies are now drastically undervalued, and we can investigate that claim by examining the relationship between gold and goldmining prices.
The prices of gold and the shares of companies who mine it should track one another over time. One should therefore be able to predict the returns for XAU, a capitalizationweighted index consisting of 16 preciousmetal mining companies, using a trendadjusted gold/XAU ratio and the corresponding historic returns for XAU that followed the ratio. Such an analysis shows that XAU is now significantly undervalued and should be about 50% higher over the next eight months.
Trend of the gold stocks relative to gold
The longest data set available as a proxy for gold stocks is the weekly Barron’s Gold Mining Index (BGMI), which dates back to 1939. Figure 1 shows this series along with the gold price, and the ratio of the two. The gold/BGMI ratio was scaled by a factor of 7.0 (the 198487 average of the BGMItoXAU ratio) to make it a proxy for the gold/XAU ratio before December 1983, the inception date of the XAU series.
From 1940 to 1968, when the price of gold was fixed at $35 per ounce, the trendline of the gold/BGMI ratio sloped downwards, indicating that gold stocks gained in value relative to gold over this time. Afterwards, starting in 1971, the gold price floated, and it began increasing as soon as the dollar was no longer directly convertible into gold. From then on, the trendline of this ratio sloped upwards, indicating that gold stocks lost value relative to gold over time.
In order to make the current ratio directly comparable to the historic ratios, one has to adjust for these trends by increasing the ratio’s values from 1968 to 2011, and decreasing them prior to 1968. See Appendix A for the trendadjusted gold/BGMI ratio and results derived from it for the period 1940 to 1965.
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 BGMItoXAU 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:
 The rate of inflation must be higher than six months earlier.
 Treasury bond yields must be lower than six months earlier.
 The NAPM Purchasing Managers Index (PMI) must be below 50.
 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:
 The adjusted gold/XAU ratio R’ was equal to or above 6.20.
 The 10year Treasury yield was lower by at least 0.50% than six months earlier.
 The sixmonth 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.
Table 1 Criteria Values and Constraints 

Criterion value: adjusted gold/XAU ratio 
Yield and Inflation Constraints 
minimum length of investment period (days) 
R' ≥ 6.2 
The yield of the 10yr TNote lower by at least 0.50% from 6 months ago. 
240 
The 6mo inflation rate higher by at least 0.50% from 6 months ago. 

R' ≥ 6.7 
The yield of the 10yr TNote lower by at least 0.25% from 6 months ago. 
240 
The 6mo inflation rate higher by at least 0.25% from 6 months ago. 

R' ≥ 7.2 
The yield of the 10yr TNote not higher than 0.50% from 6 months ago. 
240 
The 6mo inflation rate not lower than 0.50% from 6 months ago 

R' ≥ 7.5 
none 
150 
R' ≥ 7.8 
none 
150 
R' ≥ 8.1 
none 
150 
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 recalibrated 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 150day 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.
Table 2 Summary of Returns and Investment Details 1973  2011 

adjusted gold/XAU ratio 
no. of periods with neg. returns 
avg. return 
max. return all periods 
min. return all periods 
total time in market (mo.) 
% time in market 
total gain ($) 
avg. gain per month ($) 
R' ≥ 6.2 
1 of 10 
4.47% 
17.51% 
0.41% 
91.6 
24.4% 
324.1 
$ 3.54 
R' ≥ 6.7 
1 of 9 
5.12% 
14.52% 
0.45% 
101.3 
26.3% 
362.1 
$ 3.57 
R' ≥ 7.2 
0 of 9 
6.20% 
15.61% 
0.59% 
89.1 
23.0% 
410.9 
$ 4.61 
R' ≥ 7.5 
0 of 7 
4.70% 
8.30% 
2.10% 
82.5 
21.1% 
322.0 
$ 3.90 
R' ≥ 7.8 
0 of 5 
6.66% 
12.26% 
1.19% 
50.8 
13.2% 
259.1 
$ 5.10 
R' ≥ 8.1 
0 of 5 
10.08% 
20.71% 
3.82% 
41.2 
10.7% 
298.9 
$ 7.25 
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 longterm 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 KRatio, which uses the Barron’s Gold Mining Index. Relative to physical gold, as represented by the ratio, gold stocks are at the secondcheapest 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.
minimum length of investment period 
Investment Period from  to 
XAU value at start $ 
XAU value at end $ 
no. of months in each period 
absolute return for each period 
gain (loss) over period $ 
avg. return all periods 

90 days 
9/14/79 
10/6/80 
59.5 
178.0 
12.7 
199.0% 
118.5 

6/18/82 
12/5/82 
50.1 
111.7 
5.6 
122.9% 
61.6 
121.7% 

10/6/08 
6/7/09 
105.2 
150.7 
8.0 
43.2% 
45.4 


180 days 
9/14/79 
1/4/81 
59.5 
134.4 
15.7 
125.8% 
74.9 

6/18/82 
3/5/83 
50.1 
125.6 
8.5 
150.5% 
75.4 
111.4% 

10/6/08 
9/5/09 
105.2 
166.3 
11.0 
58.0% 
61.0 


270 days 
9/14/79 
4/4/81 
59.5 
116.9 
18.6 
96.4% 
57.4 

6/18/82 
6/3/83 
50.1 
141.9 
11.5 
183.0% 
91.7 
117.4% 

10/6/08 
12/4/09 
105.2 
182.0 
13.9 
72.9% 
76.7 


360 days 
9/14/79 
7/3/81 
59.5 
97.6 
21.6 
64.0% 
38.1 

6/18/82 
9/1/83 
50.1 
135.3 
14.4 
169.9% 
85.2 
97.9% 

10/6/08 
3/4/10 
105.2 
168.0 
16.9 
59.7% 
62.8 

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 trendadjusted 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.
Table A1 Summary of Returns and Investment Details 1940  1965 

adjusted Gold/XAU ratio 
no. of periods with neg. returns 
monthly avg. return all periods 
monthly max. return all periods 
monthly min. return all periods 
total time in market (month) 
% time in market 
total gain over all periods ($) 
avg. gain per month ($) 
R' ≥ 6.2 
0 of 3 
1.36% 
1.50% 
1.24% 
267.1 
88.45% 
157.6 
$ 0.59 
R' ≥ 6.7 
0 of 7 
1.07% 
1.87% 
0.48% 
242.8 
82.92% 
60.6 
$ 0.25 
R' ≥ 7.2 
0 of 5 
1.09% 
1.80% 
0.69% 
183.8 
70.45% 
44.1 
$ 0.24 
R' ≥ 7.5 
0 of 8 
1.83% 
4.22% 
0.59% 
140.7 
54.83% 
60.1 
$ 0.43 
R' ≥ 7.8 
0 of 6 
1.66% 
2.22% 
0.70% 
99.8 
42.07% 
44.3 
$ 0.44 
R' ≥ 8.1 
0 of 7 
2.32% 
4.80% 
1.50% 
80.6 
34.93% 
46.9 
$ 0.58 
R' ≥ 8.3 
0 of 6 
1.92% 
3.71% 
0.75% 
69.8 
30.28% 
32.8 
$ 0.47 
Appendix B
The trendline which fits the gold/XAU ratio best is a power curve having the equation
R = 6.83E12 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 + 6.83E12 (n^2.8869 – x^2.8869)
where,
R = unadjusted 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.