Arbitrageurs

What are arbitrageurs?

Arbitrageurs are among the five market participants (hedgers, speculators, arbitrageurs, central banks and strategically fundamental investors) whose trading decisions are jointly responsible for movements in the markets. Arbitrageurs profit from spatial or temporal differences in the price of a security which is being traded on several stock markets. During the day, a price difference can occur on different stock markets, which means that a product can be traded for less on one stock market than on another. These differences are used by arbitrageurs to reap risky profits, by which the price of a security aligns again on all the stock markets.

Here, with regard to the arbitrage opportunities, one differentiates between the first order and the second order.

1.) Arbitrage possibility of the first order (free lotteries)

The arbitrage possibility of the first order exist if, today, one has the possibility to realise profits in the future without bringing in any capital. This case is comparable with a free lottery. Hence, it is also called “free lottery”.

Example:

An example would be an investment in a secure bond with a nominal value of €100 and a coupon of 8% with maturity in exactly one year. The refinancing rate in this example is 5%. An investor could now buy the bond by taking a loan with 5% interest pa. So, he does not have to use his own money. He would always make a profit in the future if the bond is less than €102.86.

Mathematical illustration:

– Repayment sum (R) = €108.00

(Nominal value €100 + 8% interest with maturity in one year = €108.00)

– Refinancing interest rate (Z) = 5%

– Price of bond (P)

P = R / (1 + Z)

(So, the expected cash flow of the bond is discounted with the refinancing rate. Thus, one obtains the maximum price which the bond may cost.) Any price which is lower makes arbitrage of the first order possible.

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

Arbitrage is always possible if the market price of the bond is < P.

2.) Arbitrage possibility of the second order (free lanch today)

This is the case if a risk-free profit can be obtained today.

Example 1.)

For example, if a stock is being traded at two trading venues at different rates, this situation can be used to reap risk-free profits. One buys the stock cheaply at one venue and then sells it at another more expensively. The difference is then raked in as profit. It is important that the purchase and sale take place at one point in time.

Mathematical illustration:

Purchase stock trading venue1: P1 = €100

Sell stock trading venue2: P2 = €101

Profit: €1,00Arbitrage is always possible when the following applies: 0 < P2 – P1

Example 2.)

One can also illustrate the arbitrage possibility of the second order by means of the previous example with the bond.

Today, on the issue date of the bond we invest €100 with an 8% coupon and will receive €108 at the end of the term of one year. This amount of €108.00 can be used to repay the loan, which we will take today, at the end of the term. Today, we therefore take a loan of €102.857143 at 5% refinancing interest. We thus receive a €102.857143 credit, of which we only have to invest €100. Therefore, today we have a free lanch of around €2.86.

Mathematical illustration:

Profit = investment sum – (repayment sum R / (1 + refinancing interest))

Profit = €100 – (€108.00 / (1 + 0.05)) ≈ €2.86

Are arbitrage transactions still possible today?

The possibility for a risk-free profit is hardly available anymore. This is partly because of the networking of the financial centres and also the possibilities of computer trading. Automated trading systems adjust valuation differences in the blink of an eye, so that no arbitrage transactions are possible for the normal investor. Only institutional investors have the technical possibilities and the connection to the financial centres to be able to implement such transactions.

Arbitrageurs
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