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 $144 per share. Investors who think gold prices will continue to rise can make a bet on GLD or even PowerShares DB Gold Double Long ETN (DGP), which provides a 2x return. However, is there a way to find additional leverage?
Clearly, one can create additional leverage by using debt and purchasing DGP. Many investors have also gone long various gold mining stocks to create exposure as well. Gold mining stocks should continue to rise in price as gold prices rise. However, gold mining stocks often carry exposure to copper, silver and other metals. Furthermore, more marginal players have greater exposure to gold price movements than their low cost competitors. It is difficult and tedious to dig through company financials and operating statistics to determine a company's gold exposure. Fortunately, there is a better way.
For investors who ascribe to modern portfolio theory, it is very easy to simply adapt the concept of beta and apply it to gold prices to determine the "gold beta" of a given security. The calculation process would be exactly the same, but substituting gold returns for market returns when performing the covariance and variance analysis. Beta is the ratio of the covariance of market returns to a given security's returns to the variance of the market. Mathematically, this breaks down to a product of two factors:
- the correlation of those returns
- the ratio the volatility of the security to the volatility of the market
A gold beta could be constructed using GLD as a substitute for the market. The following stocks and ETFs will be used to calculate the gold beta.
| Ticker | Name | Market Capitalization or Assets ($ 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 |
| SEMFF.PK | Semafo Inc. | 2.5 |
| GDXJ | Market Vectors Junior Gold Miners ETF | 2.3 |
| EGFDF.PK | 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.
| 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 (EGFDF.PK), 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.
| 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.
| 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.
Disclosure: I am long SPY.
