Futuresintermediate

Arbitrage in Futures

Futures arbitrage exploits any deviation between the traded futures price and the cost-of-carry fair value $F_0 = S_0 e^{(r - q) T}$ . When the futures price is too high, a cash-and-carry trade buys spot, finances it at $r$ , and sells futures to lock in a riskless profit. When the futures price is too low, the reverse cash-and-carry trade short-sells spot, invests proceeds at $r$ , and buys futures. Both strategies require no net capital at inception, so any positive expected profit attracts traders until the gap closes.

Why it matters

Arbitrage is the enforcement mechanism behind futures pricing. If June crude futures trade noticeably above the cost-of-carry level, the market is offering free money to anyone willing to buy oil today, store it, and deliver it in June. The buying pressure in spot and the selling pressure in futures push prices back to fair value almost instantly in liquid markets. In illiquid or constrained markets, arbitrage bounds widen because shorting the spot is costly or transaction costs are high. Real arbitrage is bounded by transaction costs, repo specials, and credit limits, not by absolute zero.

Formulas

No-arbitrage condition

F_0 = S_0 e^{(r - q) T}

Cash-and-carry when overpriced

F_0 > S_0 e^{(r - q) T} \Rightarrow \text{sell futures, buy spot, finance at } r

Reverse cash-and-carry when underpriced

F_0 < S_0 e^{(r - q) T} \Rightarrow \text{buy futures, short spot, invest proceeds at } r

Profit equals the mispricing minus financing and transaction frictions. Hull (2022) §5.2.

Worked examples

Scenario

$S_0 = 100$ , $r = 5\%$ continuously compounded, $T = 1$ year. Market futures price is $F = 108$ .

Solution

Fair value $F_0 = 100 \times e^{0.05} = 105.13$ . Futures are overpriced by $2.87$. Cash-and-carry: borrow $100$ at $5\% $, buy one unit of spot, sell one futures at$ 108$. At delivery deliver the asset, receive $108 $, repay$ 100 \times e^{0.05} = 105.13$. Risk-free profit $= 108 - 105.13 = 2.87$ per unit, before transaction costs.

Scenario

A June ASX SPI 200 futures contract trades at 7,180 while spot is 7,200 with two months to expiry. Continuously compounded $r = 4.5\%$ and dividend yield $q = 4.0\%$ .

Solution

Fair value $F_0 = 7{,}200 \times e^{(0.045 - 0.040) \times 2/12} = 7{,}200 \times e^{0.000833} \approx 7{,}206$ . The futures price 7,180 is below fair value by about 26 points. Reverse cash-and-carry: buy futures cheap, short the index basket, invest proceeds. Profit roughly $26 \times 25 =$ A$650 per contract, less basket borrowing and short-sale costs that often eat most of it in equity markets.

Common mistakes

✗Arbitrage opportunities are common and risk-free for retail traders. They are neither. Bid-ask spreads, financing costs, and short-sale frictions consume nearly all observed mispricings in liquid markets. Studies of S&P 500 futures show pricing errors fall almost entirely inside the no-arbitrage band once full costs are accounted for.
✗Arbitrage requires capital. The textbook trade is self-financing. Borrowing funds purchase the spot, and the short side pays for itself. Capital is needed only for margin and to absorb temporary mark-to-market losses before convergence.
✗Cash-and-carry only applies to physical commodities. The logic is identical for equity index futures, bond futures, and FX futures, with the dividend or foreign rate playing the role of $q$ . Hull (2022) Chapter 5 develops each case.

Revision bullets

•Cash-and-carry sells overpriced futures and buys spot
•Reverse cash-and-carry buys underpriced futures and shorts spot
•Both strategies enforce $F_0 = S_0 e^{(r-q)T}$
•Real-world arbitrage band set by transaction costs and repo
•Short-sale frictions are the binding constraint in equity arbitrage

Quick check

If the traded futures price is below the cost-of-carry value, an arbitrageur should:

$S_0 = 50$ , $r = 5\%$ continuously, $T = 0.5$ , no income. Market futures price is 53. Per-unit arbitrage profit is approximately:

Connected topics

Cost of Carry Convergence PCP

In learning paths

Futures Path

Sources

Hull (2022), §5.2 and §5.6
Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
Standard textbook derivation of cash-and-carry and reverse cash-and-carry arbitrage that pins the no-arbitrage futures price.
Cornell & French (1983)
Cornell, Bradford, and Kenneth R. French. The Pricing of Stock Index Futures. Journal of Futures Markets, 3(1), 1983, pp. 1 to 14.
Original empirical analysis of S&P 500 futures mispricings against cost-of-carry fair value and the role of transaction costs.
MacKinlay & Ramaswamy (1988)
MacKinlay, A. Craig, and Krishna Ramaswamy. Index-Futures Arbitrage and the Behavior of Stock Index Futures Prices. Review of Financial Studies, 1(2), 1988, pp. 137 to 158.
Quantifies the no-arbitrage band in equity index futures and shows mispricings rarely exceed transaction costs.
CFTC Cash and Carry Glossary
U.S. Commodity Futures Trading Commission. CFTC Glossary: Cash and Carry. CFTC, accessed 2026.
Regulator-side definition of cash-and-carry arbitrage and the role of short selling in enforcing futures pricing.

How to cite this page

Dr. Phil's Quant Lab. (2026). Arbitrage in Futures. Derivatives Atlas. https://phucnguyenvan.com/concept/arbitrage-futures

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