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Investors continue to seek exposure to gold in the hopes the prices will keep rising. Gold has pushed past the $1,450 per troy oz. mark recently and last traded at around $1,472. Likewise, SPDR Gold Shares (GLD) has hit an all time high of $144 per share. Investors who think gold prices will continue to rise can make a bet on GLD or even PowerShares DB Gold Double Long ETN (DGP), which provides a 2x return. However, is there a way to find additional leverage?

Clearly, one can create additional leverage by using debt and purchasing DGP. Many investors have also gone long various gold mining stocks to create exposure as well. Gold mining stocks should continue to rise in price as gold prices rise. However, gold mining stocks often carry exposure to copper, silver and other metals. Furthermore, more marginal players have greater exposure to gold price movements than their low cost competitors. It is difficult and tedious to dig through company financials and operating statistics to determine a company's gold exposure. Fortunately, there is a better way.

For investors who ascribe to modern portfolio theory, it is very easy to simply adapt the concept of beta and apply it to gold prices to determine the "gold beta" of a given security. The calculation process would be exactly the same, but substituting gold returns for market returns when performing the covariance and variance analysis. Beta is the ratio of the covariance of market returns to a given security's returns to the variance of the market. Mathematically, this breaks down to a product of two factors:

  1. the correlation of those returns
  2. the ratio the volatility of the security to the volatility of the market

A gold beta could be constructed using GLD as a substitute for the market. The following stocks and ETFs will be used to calculate the gold beta.

Ticker Name Market Capitalization or Assets ($ billions)
GLD SPDR Gold Trust 51.9
XOM Exxon Mobil Corporation 425.2
WMT Wal-Mart Stores, Inc. 185.0
SPY SPDR S&P 500 Trust 95.3
MCD McDonald's Corporation 79.3
ABX Barrick Gold Corporation 53.7
GG Goldcorp Incorporated 42.5
NEM Newmont Mining Corporation (Holding Company) 28.4
AU AngloGold Ashanti Ltd. 19.8
KGC Kinross Gold Corporation 18.6
IVN Ivanhoe Mines Ltd 18.3
GFI Gold Fields Ltd. 13.1
SLV iShares Silver Trust 11.5
DIA SPDR Dow Jones Industrial Average 9.9
AUY Yamana Gold, Inc. 9.6
EGO Eldorado Gold Corp 9.4
IAG Iamgold Corporation 8.6
GOLD Randgold Resources Limited 7.8
GDX Market Vectors Gold Miners ETF 6.9
ANV Allied Nevada Gold Corp 3.5
CDE Coeur d'Alene Mines Corporation 3.2
RGLD Royal Gold, Inc. 2.9
HL Hecla Mining Company 2.7
OTCPK:SEMFF Semafo Inc. 2.5
GDXJ Market Vectors Junior Gold Miners ETF 2.3
OTC:EGFDF EUROPEAN GOLDFIELDS LIMITED 2.3
USO United States Oil Fund ETF 1.9
GRS Gammon Gold Inc. 1.4
DGP Deutsche Bank AG DB Gold Double 0.5
JAG Jaguar Mining Inc 0.5
DZZ PowerShares DB Gold Double Short ETN 0.1

Data provided by Zacks.com services and Yahoo!Finance (for ETFs)

The following table shows the gold beta calculation as well as the corresponding correlation and volatilities.

