Does you silver stock truly shine? Part 2: The Silver Stocks

By this metaphor we mean the stocks that truly are worthy being called the THE SILVER 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 white metal, than others. In this way some silver stocks might indeed be shining more than other silver securities.

As you may see in the title, this is the second part of the article. If you are familiar with the first part in which we analyzed gold stocks’ exposure and leverage to gold, we suggest you briefly run over topics already covered and focus on the parts dedicated especially to silver stocks. If this is your first contact with our essays devoted to measuring exposure and leverage then we advise you read all paragraphs before interpreting the results of our analysis.

Most of the stocks analyzed below are components of the GDX EFT. In fact out of covered silver stocks, only Silvercorp Metals Inc. is not included in this fund.

Exposure

OK, in order to find out how much exposure to the price of gold or silver 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 stock's price is explained by the price of gold or silver. 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 silver or 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/SILVER stock, right? The closer R-square gets to 100%, the more exposure to gold/silver 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

Before presenting the results of our calculations we would like to tell you a little more about the way we constructed our models. 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 reasoning behind our methodology.

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 or silver, 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/silver and gold/silver stocks should be linear?! It does not have to be linear. Company’s profit does not relate so directly to the price of 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 results 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 we will present in this essay 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 you which stocks are most influenced by price of silver – 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 silver and one of the well known silver stocks – Pan American Silver Corporation (PAAS). Please take a moment to study the chart before you continue reading.

As you may see, the chart covers the data for both silver and PAAS 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 silver and respective PAAS’ 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 fast at lower silver prices, but the pace of growth declines along with rising silver prices. These are exactly the properties of the logarithmic trend line. We’ve taken into account several types of trend lines and found that this one is best to represent the data that goes back to January 2002. We’ve chosen this 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 PAAS for the entire bull market can be best described using the logarithmic 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 logarithmic one. R-square of 92.0% means that in this model price of silver accounted for 92.0% of the PAAS’ prices’ move. This is a very good result in the long term – if you’re looking for stocks with direct exposure to silver, PAAS is sure worthy to be put into your portfolio.

In the search for a 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 / silver 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 PAAS 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 linear and the R-square value equals 57,9%. It seems that the company lost some of its exposure to the price of silver, or at least markets perception toward this exposure changed considerably. Nonetheless the true implications of this value will emerge as we compare it with results for other silver 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 silver does a particular silver stock have. It informs you exactly what percent of past observations (stock prices) have been explained by the price of silver 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 or silver) stock move if the price of the underlying asset (gold or silver) had risen by 1%. Choosing simply the coefficient that decides of the slope of the trend line (2.238 for the second stage in PAAS’ case) as the measure of the leverage can be misleading. That means that for every dollar rise in the price of silver, price of PAAS will increase on average by $2.24. 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 PAAS’ trend line so that it can be comparable to coefficients from other stocks. The result is about 1.08%. 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 silver, we get the Beta, which takes diverse values for different silver prices. In fact, only the leverage calculated for power trend lines is constant in percentage terms. In the case of PAAS, the Beta would be 1.09% with silver at $15 and 1.07% with silver at $20. As you see, the difference is not that big. Calculating leverage for a specific silver price is not much of a disadvantage, since non-linear models have different slope coefficients for different prices of metal, 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 silver. 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, and silver for PAAS). 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 silver 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 silver and silver stocks during the second phase of the bull market, almost all of them are best characterized by the power trend lines. Like we stated earlier, power trend lines mean that the stock’s leverage to metal (silver) does not change percentage-wise. Since that is the case, those of you who want to see the results are free to scroll down to the tables with R-squares and leverages, as it can be interpreted without additional information. However if you wish to know what you can do to compare stocks with different trend lines and uneven leverage then you should find the next couple of paragraphs quite interesting.

Here’s how you can deal with these conditions for different strategies:

For short term trades (for example for 60 cents move on the price of silver 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 silver) good idea might be to take into account the leverage for the average price of the metal (for PAAS it is naturally silver). So, if you expect the price to go from $15 to $20 you might want to check first the leverage for both $15 and $20 and then the leverage for the average price – $17.5 in this case. Small difference between the beginning and end values (1.09% and 1.07%) 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. The beta for 17.5 is actually 1.08%. That gives you the idea, how the stock might act in response to the price of silver at different price levels. Here the distinction is not very big, but there are stocks when the difference is sizeable.

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 silver 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 silver. 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 of this article (comming soon) or you can use the Tools section (which we recommend) on our website to get silver stock prices for any silver 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.

OK, we know what R-square means and what it does not mean. We know how we might estimate silver stocks’ leverage for different durations of transactions. Like we said earlier in this essay, we will now provide you with R-square values and leverages at several prices of silver. Please see the tables below:

It should not come as a surprise that almost all of the popular silver stocks show direct relation to the price of silver in the long term. What is really interesting is the very weak correlation between SIL and the price of the underlying metal. Most likely this is connected with hedging, but we won't go into details here. Through these numbers markets say (at least we read it as such) that although SIL does have a history and name connected with silver, it does not act like a silver stock at all. In our view this situation may change in the future, but for now, our analysis suggests using other stocks if exposure to silver is what you want. Coeur has only a fairly strong exposure to silver in the long term, but in the second stage their R-square value is far from similar. In the period from Jan 2006 Coeur's has not performed very well with regard to the price of silver. In fact the R-square value for this company decreased dramatically to 5.4%. Not only does the company trade rather independently of the price of silver but it's also declining along with rising metal prices (please note the negative leverage below). Other analyzed stocks have at least sufficient R-square about or above the 60% level, for the second stage of the bull market. These equities are recognized by the market as the true silver stocks.

Before we proceed with presenting the table with betas, please note that during the second stage of the bull market almost all of the silver stocks are best represented by power trend lines – only CDE, PAAS and SIL are suited best by a different trend lines. That means that for most stocks leverage is constant in percentage terms regardless of the silver price. PAAS’ leverage declines but the amounts by which it decreases with every dollar move in the silver is really modest and does not seem to affect stock’s overall appearance. For detailed information about silver stocks’ leverage please see the table below:

The leverage coefficients tell you how much percentage-wise you will gain when the underlying metal rises by 1% and the R-square tells you what part of this rise may be attributed to the rise in the price of the metal. All featured leverage values (betas) are standardized for 1% move in the price of silver.

As you may see on the above chart, the leverage for most of the stocks is above 1%, meaning that you get some extra profits by using these stocks as a proxy for silver instead investing in the metal itself. In fact only two stocks do not fall into this category: CDE and SIL. That’s not surprising as these stocks don’t seem to have almost any exposure to the price of silver – at least that is what our statistical analysis shows. Since they move rather independently of the metal price it’s no wonder, they don’t have any leverage to it.

The leverage for HL with regard to silver should be a little lower than that presented in the table above due to company’s exposure to gold, perhaps around 1.2% - 1.3% level. More on this topic in the full version of this essay (check our Website in several days for more details).

Before you choose your favorite silver 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 silver 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. If you want to read the full version (containing charts with trend lines for all popular silver stocks including: CDE, HL, SIL, SLW, SSRI and SVM.TO) please visit our Website in several days and browse the Research section.

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.