Arbitrageurs

What are arbitrageurs?

Arbitrageurs are one of the five groups of market participants – hedgers, speculators, arbitrageurs, central banks and strategic, fundamentally oriented investors – whose trading decisions help drive price movements in the markets. Arbitrageurs profit from price differences of the same security or asset, either between different trading venues or between different points in time, for example between the spot price and the futures price. During the trading day, price differences can arise between exchanges around the world, so that a product trades slightly more cheaply on one exchange than on another. Arbitrageurs exploit these differences to make risk-free profits – and in doing so, they bring the price of the security back into line across all exchanges.

In capital market theory, a distinction is made between arbitrage opportunities of the first type and of the second type.

Arbitrage of the first type (free lottery)

An arbitrage opportunity of the first type exists if, today, you can secure a profit in the future without investing any capital. It can be compared to a free lottery ticket: it costs nothing and can only lead to a gain, never to a loss. That is why this case is also called a "free lottery".

Example: Consider an investment in a safe bond with a nominal value of $100.00 and an 8% coupon that matures in exactly one year. In this example, the refinancing rate – the interest rate at which the investor can borrow money – is 5%. An investor could buy the bond by taking out a loan at 5% interest per year, so they would not need to use any of their own money. They would make a profit in the future whenever the bond costs less than $102.86.

Calculation:

• Repayment amount (R) = $108.00 (nominal value of $100.00 plus 8% interest, due in one year)
• Refinancing rate (i) = 5%
• Bond price (P)

P = R / (1 + i)

The expected cash flow of the bond is discounted at the refinancing rate. This gives the maximum price that can be paid for the bond. Any lower price makes arbitrage of the first type possible.

Maximum price of the bond: P = $108.00 / (1 + 0.05) = $102.857143 ≈ $102.86

Arbitrage is therefore possible whenever the market price of the bond is below P. If, for example, the bond can be bought at its nominal value of $100.00, the investor borrows $100.00, receives $108.00 after one year, repays $105.00 and keeps a profit of $3.00 – without having invested any capital of their own.

Arbitrage of the second type (free lunch today)

An arbitrage opportunity of the second type exists if you can make a profit today without taking on any payment obligations in the future. In this case, the profit is available immediately – hence the name "free lunch today".

Example 1: If a share is traded on two trading venues at different prices, this situation can be exploited to make a risk-free profit. You buy the share cheaply on one venue and sell it at a higher price on the other, keeping the difference as profit. It is important that the purchase and the sale take place at the same time.

Calculation:

• Purchase of the share on venue 1: P1 = $100.00
• Sale of the share on venue 2: P2 = $101.00
• Profit: P2 − P1 = $1.00

Arbitrage is possible whenever P2 − P1 > 0. In practice, the price difference must also exceed the transaction costs involved.

Example 2: Arbitrage of the second type can also be illustrated with the bond example. Today, on the bond's issue date, you invest $100.00 at an 8% coupon and receive $108.00 back at the end of the one-year term. You can use these $108.00 to repay a loan that you take out today and that falls due on the same date. You therefore borrow $102.857143 today at the 5% refinancing rate. This means you receive a loan of $102.857143 today, of which you only need to invest $100.00 – leaving you with a "free lunch today" of around $2.86.

Calculation:

Profit = R / (1 + i) − I = $108.00 / (1 + 0.05) − $100.00 ≈ $2.86

Here, I is the amount invested. These $2.86 are exactly the present value of the $3.00 profit from the first-type example: the same mispricing, but collected today rather than in one year.

Is arbitrage still possible today?

Risk-free profits are hardly available any more. This is due both to the close interconnection of financial centres and to the possibilities of computerised trading. Automated trading systems eliminate valuation differences within fractions of a second, so that ordinary private investors have practically no opportunity for arbitrage. Only institutional investors have the technical capabilities and the direct connections to trading venues required for this kind of transaction.