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Is Your Gold Stock Truly Golden? Part 1: The Gold Stocks
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By this "golden" metaphor we mean the stocks that truly are worth being called the GOLD STOCKS. It's not that these companies are better managed than other (however that might be the case) or that they have more appealing P/E ratio than other stocks. The point is that some stocks offer you more exposure to the price of the yellow or white metal, than others. In this way some gold stocks might indeed be called more golden than other.
Exposure
OK, in order to find out how much exposure to the price of gold a particular stock has to offer and to compare it with other companies, we need to choose a way of measuring this exposure. One way to do it is to dig into company's profile, balance sheet, profit and loss statement, cash flow statement and other documents and try to establish how high fixed and variable costs are involved, company's policy, environmental laws and so on and so forth.
Sometimes, after you would go through all that papers the situation would change dramatically and/or the market would not agree with you and value the stock differently for a long time. This is one of the reasons that we will not use these methods in this essay. Instead we will adapt a different approach. Let's see what the market thinks about particular stock. If that's true that all information are discounted in the price then perhaps we can infer the information we need straight from the price itself. We can do it by doing some statistical calculations on the prices the market gives us. We decided that the best measure here would be the R–square coefficient.
From definition (source: Wikipedia): R-square is the coefficient of determination. It is the proportion of variability in a data set that is accounted for by a statistical model. In this case R-square tells us how much of particular gold stock's price is explained by the price of gold. In other words how much of the stock is exposed to gold or silver and how much to other factors. Generally, you probably want to invest in a company, whose price depends mainly on the price of gold, not on any other thing. You want a company that uses its resources to produce a profit from its precious metals operations, not from other activities. Of course it makes sense for some companies to seek alternative profit sources - for example there are times, when some of the America's biggest car producers would not be making a profit if it weren't for their financial operations... BUT After all, you wanted a GOLD stock, right? The closer R-square gets to 100%, the more exposure to gold a particular company has.
Before we proceed with our analysis of the R–square coefficient, we have to digress a bit.
You have to be very careful when applying statistical tools and measures to finance. Sometimes the assumptions used don’t correspond to financial reality. Even if they do or the error you would have made by using them is really insignificant, you can’t be sure that the model gives you what you are looking for. It is common that the author of a particular publication makes the calculations basing on some data, that is not really relevant, or the reasoning behind choosing a particular model is not explained to the reader. Not only is this confusing to the reader as it is more difficult to understand a particular topic if one does not know what author’s assumptions were, but it can also be misleading. For example reader might not be aware (Why would he/she? Not everyone needs to be on the cutting edge of statistics or mathematics) of the fact that there were actually many models to choose from. Choosing similar (but different) set of input data could lead to dramatic change in the results and therefore greatly influence their interpretation.
This article will feature some statistical measures and their basic transformations. We will try to explain our methodology as clear as possible in order to avoid any misunderstandings. Should you have any questions, you can reach us via the Contact Section on our website at (www.sunshineprofits.com)
The results of our calculations can be found on our Website in the Research section. The following part of this essay will be dedicated to the way you can measure both exposure and leverage and the reasoning behind it. Having a chart or graph in front of one’s eyes always helps in understanding a particular topic, as you can directly see what the topic is all about. In the following part of this essay we will give you a brief introduction to the way R–square coefficient is generally used and provide you with our interpretation.
First let us show you how tricky it can be to focus just on pure numbers. We have already stated that R–square tells you which stock is explained to the greater extent by the price of gold, so you should not have any trouble playing a little game with these coefficients. Please take a look at the charts below. They both represent the relations between two theoretical gold stocks and the price of gold. We have calculated the trend lines for linear models for both stocks (on the Second Gold Stock it’s the thin, dotted line) and respective R – square values. Without looking at the answer right now, try to answer the following question:
Which of these two precious metals stocks is better explained by the price of gold?
So? What is the correct answer?
If you’ve pointed the Second Gold Stock as the one that has been better explained by the price of gold, then congratulations, you were right. The R–square value is higher in case of stock A only, if we look only at the linear relations. If we allow ourselves to calculate this coefficient for different models it becomes clear that the amount of "noise" on the chart with Second Gold Stock is smaller than in case of the first company. It’s not linear but... Who said the relation between gold and gold stocks should be linear?! It does not have to be linear. Company’s profit does not relate so directly to the price of the metal itself. It could not, as so many factors are involved. Both variable and fixed costs differ from company do company, marketing strategies give different results, management has different pay schemes and so on. Those were only the differences in profits. Now take into account different dilution of shares and you get the idea why not always the assumption of linearity needs to be fulfilled.
