1 Introduction
Industrial metals such as Copper or Nickel are important basic materials for almost all industrial products like cars or electronic devices. Hence, their demand is closely related to business cycles (Rosenau-Tornow et al., 2009). Especially due to a rapid growth in emerging markets, their production and consumption increased strongly in the past decade. For example, the Copper world mine production increased from 13.2 million tons in the year 2000 to 16.2 million tons in 2010 (U.S. Geological Survey, 2011). It is obvious that this trend might have a serious impact on the future supply situation of these commodities: With more fast growing economies in other emerging countries, the availability risk of the industrial metals Aluminum, Copper, Nickel, and Zinc, which have a very high economic importance, can increase easily to a critical level in the future (European Commission, 2010). In order to avoid disruptions in the production process, it becomes more and more relevant for manufacturers to assess the future availability of commodities. Especially for just-in-time production strategies with low stocks, a delay in supply can cause production losses and in consequence financial losses for a single company as well as for the economic system as a whole.
1引言
工業金屬，如銅或鎳是重要的基本原料，幾乎所有的工業產品，如汽車或電子裝置。因此，他們的需求是密切相關的商業周期（羅西瑙托爾諾等，2009）。特別是由于在新興市場的快速增長，在過去十年中，其生產和消費增長強勁。例如，銅世界礦山生產在2000年的1620萬噸增加至1320萬噸，在2010年（美國地質調查局，2011）。很明顯，這一趨勢可能會產生嚴重的影響，這些商品對未來供應緊張的局面：隨著快速增長的經濟體在其他新興國家，工業金屬鋁，銅，鎳，鋅的可用性風險，其中有一個非常高經濟的重要性，可以輕松地增加在未來到臨界水平（歐洲委員會，2010）。為了避免在生產過程中的中斷，它變得越來越多的制造商相關的評估未來可用的商品。特別是對于剛剛在低庫存的生產策略，供應的延遲可能會導致生產損失和嚴重后果的財務損失以及為一個單一的公司作為一個整體的經濟體制。

For a commodity’s risk assessment it is important to know its criticality which is measured by its economic importance and its supply risk (European Commission, 2010). In the literature various indicators exist for estimating the criticality of a commodity (e.g., Herfindahl-Hirschmann Index, spot prices, production volume etc.). However, all of these indicators have shortcomings. For example, there is no indicator for criticality which is at the same time (a) available with a daily frequency, (b) aggregating all relevant information, and (c) forward-looking to a sufficient extent. To close this gap we propose the convenience yield of commodity futures as an indicator for criticality.
對于大宗商品的風險評估，重要的是要知道它的重要性，這是衡量其經濟的重要性以及它的供應風險（歐洲委員會，2010）。在文獻中存在的各項指標，估計的商品（例如，赫芬達爾 - 赫斯曼指數現貨價格，產量等）的關鍵性。然而，所有這些指標有缺點。例如，有沒有指標的臨界頻率每天在相同的時間（一），（二）匯總的所有相關信息，及（c）前瞻性到足夠的程度。為了彌補這一差距，我們建議大宗商品期貨便利收益作為一個關鍵性的指標。

The central idea behind is that prices of exchange traded commodity derivatives contain all information available in the market and hence on the critcality of a commodity in the future. In particular, we focus on the convenience yield which is a component of futures prices. According to the theory of storage it is equivalent to a liquidity premium for physically holding a commodity in stock. This liquidity premium explains the difference in spot prices and futures prices and the fact that people are willing to buy and store a commodity for a higher price in the spot market now, than in the futures market. Our analysis is based on the efficient market hypothesis according to which all information on the market situation are contained in futures prices (Fama, 1970). The research question of this paper is whether the convenience yield is a good indicator for a commodity’s future criticality which avoids the shortcomings of existing criticality indicators. It would provide managers and policy makers an appropriate, easy and continuously accessible information source with essential information on criticality.  http://www.ttc-switch.com/dissertation_writing/Marketing/
隱含的中心思想是交易所買賣商品衍生工具的價格包含提供的所有信息，因此在市場上的商品在未來的critcality。特別是，我們專注于便利收益，這是期貨價格的一個組成部分。根據存儲的理論，它是相當于實際持有商品庫存的流動性溢價。這種流動性溢價，說明現貨價格和期貨價格的事實，人們都愿意以更高的價格在現貨市場上購買和儲存商品，比在期貨市場上的差異。我們的分析是基于有效市場假說，根據市場形勢上的所有信息都包含在期貨價格（FAMA，1970）。本文所研究的問題是，便利收益是否是一個很好的指標商品的未來的重要性，避免了現有的關鍵性指標的缺點。管理者和決策者提供一個合適的，容易和連續訪問信息關鍵性的重要信息源。

