Term Structure Arbitrage: Identifying and Exploiting Mispricings in the Metals Curve

Statistical Arbitrage in Metals Futures Curves

Term structure arbitrage in metals futures, such as gold, silver, and copper, involves identifying and exploiting temporary mispricings along the forward curve. Unlike risk arbitrage, which seeks to profit from a known future event, statistical arbitrage relies on quantitative models to identify deviations from historical pricing relationships. The assumption is that these deviations will revert to the mean over time.

Identifying Mispricings with Cointegration

A effective statistical tool for identifying arbitrage opportunities is cointegration. If two or more futures contracts on the same underlying metal are cointegrated, it means that there is a long-run equilibrium relationship between their prices. A linear combination of their prices will be stationary. We can define a spread:

Spread = Price_A - (beta * Price_B) - alpha*

Where Price_A and Price_B are the prices of two different futures contracts, and beta and alpha are the cointegration parameters. When this spread deviates significantly from its mean of zero, it signals a potential arbitrage opportunity. A trading rule could be:

• If Spread > (Mean + 2 * StdDev), short the spread (sell contract A, buy beta units of contract B).
• If Spread < (Mean - 2 * StdDev), long the spread (buy contract A, sell beta units of contract B).

The Role of the Cost of Carry Model

For physically-settled commodities like metals, the cost of carry model provides a theoretical framework for the term structure. The futures price should be a function of the spot price, interest rates, storage costs, and any convenience yield.

Futures_Price = Spot_Price * e^((Interest_Rate + Storage_Cost - Convenience_Yield) * Time_to_Maturity)

Deviations from this theoretical price can signal arbitrage opportunities. For example, if a futures contract is trading significantly below its theoretical price, an arbitrageur could buy the futures contract, sell the physical metal short, and lock in a risk-free profit, assuming they can borrow the metal to short.

Execution and Risk Management

Execution is important in statistical arbitrage, as the mispricings are often small and short-lived. High-frequency trading infrastructure and direct market access are often required. The risks include:

• Model Risk: The statistical model may be misspecified or the historical relationships may break down.
• Execution Risk: Slippage and transaction costs can erode the small profits from each trade.
• Liquidity Risk: The arbitrage may be identified in illiquid contracts that are difficult to trade.

Despite these risks, statistical arbitrage of the metals term structure can be a highly profitable strategy for sophisticated quantitative traders with the right infrastructure and expertise.