In this section I will provide correlation estimates for a variety of markets, instruments versus Gold. As noted before, the London PM Gold FIX and the StreetTracks Gold Trust price series have their own advantages and disadvantages for estimating correlation. Depending on the characteristics of the given instrument (mainly the time of day that it is sampled), I will estimate the correlation with Gold using the more appropriate of the two Gold price series.
In the interests of conserving space, I will present the numbers in tabular rather than graphical form. The labels of the columns of the tables are a bit terse, so a more detailed explanation of them is in order;
N
The number of samples used in the correlation estimate. This will vary a little even for identical start dates due to differing holidays, missing or bad data, etc.
STD
This represents the standard deviation of the logarithm of the daily returns. To make the values easier to mentally digest, the computed value of standard deviation is converted to units of percent change using the formula 100*(exp(x)-1).
RHO
The sample or Pearson correlation statistic for the case of no timeshift, or a lead, lag of zero.
UNC
This is the statistical uncertainty of the correlation estimates that is associated with the sample size, given by N. The actual correlation could be anywhere in the range of the reported value, plus or minus the given uncertainty.
Table 1 above shows the correlation of the various London Precious Metals Fixes versus the PM Gold FIX. Of these, Silver is most positively correlated with Gold. The correlation for Silver is understated a little bit here because the once daily Silver FIX happens at 12 PM London time (or 3 hours before the PM Fixes). In this case, there was some "bleeding" into a lead, lag of plus one, or 0.164 to be specific. Palladium distinguishes itself as being the most volatile, with Silver not too far behind. Gold is actually the least volatile of the four (on average).
For the COMEX metals, Copper is the least correlated with Gold and not surprisingly, COMEX Gold the most. (One would not expect perfect correlation with COMEX Gold, since it settles 2 1/2 hours before the StreetTracks ETF). The Energy and Agricultural contracts exhibit positive but weaker day to day correlation. The Interest Rate markets shown are uncorrelated with Gold (they are well within the uncertainty bands).
The foreign exchange data used to construct table 3 above was obtained from the US Federal Reserve, see [2]. This seemed like a good choice for correlating against the London PM FIX because the rates are collected around noon time New York, (according to the Fed website). All data series were first converted to units of US Dollars per currency unit. In other words, a positive correlation corresponds to both the foreign currency and Gold weakening (or strengthening) against the US Dollar.
An inspection of table 4 above shows that all the other popular Gold share indices exhibit strong correlation with Gold on a day to day basis. Energy shares are also positively correlated with Gold, but more weakly.
For those with an interest in the day to day correlation of Silver versus Gold, table 5 above includes an estimate of the IShares Silver Trust versus the StreetTracks Gold Trust. Keep in mind that the Silver Trust was established about this time last year, making for a more limited trading history and greater uncertainty in the correlation estimate.
In the case of the US Stock Indices, I have shown correlation estimates against both the London PM Gold FIX and the more limited data for the StreetTracks Gold Trust. Using the StreetTracks price series which only goes back to late 2004, stocks show a positive but weak day to day correlation with Gold. Going back further in time by using the London PM Gold FIX, the message is a bit different suggesting they are uncorrelated, and in some cases slightly negative correlated. This should serve as a reminder of the non-stationary characteristics of financial series. (For the case of the London PM FIX, despite the mis-match in the time of day when the data was collected, there wasn't any significant "bleeding" into non-zero lead, lags).
Tables 8 and 9 above show the correlation estimates for a small selection of Bank and Financial stocks that the Gold community has come to love to hate. Going all the way back to 2000, they are uncorrelated with Gold on a day to day basis.
Correlation versus Causal Relationships
I am always surprised at the number of authors who clearly don't realize the difference between correlation and a causal relationship that might explain the correlation. So far I have only provided quantitative evidence of correlation (or certain tendencies) in the daily returns of other instruments versus Gold. However, the presence of correlation does not in any way imply the existence of some causal relationship between the two [1]. Pure coincidence is always one possible explanation as well.
