Cash-and-carry arbitrage is a trading strategy that involves buying an asset in the spot market and selling a futures contract on the same asset. The goal is to profit from the difference between the spot price and the futures price, which should be equal in an efficient market. The arbitrageur holds the asset until the expiration date of the futures contract, and then delivers it to the buyer. The profit is guaranteed as long as the cost of buying and holding the asset is lower than the revenue from selling the futures contract.
For example, suppose an arbitrageur buys a barrel of oil for $100 in the spot market, and sells a one-month futures contract for $104. The arbitrageur also incurs a carrying cost of $3 for storing and insuring the oil for one month. At the end of the month, the arbitrageur delivers the oil to the buyer of the futures contract and receives $104. The net profit is $104 – $100 – $3 = $1. This is a risk-free profit, as the arbitrageur does not need to worry about the price fluctuations of the oil in the market.
Cash-and-carry arbitrage is a market-neutral strategy, meaning that it does not depend on the direction of the market. It only exploits the mispricing between the spot and futures markets. However, cash-and-carry arbitrage opportunities are rare and may not last long, as other arbitrageurs will quickly close the price gap. Therefore, cash-and-carry arbitrage requires fast execution and low transaction costs.
Basic Theory:
Cash-and-carry arbitrage takes advantage of temporary mispricing between the spot and futures markets. According to the theory, the cost of acquiring an asset in the spot market and carrying it until the delivery date should be equal to the futures price. Any deviation from this equilibrium presents an opportunity for arbitrage.
Procedures:
- Identify Opportunity: Look for instances where the spot price is lower than the futures price, creating a potential arbitrage opportunity.
- Execute the Strategy:
- Buy the underlying asset in the spot market.
- Simultaneously, sell a futures contract for the same asset.
- Invest Proceeds: Invest the proceeds from selling the futures contract in a risk-free asset, such as a government bond.
- Wait for Expiry: Hold the positions until the futures contract expires.
- Profit: At expiration, the trader delivers the asset from the spot market against the futures contract and pockets the price difference.
Comprehensive Explanation:
Let’s consider a scenario with the following details:
- Spot price of Asset X: $100
- Futures price of Asset X (3-month contract): $105
- Risk-free rate: 2% per annum
Excel Calculation:
- Calculate Initial Investment:
- Initial Investment = Spot Price – (Futures Price / (1 + Risk-free rate)^(Time to Expiry))
- Initial Investment = $100 – ($105 / (1 + 2%)^(3/12))
- Determine Future Value of Initial Investment:
- Future Value = Initial Investment * (1 + Risk-free rate)^(Time to Expiry)
- Future Value = Initial Investment * (1 + 2%)^(3/12)
- Calculate Profit:
- Profit = Future Value – Futures Price
- Profit = Future Value – $105
Excel Table:
| Scenario | Values |
|---|---|
| Spot Price | $100 |
| Futures Price | $105 |
| Risk-free Rate | 2% per annum |
| Time to Expiry | 3 months |
| Initial Investment | = $100 – ($105 / (1 + 2%)^(3/12)) |
| Future Value | = Initial Investment * (1 + 2%)^(3/12) |
| Profit | = Future Value – $105 |
Scenario Calculation:
- Initial Investment = $100 – ($105 / (1 + 2%)^(3/12)) ≈ $98.04
- Future Value = $98.04 * (1 + 2%)^(3/12) ≈ $99.02
- Profit = $99.02 – $105 ≈ -$5.98
Result:
In this scenario, the trader incurs a loss of approximately $5.98 due to the mispricing between the spot and futures markets.
Other Approaches:
- Reverse Cash-and-Carry: Exploits situations where the futures price is lower than the spot price.
- Calendar Spread: Involves taking offsetting positions in futures contracts with different expiration dates.
- Dividend Arbitrage: Applied when a stock pays dividends, aiming to capitalize on differences in futures pricing and the expected dividend payments.