Since R–square can be calculated for various models, we will present you with our interpretation (and results on our Website) of calculating these coefficients for best models. Before choosing your favorite gold/silver stocks and putting your money on the table please note that using R–squares obtained from different models may be sometimes misleading. R–square as such does tell you how well this particular model reflects used data. Higher R–square values may not always mean exactly that a particular gold/silver stock is more influenced by price of gold/silver (as it was in the case of presented theoretical gold stocks). If stock A has higher R–square than stock B, it may also mean that the model applied to stock A suits it better, than the model applied to stock B suited stock B. Keeping that in mind you need to be careful when comparing similar values of this coefficient. The table that, can be accessed on our website, was created using different models – for each stock we chose the best trend line and calculated R–square for this particular model. R–squares’ comparability is therefore limited. We take the view that you can compare stocks only if the difference between coefficients is not minor. For example we would not differentiate between stocks that have R–squares of 71% and 73%, but we certainly would if they equaled 30% and 80%.
Having said that let’s get to the merit of this article – we’ll going to tell, how can you tell, which stocks are most influenced by price of gold – in other words those that give you the biggest bang for the buck.
Below you will find chart which shows the relation between the price of gold and the Theoretical Gold Stock (TTGS). We have artificially created prices of this non-existing stock to better suit the needs of this essay. This stock performance if similar to what you may see among real gold stocks. Please refer to our website for more details. Right now please take a moment to study the chart below before you continue reading.
As you may see, the chart covers data for both gold and TTGS back to the beginning of this bull market, when gold traded below $300, silver was well below $5 and neither of them was a very popular investment to say the least. Basing on the price of gold and respective TTGS share price, we calculated and attached the trend lines which best represents the relation between both variables. Not all of this data is used for each trend line, as you may see on the chart, but we’ll get back to this later in this essay. Right now we would like you to focus on the shape of the trend lines. Please note that the dotted, thin line rises exactly at the same pace for every dollar move on the price of gold. That is pretty obvious statement, but for the record – that is a linear trend line. Trend lines don’t always have to be linear. For example the shorter, thicker line is in fact a logarithmic trend line. This type of trend line rises at higher pace at lower gold prices but then this pace declines along with higher prices of gold. We’ve taken into account several types of trend lines and found that these two are best to represent the data that goes back to January 2002 for the thin line and January 2006 for the thick line. We’ve chosen the first date as it represents the moment when both gold and the HUI index broke out of their long-term downtrends. One may argue whether time between 2000 and 2002 was still bear market or was it already bull market, but most people (of course except for the gold perma-bears, who will still deny the bull’s existence) agree that in 2002 we either began or already were in the first stage of the bull market in precious metals. So, the share price of TTGS for the entire bull market can be best described using the linear model. We can say that, because we’ve checked R–square values on the same data for different models. We’ve chosen from linear, logarithmic, power and exponential trend lines. All other models gave R–square values lower than the linear one. R–square of 93% means that in this model price of gold accounted for 93% of the TTGS prices’ move. This is a very good result in the long term – if would be looking for stocks with direct exposure to gold, and TTGS really existed, it would surely be worthy to be put into your portfolio.
In the search for coefficient that might better match current time, we separately calculated trend lines and R–square for shorter term – for the second stage of this bull market.
In the second stage new groups of investors enter the market. In this case that would be financial institutions recognizing the presence of the bull, as well as foreign investors, who see precious metals appreciate in their local currencies. Since we have different investors, we might infer that the average way of perceiving risk and leverage associated with mining stocks will also change accordingly. In our view, we are still in the early part of this phase, so it makes sense to develop unique tools and make specific predictions with this stage in mind. This is why our research towards estimating particular gold stocks’ exposure and leverage to precious metals will focus on this time frame.
For this, more detailed analysis we will use the data that goes back to the beginning of 2006. That was the time, when gold broke out of its trading range in Euro and stayed above previous resistance long enough to attract new capital. One might argue whether this is precise time when the second stage of this bull market began (some prefer to think of the breakout date as the exact beginning) or not, but choosing this date has also additional advantage to our analysis.