A recent article from Barron's [3] makes the later point very nicely. The article claimed that the price of Gold is correlated with the popularity of the Mr. T character from the old television series The A Team. While the popularity of a celebrity is certainly subjective and open to debate, I will give the author a "Mulligan" and assume that the claimed correlation really exists. The author makes no attempt to provide a plausible causal relationship that is behind the observed correlation. I think most of you will agree that it would be difficult to come up with anything along these lines. Most likely the correlation can be attributed to plain "dumb luck".
I will wrap this up with a few thoughts about some causal relationships that might explain some of the observed correlations. I make no pretense that this list is exhaustive. Consider these as food for thought, there will most certainly be other possible explanations. These are hypothesis only, the observed correlations do not serve as any sort of proof. The evidence for that must come from somewhere else.
Common Order Flow
An obvious explanation for the observed correlation of Copper and Gold, as well as Gold shares and Gold is that orders (of sufficient size to influence prices) are hitting both markets from entities who have a similar long term view of both markets and an interest in taking positions in both of them.
There is much talk of China putting its huge foreign currency reserves to work by purchasing and hoarding tangible resources. The observed correlations in Copper versus Gold are consistent with that hypothesis.
Sympathetic Moves
In the case of Gold shares and Gold it's easy to see how a move up or down in physical Gold can inspire sympathetic buying or selling interest in Gold shares. The shares serve as an alternate or more leveraged vehicle that has similar fundamental factors. This phenomena is common to any commodity and the shares of the companies that produce it (e.g. Natural Gas versus shares of Natural Gas producers).
For two markets that don't have such a relationship, such as Copper and Gold, I am in general more skeptical of this being a contributing factor. I say this in part because in just over 20 years of trading futures, I have never once placed an order in a market just because of some move in a different, unrelated market. Many """journalists""" in our financial press will trot out sympathy as the thinking behind a move in a market, but in general I don't buy it.
There is mechanism that could rightly be labeled as sympathetic that can be a contributing factor, namely the "Black Box" hedge funds that enter and exit positions based on trend following indicators. (Funds that use the moral equivalent of a low pass filter of prices to make decisions, such as the cross over of different length moving averages). I can envision how order flow from a common source might trigger short term "Black Box" players to follow in sympathy in two or more different markets at once.
Summary
In this article I presented estimates of the day to day correlation for a variety of markets, instruments versus Gold. This was accomplished by first converting commonly available daily closing price data to daily returns, taking the logarithm, and computing the sample correlation of the result. Several possible causal relationships were offered that are consistent with the observed correlations.
Getting back to the original question, Copper is indeed positively correlated with Gold on a day to day basis. An estimate of about 0.5 was arrived at using COMEX HG Copper and the StreetTracks Gold Trust. This is weaker than the correlation of Silver versus Gold, but stronger than Palladium or Platinum versus Gold.
I hope that this article has given the reader a better perspective of the nature of day to day correlations of various markets. I think many people enter the world of investments with the implicit assumption that certain markets should behave as if they are "chained at the hip". While this is true to a certain degree, the data shows that this coupling on a day to day basis is often quite weak. In these situations the correct mental image might be very stretchy bungee cords rather than chains.
Acknowledgments
The calculations presented in this article were performed using R, an application specifically designed for statistical computation and graphics. It is almost 100 percent compatible with the S language [4] originally developed by John Chambers [5] of AT&T Bell Labs. R is open source licensed and is available at no cost. It is (in my opinion) comparable to commercial applications that cost many hundreds or thousands of dollars (e.g. SAS, SPSS, Stata). The author wishes to thank the many statisticians and programmers around the world that have made generous contributions of time and effort to the development and maintenance of R.
For more information visit the R project website [6]. Readers with an interest in using it for computational finance are encouraged to visit the CRAN task view which focuses on that subject [7]. It is maintained by Dirk Eddelbuettel who is also the author of the Quantian Live DVD [8], which includes R along with several hundred CRAN add-on packages pre-installed.
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