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Arbitrage using Futures

Arbitrage is the simultaneous purchase and sale of an asset in different markets to profit from price discrepancies. Futures contracts can be used in arbitrage strategies.

Cash-and-Carry Arbitrage: This strategy exploits mispricing between the futures market and the spot market.

Scenario: The futures price is higher than the theoretical fair value based on the cost of carry model.

Steps:

  1. Short the futures contract.
  2. Buy the underlying asset in the spot market.
  3. Store (carry) the asset until the futures contract's expiration.
  4. Deliver the asset against the short futures position.

Profit: The profit is the difference between the futures price (at which you sold) and the spot price plus carrying costs (at which you bought and held the asset).

Example:

  • Spot price of silver: $25 per ounce
  • One-year silver futures price: $28 per ounce
  • Financing cost: 2% per year
  • Storage cost: $0.50 per ounce per year

Theoretical futures price (fair value): $25 + ($25 * 0.02) + $0.50 = $26

Arbitrage Opportunity: The futures price ($28) is higher than the theoretical price ($26).

Actions:

  1. Short a silver futures contract at $28.
  2. Buy silver in the spot market at $25.
  3. Store the silver for one year.

At expiration:

  • Deliver the silver against the futures contract and receive $28 per ounce.
  • Total cost: $25 (spot price) + $0.50 (financing) + $0.50 (storage) = $26
  • Profit: $28 - $26 = $2 per ounce

Reverse Cash-and-Carry Arbitrage: This is the opposite scenario, where the futures price is lower than the theoretical fair value.

Steps:

  1. Long the futures contract.
  2. Short sell the underlying asset in the spot market. (Borrow the asset and sell it immediately).
  3. Invest the proceeds from the short sale at the risk-free rate.
  4. At expiration, buy the asset in the spot market using the proceeds from the short sale plus interest earned, and take delivery through the long futures position.

Important Considerations for Arbitrage:

  • Transaction Costs: Trading fees, storage costs, and other expenses can erode arbitrage profits.
  • Market Efficiency: Arbitrage opportunities tend to be short-lived as market participants quickly exploit them, driving prices back to their fair values.
  • Execution Risk: Delays or difficulties in executing trades can affect the profitability of arbitrage.
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