Arbitrage and Consistent Prices

ArbitrageArbitrage is the practice of taking advantage of a difference in prices in two or more markets – striking a combination of matching deals to capitalize on the difference, the profit being the difference between the market prices at which the unit is traded. Arbitrage has the effect of causing prices of the same or very similar assets in different markets to converge.Read on Wikipedia → uses a difference between prices to secure a profit through linked trades. It does not require a forecast that an asset will rise or fall. The opportunity comes from prices available when the trades are made.

To understand the idea, follow one share traded in two markets. The example assumes the shares are equivalent and can be bought and sold on the required terms.

Comparing two prices in the same currency

In the chapter’s example, the share costs $120 in New York and £100 in London. The exchange rate is $1.2300 per pound. The London price must first be converted to dollars:

£100 × $1.2300 per pound = $123

The equivalent share is $3 more expensive in London. A trader can buy 100 shares in New York for $12,000 and sell 100 in London for £10,000. At the agreed exchange rate, those pounds provide $12,300.

Before costs, the difference is:

$12,300 received − $12,000 paid = $300

The purchase, sale, and currency conversion must be arranged together so the result does not depend on a later price change. The trader also needs the shares available for sale, or a way to borrow and deliver them. Buying now and hoping to find a higher sale price later would leave a market risk.

Checking whether the profit survives the costs

The $300 is a difference before costs, not the amount the trader will necessarily keep. Commissions, currency conversion, funding, and any cost of borrowing shares reduce it.

If the total cost is represented by C, measured in dollars:

Net profit = $300 − C

There is a positive profit only if those costs are below $300. Hull notes that costs can remove an opportunity for a small trader while leaving it available to a bank with lower trading costs.

The shares must also be genuinely interchangeable. Similar names or similar price histories are not enough. Different rights, delivery dates, or settlement arrangements may prevent the two trades from providing matching obligations.

Why this helps explain derivative prices

As traders buy the cheaper share, they tend to push its price up. Selling the more expensive share tends to push that price down. This activity reduces the difference, until it may no longer cover the costs.

The same reasoning connects the prices of derivativesIn finance, a derivative is a contract between a buyer and a seller. The derivative can take various forms, depending on the transaction, but every derivative has the following four elements:an item that can or must be bought or sold, a future act which must occur, a price at which the future transaction must take place, and a future date by which the act must take place.Read on Wikipedia → and their underlying assets. If two ways of obtaining the same future result have different costs, traders may be able to buy the cheaper one and sell the more expensive one.

The no-arbitrage principleArbitrage is the practice of taking advantage of a difference in prices in two or more markets – striking a combination of matching deals to capitalize on the difference, the profit being the difference between the market prices at which the unit is traded. Arbitrage has the effect of causing prices of the same or very similar assets in different markets to converge.Read on Wikipedia → assumes prices do not leave such a profit available under the model’s conditions. It is a starting point for calculating consistent prices, rather than a claim that markets never make mistakes.

The forward article applies this reasoning to a $60 share that pays no dividends. If borrowing and lending for a year both cost 5%, with no fees or other restrictions, buying and financing the share costs $63 after a year. A different forwardIn finance, a forward contract, or simply a forward, is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed on in the contract, making it a type of derivative instrument. The party agreeing to buy the underlying asset in the future assumes a long position, and the party agreeing to sell the asset in the future assumes a short position. The price agreed upon is called the delivery price, which is equal to the forward price at the time the contract is entered into.Read on Wikipedia → price can create an opportunity using the share, financing, and a forward together.

An expected return is not necessarily an arbitrage profit. If a strategy depends on two prices moving closer in the future, the trader still needs to consider what happens if that move is delayed or never occurs.

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