What is cash-and-carry arbitrage (plain language)
– Cash-and-carry arbitrage is a trade that tries to lock in a risk‑free profit by buying an asset today (the cash or spot market) and simultaneously selling a futures contract on that same asset. If the futures price is higher than the spot price plus all costs of holding the asset until delivery, an arbitrageur can “carry” the asset to the futures expiry and deliver it against the short futures position to capture the difference.
Key definitions (first use)
– Arbitrage: buying and selling equivalent or closely related instruments to profit from price differences, ideally without market risk.
– Spot (cash) market: the market for immediate purchase/delivery of an asset.
– Futures contract: a standardized agreement to buy or sell an asset at a specified future date and price.
– Carrying costs (cost-of-carry): all costs required to hold the asset until the futures delivery date — typically financing (interest), storage, insurance, and sometimes transportation.
– Convenience yield: the non‑monetary benefit of holding the physical asset (e.g., ensuring supply), which effectively reduces the cost of carry.
How the logic works (concise)
1. Compute the theoretical futures price by adding the cost of carrying the asset to the current spot price. For a simple discrete-time view:
Theoretical futures price ≈ Spot + Carrying costs.
For continuous interest and asset convenience/income, a common model is:
F = S * e^{(r + u – y)T}
where F = futures price, S = spot price, r = risk‑free rate, u = storage/other carrying costs (as a rate), y = convenience yield or asset income, and T = time to maturity (in years).
2. If the actual quoted futures price > theoretical price + transaction costs, buy spot and short futures. Hold the asset, pay carrying costs, and deliver into the futures contract at expiry. Net profit ≈ futures price − (spot price + all carrying and transaction costs).
Step‑by‑step execution checklist
– Confirm price discrepancy: futures price must exceed spot + all estimated carrying costs + transaction costs + taxes.
– Measure carrying costs: include interest on funds used to buy the asset, storage, insurance, transport, and any asset-specific costs.
– Include financing and margin mechanics: determine how you will pay for the asset (cash vs. borrowing) and how much margin the short futures position requires.
– Confirm deliverability and contract terms: is the futures contract physically settled or cash‑settled? Physical delivery is required for classic cash‑and‑carry; cash settlement requires offsetting the futures prior to expiry.
– Check liquidity: ensure both the spot and the futures legs are sufficiently liquid to enter and exit without large slippage.
– Account for counterparty, operational, and regulatory risk: verify exchange rules, delivery procedures, and potential for margin hikes.
– Factor taxes and timing: net profit after taxes and the timing of cash flows can materially change the economics.
– Run a full P&L sensitivity: test outcomes for higher carrying costs, unexpected margin calls, or failure to deliver.
Worked numeric example (simple)
– Given: Spot price S = $100, one‑month futures price F = $104
Assume:
– annual financing rate r = 2% (so one‑month financing ≈ 0.02/12 = 0.001667),
– no storage cost,
– no dividends during the month,
– futures are physically settled or cash‑settled with offset before expiry (doesn’t change P&L if offset is used),
– transaction costs and taxes are ignored for the base case (we’ll add them later).
Step 1 — Compute the break‑even futures price
The discrete break‑even futures price for holding the asset financed at rate r for time T (in years) is approximately
F_break = S × (1 + r×T) + carrying costs − PV(dividends).
For one month, T = 1/12, carrying costs = 0, dividends = 0:
F_break = 100 × (1 + 0.02/12) = 100 × 1.0016667 = 100.16667.
Step 2 — Compare market futures price to break‑even
Market futures F = 104 > F_break ≈ 100.1667. That implies a cash‑and‑carry arbitrage opportunity in the frictionless base case.
Step 3 — Construct the trade (cash‑and‑carry)
– At t = 0: buy 1 unit of the underlying at $100 (pay $100); simultaneously sell one futures contract at $104.
– Finance the $100 purchase by borrowing at the 2% annual rate (or through repo, margin financing, etc.).
– Hold the underlying to delivery (or hold until you offset the futures).
– At expiry (t = 1 month): deliver the underlying against the short futures and receive $104; repay the loan of $100 plus interest $100×0.02/12 = $0.16667.
Step 4 — P&L calculation (per unit)
Cash inflows at expiry: +$104.
Cash outflows at expiry: repay loan = $100 + $0.16667 = $100.16667.
Net profit = 104 − 100.16667 = $3.83333 per unit.
Step 5 — Return measures and capital considerations
– Profit per dollar of notional underlying = 3.83333/100 = 3.8333% for one month.
– If you financed the entire $100 with debt, initial cash equity outlay might be small (only margin/fees). But most retail accounts cannot borrow 100% without collateral; practical return on actual posted capital depends on margin rules and collateral requirements.
– If instead you fund partially with equity, compute ROI on actual equity posted.
Add realistic frictions (adjust the base case)
Recompute net profit after plausible frictions:
– Bid‑ask and
– Bid‑ask and execution costs — the spreads you pay when buying the spot (ask)