Beginning of 2006 is also the moment when prices of precious metals reached important levels: $550 for gold and $10 for silver. Once these milestone were achieved, the price accelerated and peaked a few months later. Since then we have endured a long consolidation phase, during which these important milestones have been tested and verified as new super-strong resistance levels. That gives us reasoning for making the assumption that we will not see these levels breached to the downside in the near future - by that we mean at least the second phase of this bull market. Of course everything is possible in these volatile markets, but some events such as this one are very unlikely.
The bold line on the above chart of TTGS represents the trend line, which is based on the data exclusively from the second stage of the bull market. This time the trend line is logarithmic and the R–square value equals 83.2%. It seems that the company might have lost some of its exposure to the price of gold, but it’s a tough call, as the difference between both R–square values is really not major. Nonetheless the true implications of these values would emerge as you would compare them with results obtained for other – real – gold stocks.
We already know what information we might infer from the value of R–square coefficient, now we have to be sure that we know what this coefficient does not tell us.
R-square does NOT tell you how much leverage to gold does a particular gold stock have. It informs you exactly what percent of past observations (stock prices) have been explained by the price of gold in particular model and that's it.
Leverage
If you want to know the real leverage you need to find out exactly how much percentage-wise (theoretically) should a particular gold stock move if the price of the underlying asset (gold) had risen by 1%. Choosing simply the coefficient that decides of the slope of the trend line (0.136 in the case of TTGS) as the measure of the leverage for the whole bull market can be misleading. That means that for every 100 dollar rise in the price of gold, price of TTGS will increase on average by $13.6. Unfortunately that is not comparable to coefficients of other stocks, as the nominal prices of stocks are different.
For example if you have stock A that trades at $100 with slope coefficient of 0.5 and stock B that trades at $1 with slope coefficient of 0.1, which one of them has higher leverage to the price of gold? Remember the slope coefficient tells you how much will the stock gain in dollar terms if the underlying metal rises by one dollar. The answer is stock B. That is the case, since when gold rises 1$ the price of A rises by 50 cents which is 0.5%, while the stock B would rise 10 cents which is 10% of the stock value. If you want to be leveraged, which stock would you prefer - the one that moves by half percent with every dollar move on the price of gold or the one which moves twenty times more - by 10% percent?
Of course the answer is: Stock B.
Therefore we have transformed the slope coefficient of TTGS’ second stage (since 2006) trend line so that it can be comparable to coefficients from other stocks. The result is about 1.22% for gold in the $800 - $1000 range. Please note the word "about" – we cannot say accurately, because is the selected (linear) trend line, the leverage is constant in dollar terms, but if we take into account the share price and the price of gold, we get beta, which takes diverse values for different gold prices. In fact, only the leverage calculated for power trend lines is constant in percentage terms. In the case of TTGS, the beta would be 1.45% with gold at $800 and 1.10% with gold at $1000. Calculating leverage for a specific gold price is not much of a disadvantage, since non-linear models have different slope coefficients for different gold prices, so the distinction between different prices and following different betas would have to be made anyway.
Astute reader might ask about the slope coefficient, as for example logarithmic function does not have one defined slope. This is why we take the slope at exact price of gold. For one, precise point we might calculate the slope coefficient for the tangent of the trend line. Please take look at the following chart – we used the same theoretical data as in earlier example:
Please note how the leverage changes along with the slope of the tangent, which of course changes along with the price of underlying metal (gold in this case). Although the price of the Second Stock is very well explained by the price of gold (R–square = 98,7% ), the leverage that the company has to offer is very discouraging at higher gold prices. With gold at $550 the price of this stock will rise on average by about half percent, when gold moves one percent. One could even say in a sarcastic tone, that it is the gold that has leverage to this stock, as it outperforms it without the inherent risk that the stocks carry.
What are the implications of this all this for gold stock investors and speculators? First consequence is quite obvious – you need to know the time frame for which you want to invest or speculate. In the above example if the price of gold were at $100 and you would want to bet your money on the move to the $200, then this stock would be great. On the other hand, if current gold price were $800 and your strategy was to hold this stock until gold reaches $1000 then you should probably consider other options.
Our research shows that when it comes to gold and gold stocks during the second phase of the bull market, they are best characterized by the linear, power and logarithmic trend lines. Like we stated earlier, power trend lines mean that the stock’s leverage to metal (gold) does not change percentage-wise. For other types of trend lines the leverage (beta) changes along with gold prices.