We compared the convenience yields of futures on five different industrial metals at certain points in their lifetimes with known criticality indicators lagged until the time to maturity. Thereby we were able to empirically analyze whether the convenience yield has predictive power for a high criticality of a commodity in the future. In the following, we first introduce the underlying theory of commodity criticality as well as on commodity futures and the convenience yield. Derived from theory, we then formulate our hypotheses and explain the details of the methodology. To test our hypotheses we calculated convenience yields from historical spot and futures prices of the London Metal Exchange for five major industry metals (Aluminum, Copper, Lead, Nickel, Zinc) with different maturities (3, 15, 27 months). After preparing both the methodology and the data, we empirically test our hypotheses on statistical significance and conduct several robustness checks. Based on the results of the empirical analysis we furthermore analyze the ability of the convenience yield to serve as indicator for a commodity’s future criticality by means of an in-sample test with our data. Finally, the knowledge gained by our empirical analysis is summarized and some suggestions concerning the extension of our work are also provided.

2 Theory and Hypotheses
2.1 Criticality of Commodities
The supply situation of a commodity is influenced by a variety of different factors which determine the supply risk. In order to identify commodities with a potentially critical supply situation, appropriate indicators have to be developed. According to Rosenau-Turnow et al. (2009) the supply risk of a commodity is determined by the following risk factors:
- Supply and demand situation which is influenced by the market balance, the stock keeping and the utilization of resource production facilities
- Cost of production, e.g., for mining or transport
- Geostrategic risks, such as the distribution of production facilities on different countries alongside with the country specific risk
- Market power due to concentration of mine production on few powerful companies
- Future supply and demand situation, which is determined by the degree of exploration, the investments in new refining facilities and the future market balance

As already mentioned, in the literature a variety of methods exists to derive criticality indicators from these risk factors. Some of the indicators can be gained immediately from the risk factor, as it is the case for the current stock of a resource or a market balance. On the other hand a concentration of production facilities on country or company level is more difficult, as an appropriate measurement method has to be applied. One of the widely accepted measures in this context is the Herfindahl-Hirschmann Index. To quantify country risks the World Bank Governance Index is often applied (Rosenau-Tornow et al., 2009). Other indicators cited in the literature are relative and real prices of commodities (Krautkraemer, 1998; Brown and Wolk, 2000). A more qualitative approach is the cumulative availability curve, which accounts also for dynamic effects (Yaksic and Tilton, 2009).

But all of these indicators have shortcomings. To the best of our knowledge, no comprehensive indicator exists up to now which aggregates all information from the different criticality indicators to one measure in a scientifically appropriate way. Also the calculation of indicators with a daily frequency is at least partially not possible as the necessary data is not accessible (e.g., in the case of production data, which is published with some delay). Furthermore, most existing indicators rely on historical and current fundamental data for their calculation and though have only limited value for prediction of future criticality.

To close this gap in the scientific literature, we focus on exchange traded commodity derivatives as a source of information on resource criticality. Under the efficient market hypothesis they are assumed to contain all information from past prices (weak form of efficiency) and all publicly available information (semi-strong efficiency) in their trading prices (Fama, 1970; Fama, 1991). This means that market expectations which include the future criticality of the resource are reflected in prices as well. This paper focuses on commodity futures and their term structure to gain insight into the criticality of the underlying commodity in the future. The difference between a commodity’s spot price and its futures price is determined to a large extent by the convenience yield of the commodity, which can be seen as a premium for having the commodity physically in stock (Copeland et al., 2004; Geman, 2005). We test whether the convenience yield is a predictor for the criticality at the maturity of the related futures contract. This is especially appealing as many commodity futures with different delivery dates are traded daily on international stock exchanges which allows for comparisons between different commodities as well as for intertemporal analysis and reflection of historical events in the time series.

2.2 Commodity Futures and Convenience Yields
In large industrial commodity markets most of the transactions are made via standardized futures contracts. The dependence of the futures price on the time to maturity (delivery date) is called the term structure which is displayed in the forward curve. Futures prices of financial assets, like stocks or bonds, usually have a forward curve with a positive slope (i.e., longer dated contracts have a higher price than shorter dated ones), which is called contango. This is due to the cost of carry which arise from buying the duplication portfolio and which the buyer of the underlying will be charged at the maturity.

