Shanghai Copper Price and the Inventories Puzzle

After the financial crisis in 2008, there had been a structural break in the copper market. Until this break, the development of the copper price could be well explained by economic and financial market data of industrialized countries, like LME warehouse inventories, total OECD leading indicator, the US dollar index and the S&P 500 stock index. Although China had already risen to the world’s top copper consumer, this data provided a better fit for the LME copper price than the OECD leading indicator for China or the Shanghai Stock Exchange Composite index. After the financial crisis, Chinese data explained the copper price development better.

However, focusing on Chinese data had led to another problem, especially for the analysis of refined copper supply and demand. The identity equation that production plus net imports have to equal consumption plus change of inventories is the basis for the supply and demand analysis. The left hand side of this equation can be estimated with sufficient reliability. The Chinese Customs Office records exports and imports. Also the copper production could be estimated by China’s National Bureau of Statistics as companies have to report their production figures. The problems are on the right hand side of the equation as copper consumption is not directly observable.

Therefore, a concept of estimating apparent consumption is applied. Consumption is estimated by subtracting the change of inventories from the sum of copper production plus net imports. But the problem with this approach is that data on inventories is available for the state reserves and inventories in SHFE warehouses. However, private inventories – mostly held in bonded warehouses in the Shanghai region – are hidden. Thus, apparent consumption would be overestimated if the change of hidden inventories is underestimated and vice versa. Therefore, having a reliable estimate of the change in hidden inventories is essential for an analysis of supply and demand (consumption).

Since the report for global copper supply and demand in November 2013, the International Copper Study Group (ICSG) provides an estimate for adjusting apparent consumption in China. The ICSG applies the estimates of three consulting companies for this adjustment. If there is a significant change in the relationship of hidden inventories to official SHFE warehouse copper stocks then there should be a structural break in the link between SHFE copper price and inventories.

The chart above shows the development of the 3^rd month copper price at the Shanghai Futures Exchange and the inventories held in warehouses licensed by the SHFE. Already a visual inspection shows that there was a close relationship between the development of the copper price and the inventories in the period from the beginning of 2009 until the end of 2011. Since 2012, there appears to be a structural break. This could be verified empirically by an econometric test.

For a quantitative analysis, it is not sufficient to estimate just a linear relationship between the copper price and the inventories. If other factors have an influence on the copper price, then the regression coefficient would be overestimated in the case those other factors were excluded. Therefore, econometric models are usually formed to explain the price development by some more explanatory variables than merely the copper inventories. As the chart below shows, there is also a close relationship between the Shanghai Stock Exchange Composite index and the copper price. What is important for the analysis is that this relationship is also staple in the period after the start of 2012. This is also confirmed by econometric test for a structural break. The same applies for the SHFE 3^rd month copper price and the US dollar index. If a trend variable is included also in the model for the copper price, then there is also a structural break at the start of 2012.

Thus, in a typical model, the price of copper would be a function of inventories, the Shanghai Stock Exchange index and the US dollar index. It is well known from basic algebra, that this function could be rearranged that the inventories are a function of the other variables. Under the assumption that the relationship, which held in the period between the start of 2009 and the end of 2011, also held after 2011 if the development of the hidden inventories were taken into account in the inventory variable, one might derive an estimate for the change of hidden inventories. First, the regression coefficients for the period from 2009 until 2011 are estimated. Second, based on these parameters for the period from 2012 on, the copper inventories are estimated. Finally, the difference between the estimated inventories and the actual SHFE warehouse inventories provide an estimate of the development of hidden inventories since 2012. However, it should be noted that this figures would only be an estimate of the change in hidden inventories and not an estimate of the absolute level.

The empirical results of those estimates provide some surprises. First, there is a positive regression coefficient for the relationship between the price of copper and the SHFE warehouse inventories. This is in clear contrast to the theory of inventories, which postulates that prices should rise if inventories are falling and vice versa. This theory is also widely used to explain the development of the convenience yield of commodities.

The empirical results of those estimates provide some surprises. First, there is a positive regression coefficient for the relationship between the price of copper and the SHFE warehouse inventories. This is in clear contrast to the theory of inventories, which postulates that prices should rise if inventories are falling and vice versa. This theory is also widely used to explain the development of the convenience yield of commodities.

