Cash and carry arbitrage

What Is Cash and Carry Arbitrage?

Cash and carry arbitrage is a strategy in the realm of arbitrage within financial markets that seeks to profit from temporary mispricings between an underlying asset in the spot market and its corresponding futures contract. This strategy involves simultaneously buying an asset in the spot market and selling a futures contract on the same asset. The expectation is that the futures price will converge with the spot price by the expiration date, allowing the arbitrageur to profit from the difference, less the cost of carry. This strategy is a cornerstone concept in derivatives pricing, suggesting that in efficient markets, the futures price should theoretically equal the spot price plus the cost of holding the asset until the futures contract matures.

History and Origin

The concept of cash and carry arbitrage is as old as organized commodity markets themselves. As early forms of "to-arrive" contracts emerged in the mid-19th century at places like the Chicago Board of Trade (CBOT) for agricultural commodities, the conditions for such arbitrage naturally arose. These early forward and futures contracts, standardized in 1865, provided a mechanism for participants to lock in future prices, which in turn created opportunities when those prices deviated from the economic realities of holding the physical commodity. The evolution of futures markets, particularly with the introduction of financial futures in the 1970s, expanded the scope for cash and carry arbitrage beyond tangible goods to financial instruments. The Chicago Board of Trade, founded in 1848, was instrumental in developing the world's first futures exchange and standardizing contracts, paving the way for the sophisticated arbitrage strategies seen today.¹⁰, ¹¹, ¹², ¹³

Key Takeaways

Cash and carry arbitrage is a low-risk strategy exploiting pricing discrepancies between an asset and its futures contract.
It involves buying the underlying asset in the spot market and simultaneously selling a futures contract.
The profit potential is driven by the difference between the futures price and the spot price, adjusted for the cost of carry.
The strategy relies on the convergence of spot and futures prices as the contract approaches maturity.
Arbitrage opportunities in efficient markets are typically short-lived and require rapid execution.

Formula and Calculation

The theoretical price of a futures contract, assuming no arbitrage opportunities exist, is determined by the spot price of the underlying asset plus the cost of carry over the life of the contract. The cost of carry generally includes interest rate expenses, storage costs (for physical commodities), and less any income generated by the asset (like dividends).

The no-arbitrage futures price ((F_0)) can be expressed as:

F_0 = S_0 \times (1 + r)^T - \text{FV(Dividends)}

Where:

(F_0) = Theoretical Futures Price
(S_0) = Current Spot price of the underlying asset
(r) = Risk-free rate (annualized)
(T) = Time to maturity of the futures contract (in years)
(\text{FV(Dividends)}) = Future Value of any dividends or income expected from the asset during the period (T).

If the actual futures price deviates from this theoretical price, a cash and carry arbitrage opportunity may exist. The arbitrageur buys the asset at (S_0), funds the purchase by borrowing at rate (r), and simultaneously sells the futures contract at its current market price. At maturity, they deliver the asset (or settle the cash equivalent) against the futures contract, repay the loan, and collect the profit.

Interpreting Cash and Carry Arbitrage

Cash and carry arbitrage fundamentally relies on the principle of market efficiency. In perfectly efficient markets, such opportunities would rarely, if ever, exist because prices would instantly adjust to reflect all available information, thereby eliminating any mispricing. However, real-world markets are not perfectly efficient, and minor, fleeting discrepancies can arise due to factors like transaction costs, liquidity constraints, information lags, or temporary supply-demand imbalances. The persistence of cash and carry opportunities suggests that the market price of the futures contract is either too high relative to the spot price and the cost of carry, or vice versa.⁶, ⁷, ⁸, ⁹

Hypothetical Example

Consider an arbitrageur observing the following:

Current spot price of a stock: $100
Three-month futures contract on the same stock: $102
Three-month risk-free rate: 4% per annum (1% for three months)
No dividends expected during the three-month period.

Step-by-step arbitrage transaction:

Borrow Funds: The arbitrageur borrows $100 at a 1% interest rate for three months. The total repayment will be $100 \times (1 + 0.01) = $101.
Buy Spot: With the borrowed $100, the arbitrageur immediately buys one share of the stock at the current spot price of $100.
Sell Futures: Simultaneously, the arbitrageur sells one three-month futures contract on the same stock at $102.
Hold and Deliver: At the end of three months, the futures contract matures. The arbitrageur delivers the stock (which they own) and receives $102 from the party on the other side of the futures contract.
Calculate Profit: The arbitrageur receives $102 from the futures contract. They repay the borrowed $101.
- Arbitrage Profit = $102 (from futures) - $101 (loan repayment) = $1.