12 Month Gold Beta
Ticker Correlation 12 months Volatility Ratio of Volatility to GLD Volatility Implied Gold Beta
GLD 100.0% 3.7% 100% 1.0
CDE 64.3% 13.5% 365% 2.3
HL 55.5% 15.3% 415% 2.3
DGP 100.0% 7.5% 202% 2.0
ANV 58.7% 12.2% 331% 1.9
GG 83.8% 8.5% 230% 1.9
SEMFF.PK 53.7% 12.5% 338% 1.8
GDXJ 78.3% 8.3% 226% 1.8
SLV 78.4% 8.2% 223% 1.7
AUY 77.9% 8.1% 219% 1.7
EGO 64.4% 9.7% 262% 1.7
ABX 81.9% 7.4% 201% 1.6
GDX 92.4% 6.5% 176% 1.6
AU 88.5% 6.6% 180% 1.6
RGLD 83.4% 6.9% 188% 1.6
GFI 74.4% 6.3% 172% 1.3
NEM 63.7% 7.2% 194% 1.2
GOLD 50.4% 6.8% 184% 0.9
KGC 49.2% 6.7% 182% 0.9
GRS 22.8% 13.5% 365% 0.8
IAG 34.3% 8.7% 237% 0.8
JAG 12.4% 11.2% 304% 0.4
MCD 23.5% 3.4% 92% 0.2
USO -10.9% 7.5% 204% -0.2
SPY -20.6% 5.0% 135% -0.3
DIA -27.4% 4.4% 120% -0.3
EGFDF.PK -36.2% 3.9% 105% -0.4
XOM -29.7% 5.6% 152% -0.5
WMT -53.6% 4.2% 115% -0.6
DZZ -100.0% 7.5% 202% -2.0
IVN -51.3% 14.7% 398% -2.0

Source: Yahoo!Finance for monthly split and dividend adjusted closing prices.

As one would expect, the leverage ETFs matched gold betas exactly to their expectations. The junior miners ETF also showed a 1.8 12 month beta calculation, suggesting that it is close to the 2x leverage ETF. Junior miners Coeur d'Alene Mines Corp. (CDE) and Hecla Mining Co. (HL) offer betas over 2, providing potentially additional leverage beyond a DGP. SPY and DIA show limited correlation to GLD as expected and have a -0.3 gold beta. The interesting examples are Ivanhoe Mines Ltd. and EUROPEAN GOLDFIELDS (OTC:EGFDF), which showed a negative correlation to GLD over the past 12 months. The next look will be at a 36 month gold beta and a 60 month gold beta to check the stability of the betas.

Gold Beta over Different Time Frames
Ticker Market Capitalization Implied Gold Beta (12 month) Implied Gold Beta (36 month) Implied Gold Beta (60 month)
GLD 51.9 1.0 1.0 1.0
GDXJ 2.3 1.8 NA NA
AUY 9.6 1.7 2.4 2.4
IAG 8.6 0.8 2.4 2.1
HL 2.7 2.3 2.4 1.8
GRS 1.4 0.8 2.3 2.1
GG 42.5 1.9 2.2 2.1
JAG 0.5 0.4 2.1 NA
ABX 53.7 1.6 2.1 1.9
DGP 0.5 2.0 2.0 NA
GDX 6.9 1.6 2.0 NA
SEMFF.PK 2.5 1.8 1.9 1.8
KGC 18.6 0.9 1.8 1.9
CDE 3.2 2.3 1.8 1.7
GFI 13.1 1.3 1.8 1.5
EGO 9.4 1.7 1.7 1.7
NEM 28.4 1.2 1.7 1.5
RGLD 2.9 1.6 1.7 1.5
GOLD 7.8 0.9 1.6 1.7
ANV 3.5 1.9 1.6 NA
AU 19.8 1.6 1.6 1.3
SLV 11.5 1.7 1.4 NA
USO 1.9 -0.2 0.4 NA
MCD 79.3 0.2 0.3 0.2
XOM 425.2 -0.5 0.3 0.2
IVN 18.3 -2.0 0.1 0.3
SPY 95.3 -0.3 0.1 0.0
DIA 9.9 -0.3 0.1 0.0
WMT 185.0 -0.6 0.0 -0.1
EGFDF.PK 2.3 -0.4 -0.3 -0.2
DZZ 0.1 -2.0 -2.0 NA

Source: Yahoo!Finance for monthly split and dividend adjusted closing prices. Market capitalization data provided by Zacks.com services

Again, it shows that SPY and DIA have limited gold betas over longer periods of time. It also showed that IVN had an improved beta that was positive, which suggests a positive correlation to gold prices as one would expect for a gold mining stock. McDonald's (MCD), Exxon (XOM), and Wal-Mart (WMT), a couple large capitalization stocks, had limited exposure. It is also key to note that the 36 month and 60 month betas were more aligned. Twelve data points is often not statistically valid. The other observation is that the smaller mining companies-- the junior companies-- were typically the only ones that had gold betas over 2. However, there was a reasonable dispersion of companies of different size across the spectrum of gold betas. Also, as one would expect, most companies offered more than just 1x leverage to GLD.