Therefore, the question arises: “What could explain the positive relationship between inventories and copper prices at the SHFE during the period from 2009 to 2011”? One possible explanation would be that speculation did not only take place in the futures market but also in the cash market. After the collapse of Lehman Brothers, China was very quick to announce measures to stimulate the economy and to prevent a major crisis. Also the state reserve bureau bought copper. Thus, speculators might also have bought copper and stored it in SHFE warehouses. This procedure gave them more flexibility in managing the trade by having the opportunity to sell a future and to deliver into this future at expiration if the market turns against their positions. 

Another possible explanation is arbitrage. If the copper market in Shanghai is in a contango, then there could be an incentive to buy copper in the cash market, store the copper in an exchange licensed warehouse and sell short a copper future with a more distant maturity. If the market is in backwardation, then there is an incentive to take out inventory.

Thus, we included another variable in the regression equation for the SHFE inventories, the spread between the 3^rd and the 1^st month copper price. The regression coefficient for the curve spread is highly significant and it also has the right sign. If the difference between the 3^rd and the 1^st month copper price widens then the inventories tend to increase, just as the theory suggests. In addition, including the curve spread as an explanatory variable for the SHFE warehouse inventories leads to a reduction of the regression coefficient of the copper price, but there is still a positive relationship. Therefore, another factor might explain this unusual correlation between the copper price and the inventories during this period.

It has often been reported that copper is used as a collateral for funding. Given the lower interest rates in the US dollar money market and the trend of the Chinese Yuan appreciating against the US dollar, it makes sense to fund in US dollars and to invest the proceeds in Yuan. Thus, the spread of the 3mth Shanghai interbank rate and the 3mth US Dollar Libor has been added as a further independent variable in the regression equation. But this procedure leads to the problem of multicolinearity as the interest rate spread is highly correlated with the copper price development. However, this is exactly what had been sought as the copper price could be dropped out of the equation explaining the development of the inventories. Thus, the four variables – copper curve spread, interest rate spread, Shanghai Stock Exchange Index and US dollar index explain quite well the movements of copper inventories held at the SHFE warehouses. The regression coefficients are all highly significant different from zero.

The second surprise is the comparison between the actual and estimated inventories since the start of 2012. The chart above shows the development of the SHFE inventories and the estimate according to the multiple regression model. Already from visual inspection, it is quite obvious that the model failed to predict the development of inventories, but this had been expected given the discussion about a rather strong build of hidden inventories. The surprise is the sign of the average forecast error.

For the period from 2009 until the end of 2011, over which the regression coefficients have been estimated, the average of the deviations between the actual inventories and the fitted values is zero by definition. However, for the period from January 2012 until the end of March 2014, the average of the difference between actual and estimated inventories is 82,340 tons. The t-test shows that this average is significantly different from zero at less than the 1% (error) level. During the last 2 and a quarter years, the average of inventories held in SHFE warehouses was 180,268 tons. This indicates that the inventories were on average 84.1% higher than what the model predicted based on the relationships prevailing from the start of 2009 until the end of 2011. If the assumption of constant regression coefficients and a stronger build of hidden inventories in bonded warehouses were correct, one would expect that actual inventories since 2012 were lower and not higher than the model estimate.

Thus, there had been a structural break in the model, which is also confirmed by an empirical test. The Chow test also allows to test, which variable caused the structural break. For the stock index, the US dollar index and the curve spread, the hypothesis of no structural break cannot be rejected. However, for the constant term and the interest rate spread, the hypothesis of no structural break can be rejected at the 1% significance level. The constant term alone explains around 62,000 tons of the higher inventories during the out-of-sample period. For the interest rate spread, the sign changed to negative during the period beginning in January 2012.

Thus, there had been a structural break in the model, which is also confirmed by an empirical test. The Chow test also allows to test, which variable caused the structural break. For the stock index, the US dollar index and the curve spread, the hypothesis of no structural break cannot be rejected. However, for the constant term and the interest rate spread, the hypothesis of no structural break can be rejected at the 1% significance level. The constant term alone explains around 62,000 tons of the higher inventories during the out-of-sample period. For the interest rate spread, the sign changed to negative during the period beginning in January 2012. 

The model failed to provide an estimate of the change of hidden copper inventories held in bonded warehouses, which would confirm the prevailing narrative. However, the structural break of the constant term indicates that also a shift of inventories from bonded into registered warehouses is a distinct possibility.