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According to the theory of storage and no-arbitrage pricing principles, the commodity stocks determine both spot prices and futures prices. In this paper we analyze how the stocks of commodities affect the basis, i.e. the difference between spot prices and futures prices, and the price volatility by using the datasets on Shanghai copper, aluminum and zinc. As to the theory of no-arbitrage, the marginal cost of storage must equal to the expected marginal revenue of stocks carried to the future. The marginal cost of storage, from the theory of storage, including the rent for storage space, insurance and interest, is usually constant. On the other hand, the marginal expected revenue is the sum of marginal convenience yield, which is an increasing function of the quantity of stocks, and the difference between future spot prices and spot prices, which can be locked by futures contracts and equal to opposite of basis. Therefore, the basis is negatively correlated to the level of stocks. Moreover, the theory also implies that spot prices are more variable than futures prices when the quantity of stocks changes. When the level of stocks declines, the spot prices raise more than futures prices, and then the basis strengths. This is because the supplies and demands can adjust their schedules to the spot prices, and then the futures prices react slightly to the shock of stocks. However, when the stocks level is high, marginal convenience yield is low and approaches zero, so the spot prices and futures prices have similar volatility. In this paper we set up time-series models to test whether the level of stocks determines the basis and volatility for Shanghai copper, aluminum and zinc. As the theory implies, the basis have significant inverse correlation to quantity of stocks. However, the relationship between stocks and volatility is not consistent with the predictions of theory. The reason may be excessive speculation in China futures markets.
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