Commodity forward curves often have a negative slope, which is called backwardation. This phenomenon of ‘negative cost of carry’ occurs despite the additional storage expenses for holding the commodity until the contract’s maturity. To explain backwardated forward curves the widely accepted theory of storage can be applied (Kaldor, 1939; Working, 1948; Working, 1949). According to this, the futures price at the time t for a later delivery in T can be calculated from a commodity’s spot price St plus the cost of carrying the commodity until the maturity of the contract minus the benefits from holding the commodity physically (liquidity premium). The cost of carry consists of the cost of capital which can be calculated with the interest rate rtT, and the cost of storage, expressed as a rate ctT which covers all expenditures for storing the commodity (e.g., warehouse rent or insurance fees). The benefits of holding the commodity physically can be seen as a flow of services respectively as a liquidity premium which the owner of a resource receives during the time to maturity (Copeland et al., 2004). In analogy to stock futures this is quantified like a dividend payment for the owner of the underlying and hence has to be subtracted from the futures price.

Especially the case of industrial metals illustrates the economic meaning of the liquidity premium. The owner of the commodity is prepared for unexpected shortages in supply or increases in demand. E.g., a producer of industrial goods can avoid a disruption in its manufacturing process, if he/she has the commodity in his/her warehouse. This liquidity premium or flow of services during the contract’s lifetime is quantified by the convenience yield CYtT in the form of a rate.

3 Data Sources
For the test of the hypotheses with the above mentioned regression models we use time series data with daily frequency of Aluminum, Copper, Lead, Nickel and Zinc. The data for the spot and futures prices as well as the inventory and the turnover are retrieved from the London Metal Exchange (LME), which is one of the leading markets for industrial commodities worldwide. The descriptive statistics of these time series is presented in Table 1. LME inventory levels of these commodities can amount on average to about 2-3% of the world production of one year (except for Lead which amounts to less than 0.1%). As the LME warehouse network has more than 600 warehouses in Europe, USA and Asia, we assume their inventory as well as their prices and turnover as representative for the world market of the respective commodity. In our analysis we use cash and futures prices for Aluminum, Copper, Lead, Nickel and Zinc with a daily frequency in the time period from 1999-01-04 until 2011-03-15. The maturities of the contracts are 3, 15, and 27 months (M) (for Lead are only 3M and 15M available with a sufficient long-term record), the price quotation is in US $ per metric ton (MT). The contracts with 3 months maturity are settled on a daily basis whereas for the 15 and 27 months the settlement date falls normally on the third Wednesday every month. For reasons of simplicity we assume in our further analysis the 15 and 27 months contracts to settle on a daily basis as well. The five metals were chosen because of their economic importance for many sectors, e.g., the electronic or the automotive industry. Also the supply situation of Aluminum, Copper, Nickel, and Zinc can become unsecure in the future (European Commission, 2010).

To estimate the storage costs we draw on the LME warehouse rents, which are fixed as a price in US-Cent/MT/day for one year and are specific for a commodity. 2 We calculate the storage cost rate by relating the rental fee to the daily spot prices and transform it into a continuous rate. We obtain on average rates between of 0.5% and 2.5% p.a., depending on the price of the commodity. The descriptive statistics (Table 1) of the convenience yields calculated with equation (2) reveals that they in general increase with the futures’ time to maturity as indicated by the averages and medians. Furthermore, we observe that the standard deviation decreases with the time to maturity.

This is in accordance with the Samuelson Effect which predicts decreasing volatility of futures prices with increasing time to maturity (Samuelson, 1965). This also explains the increasing minimum respectively decreasing maximum values of the yield series. For all commodities we can observe negative minimum values for the convenience yields. Compared to the maxima their absolute value is much smaller. According to Tilton et al. (2011), this is a situation of strong contango in the forward curve.

4 Tests and Results
4.1 Hypothesis H1
The result of the test of H1 with the linear regression model and the average static lifetime from equation (3): X is presented in Table 2. We obtain in all cases except for Lead highly significant negative values for the α1 coefficient. According to the regression model this means that the average static lifetime of stocks decreases with the convenience yield. In the case of Lead we obtain very small, but positive results. The explanatory power of the regression is for Copper, Nickel and Zinc in the range between 0.272 and 0.379 except for 3M Zinc and 27M Nickel with 0.18 respectively 0.083. For Aluminum we obtain in all cases an explanatory power of 0.110 and below.3