This $1 profit is a risk-free rate gain, assuming negligible transaction costs. The basis between the spot and futures price created this opportunity.

Practical Applications

Cash and carry arbitrage, while often subtle and short-lived in highly developed markets, is a fundamental force driving market efficiency. Its practical applications are primarily seen in:

Derivatives Pricing: The theoretical framework of cash and carry arbitrage underpins the pricing models for futures contracts and other derivatives. Deviations from the "no-arbitrage" price indicate potential mispricing.
Algorithmic Trading: High-frequency trading firms extensively employ algorithms to detect and execute cash and carry arbitrage strategies, leveraging speed to capture small, fleeting profits.
Market Oversight: Regulators, such as the Commodity Futures Trading Commission (CFTC) in the United States, monitor market activities to ensure fair and competitive markets, where such arbitrage helps keep prices aligned. The CFTC's mission includes protecting market users and the public from fraud and manipulation, while fostering open and competitive markets.³, ⁴, ⁵ This oversight indirectly ensures that conditions for arbitrage exist, promoting price discovery and preventing prolonged mispricing.
Hedging: While arbitrageurs profit from mispricing, the underlying principle also informs hedging strategies for market participants seeking to mitigate price risk.

Limitations and Criticisms

Despite its theoretical elegance, cash and carry arbitrage faces several practical limitations and criticisms:

Transaction Costs: Brokerage fees, exchange fees, and taxes can erode the small profit margins characteristic of arbitrage opportunities. These costs can make seemingly profitable spreads uneconomical.
Market Frictions: Real-world markets are not perfectly liquid. It may be challenging to buy or short selling the necessary quantities of the underlying asset or futures contract quickly enough and at the expected prices.
Funding Costs: While the risk-free rate is assumed, actual borrowing costs can vary based on the arbitrageur's creditworthiness and the specific market conditions, impacting profitability.
Execution Risk: Even with sophisticated algorithms, there is a risk that prices may move unfavorably between the initiation of the trades, eliminating the arbitrage opportunity before completion.
Regulatory Changes: New regulations or changes in market rules can impact the viability or cost-effectiveness of arbitrage strategies.
Unexpected Market Movements: While theoretically risk-free, unexpected market events, such as extreme volatility or liquidity crises, can disrupt the expected convergence of spot and futures prices. For example, some quantitative hedge funds, which often employ arbitrage strategies, have faced challenges when markets experience unusual and rapid shifts, making it difficult for their algorithms to adapt to new trends.¹, ²

Cash and Carry Arbitrage vs. Reverse Cash and Carry Arbitrage

Cash and carry arbitrage and reverse cash and carry arbitrage are two sides of the same coin, both exploiting mispricings between the spot price of an underlying asset and its futures contract.

Cash and Carry Arbitrage: This strategy is employed when the futures contract is overpriced relative to its theoretical value (spot price plus cost of carry). The arbitrageur buys the asset in the spot market and simultaneously sells the futures contract.
Reverse Cash and Carry Arbitrage: Conversely, this strategy is utilized when the futures contract is underpriced. The arbitrageur engages in short selling the underlying asset in the spot market and simultaneously buys the futures contract. The goal is to profit from the futures price increasing to its fair value by maturity.

The core distinction lies in the direction of the mispricing and, consequently, the inverse actions taken by the arbitrageur. Both strategies aim to lock in a risk-free rate profit by exploiting temporary discrepancies.

FAQs

What assets are typically involved in cash and carry arbitrage?

Cash and carry arbitrage can involve a variety of assets where liquid spot and futures markets exist. This includes commodities (like gold, oil, grains), financial instruments (like stock indices, currencies, and bonds), and even individual equities with corresponding derivatives markets.

Is cash and carry arbitrage truly risk-free?

In theory, cash and carry arbitrage is considered risk-free rate because the arbitrageur locks in a profit by simultaneously executing offsetting trades. However, in practice, risks like transaction costs, liquidity constraints, unexpected market movements, and execution challenges introduce minor operational risks that can erode or even negate the expected profit.

How quickly do cash and carry arbitrage opportunities disappear?

In highly liquid and efficient markets, cash and carry arbitrage opportunities are typically fleeting, often lasting only milliseconds or seconds. Automated trading systems and arbitrageurs quickly identify and exploit these mispricings, causing prices to realign almost instantaneously.

What is the role of the "cost of carry" in this strategy?

The cost of carry is crucial because it represents the net expenses (or income) incurred for holding the underlying asset from the spot purchase date until the futures contract matures. It includes financing costs (interest rate), storage, and insurance, minus any income generated by the asset, such as a yield or dividend. Accurately calculating this cost is essential for determining a true arbitrage opportunity.