Breaking down the 36 month beta even more shows that gold mining stock correlations ranged from -29% for EGFDF.PK to 87% for ABX and 85% for GFI. However, there were also much lower correlations including 4% for IVN and 51% for JAG.

Conclusion

The final test is to look at the relationship between gold beta and historical performance. Ideally, there would be a strong correlation between the two; however, a positive correlation would be important. Since these are individual stocks, there are a host of issues that impact both the volatility and returns of the stocks ranging from management decisions (hedging, capital deployment) to specific risks. A company could have poor performance simply due to significant operational issues.

Gold Beta and Returns
Ticker 36 Month Beta 36 month Correlation 1 Year Return 2 Year Return 3 Year Return 4 Year Return
GLD 1.0 100% 24.5% 64.6% 65.8% 120.7%
GDXJ NA NA 56.4% NA NA NA
AUY 2.4 81% 23.4% 70.1% 6.2% -2.2%
IAG 2.4 77% 29.8% 191.7% 293.5% 192.4%
HL 2.4 57% 63.5% 295.1% -4.9% 10.8%
GRS 2.3 59% 41.5% 55.6% 37.4% -35.0%
GG 2.2 79% 26.6% 99.9% 54.9% 128.7%
JAG 2.1 51% -49.7% -5.6% -39.5% -23.2%
ABX 2.1 87% 26.4% 91.0% 45.6% 101.9%
DGP 2.0 100% 50.0% 147.3% 119.4% NA
GDX 2.0 87% 27.5% 96.1% 48.0% 65.9%
SEMFF.PK

1.9 66% 42.9% 403.3% 580.9% 382.3%
KGC 1.8 73% -11.9% 8.7% -10.8% 26.8%
CDE 1.8 53% 104.7% 165.9% 19.5% -10.3%
GFI 1.8 85% 39.8% 83.3% 45.0% 10.0%
EGO 1.7 68% 18.1% 125.6% 167.0% 205.9%
NEM 1.7 82% 4.4% 46.7% 34.9% 44.3%
RGLD 1.7 74% 6.3% 51.6% 95.3% 90.1%
GOLD 1.6 73% 3.5% 80.6% 92.6% 267.0%
ANV 1.6 45% 121.9% 651.1% 717.7% NA
AU 1.6 73% 22.6% 67.4% 51.7% 16.8%
SLV 1.4 78% 118.3% 226.5% 138.4% 198.8%
IVN 0.1 4% 77.7% 338.5% 192.5% 126.1%
EGFDF.PK

-0.3 -29% -6.1% -6.8% -22.7% -17.6%
DZZ -2.0 -100% -39.1% -69.7% -75.5% NA

Source: Yahoo!Finance

The above table shows that there is indeed a positive correlation between the gold beta and the returns. It is also a stronger correlation than looking at just the correlation coefficient. This list represents a good starting point for additional research to create leverage to gold prices. However, since very few companies offer a gold beta substantially higher than 2, DGP represents a good opportunity. Investors seeking even more leveraged returns would have to look at the junior miners, making GDXJ a good possible option. For investors, seeking to maximize exposure with large capitalization miners, ABX and GG appear to be best choices.

Clearly, when investing in a stock it is critical to look at fundamentals and overall strategy. This analytical review provides a good starting point, but makes no comment as to whether any stock is overvalued or undervalued. It is quite clear that some stocks have had tremendous 4 year returns. These were probably extremely marginal players (i.e., with a high percentage of reserves at high recovery costs) that have substantially moved into the money as the gold price climbed. A stock that has underperformed might have been due to management decisions related to hedging sales too early.

Disclaimer: This article is for informational and educational purposes only and shall not be construed to constitute investment advice. Nothing contained herein shall constitute a solicitation, recommendation or endorsement to buy or sell any security.

Source: Using Gold Betas to Optimize Exposure to Gold Price Movements