Here’s how you can deal with these conditions for different strategies:
For short term trades (for example for 50 dollar move on the price of gold that you expect to take place within next couple of weeks) you will not make a big mistake by choosing stocks basing on their current betas.
For medium term transactions you may also stick to current betas, as long as you make sure that the leverage will not change dramatically during your the time you want to hold your position. The table in the later part of this essay might prove helpful in this approach.
If you plan to hold your stocks for some time (and take advantage of large upleg in gold) good idea might be to take into account the leverage for the average price of the metal (for TTGS it is naturally gold). So, if you expect the price to go from $800 to $1200 you might want to check first the leverage for both $800 and $1200 and then the leverage for the average price – $1000 in this case. Small difference between the beginning and end values tell you that the leverage is pretty stable in this price range and that you really don’t need to make any adjustments – results are informative enough.
If there is a huge difference between leverages for a particular stock, you should calculate them manually. That means putting the initial and final price of gold for your transaction into the equation of appropriate trend line. Then you have to see how much percentage-wise your stock would rise and compare it with other stocks for the same rise in the price of gold. The one which rises most percentage-wise is obviously most leveraged. You can do these calculations roughly reading the values from the charts (not precise), you may find in the full version (will be posted soon) of this article or you can use the Tools section (which we recommend) on our website to get gold stock prices for any gold price.
Without having proper (sometimes non-linear) trend lines and without realizing that the leverage usually changes along with the price, your chance for choosing optimal stocks for your portfolio is limited.
This ends the main part of this essay, if you would like to see the result of our calculations for most of the popular gold stocks, please visit our website at (www.sunshineprofits.com) and browse the Research section.
Before you choose your favorite gold stocks and make a purchase or add to your positions we strongly encourage you to make additional analysis covering fundamental and technical aspects of these companies. Also please remember that it’s not a bad idea to diversify your holdings, meaning that it’s prudent to hold more than just one gold stock.
Although we strongly believe that the statistical measures used in this essay are very helpful tool in choosing stocks for one’s portfolio and we use it ourselves, we must inform you about possible risks involved in using statistics for making your trading decisions. Not all assumption made in statistical models are necessarily fulfilled in the capital markets.
If we used statistical tools directly to trading we would have to be sure that these unrealistic assumptions will not make us lose our money. They are of lesser meaning if we use this data to compare stocks between themselves. Even if each calculated coefficient is biased as a result of assuming normal distribution of returns, it does not pose a serious threat as long as you only use the results for comparison. If all results were biased from the same reason, most likely the relations between them would not be affected.
This is the shorter version of the essay. The full version (containing charts with trend lines for all popular gold stocks including: KGC, NEM, GG, ABX and more) will be posted soon on our website at (www.sunshineprofits.com) - just browse the Research section in a few days.
Want to know exactly how much will a particular stock have leverage at given silver or gold price? We designed a model that will provide you with that information. Visit our Tools section on (www.sunshineprofits.com) for details.
P. Radomski
March 21-st 2008
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All essays, research and information found above represent analyses and opinions of Mr.Radomski and Sunshine Profits' associates only. As such, it may prove wrong and be a subject to change without notice. Opinions and analyses were based on data available to authors of respective essays at the time of writing. Although the information provided above is based on careful research and sources that are believed to be accurate, Mr. Radomski and his associates do not guarantee the accuracy or thoroughness of the data or information reported. The opinions published above belong to Mr. Radomski or respective associates and are neither an offer nor a recommendation to purchase or sell securities. Mr. Radomski is not a Registered Securities Advisor. Mr. Radomski does not recommend services, products, business or investment in any company mentioned in any of his essays or reports. Materials published above have been prepared for your private use and their sole purpose is to educate readers about various investments.
By reading Mr. Radomski's essays or reports you fully agree that he will not be held responsible or liable for any decisions you make regarding any information provided in these essays or reports. Investing, trading and speculation in any financial markets may involve high risk of loss. We strongly advise that you consult a certified investment advisor and we encourage you to do your own research before making any investment decision. Mr. Radomski, Sunshine Profits' employees and affiliates as well as members of their families may have a short or long position in any securities, including those mentioned in any of the reports or essays, and may make additional purchases and/or sales of those securities without notice.
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