one mark = 2.25 francs one franc = 46 yen one yen = 0.009 marks.
Given these rates, the trader should
1. speculate by purchasing francs with marks, then yen with francs, and then marks with yen.
2. conduct arbitrage by purchasing francs with marks, then yen with francs, and then marks with yen.
3. speculate by purchasing yen with marks, then francs with yen, and then marks with francs.
4. conduct arbitrage by purchasing yen with marks, then francs with yen, and then marks with francs.
Choose the option that yields the correct answer.
The correct option is 4. The easiest way to see this is to convert one hypothetical mark into 2.25 francs, then the 2.25 francs into yen at the exchange rate of one franc for 46 yen to obtain 103.5 yen, and finally convert the 103.5 yen back into marks at the exchange rate of one yen for .009 marks. This will yield .9315 marks, which is less than we started out with. The proper arbitrage transaction is therefore to do the reverse---convert marks into yen, then yen into francs and then francs into marks. This is arbitrage rather than speculation, as the two concepts are defined, because a profit occurs at the existing exchange rates and does not require exchange rates to move in a particular direction.
Start with one million marks. Convert these into yen at the exchange rate of one yen = 0.009 marks to obtain 111.11 million yen. Now convert these yen into 2.41 million francs at the exchange rate of one franc for 46 yen. These francs can now be converted back into marks at the rate one mark for 2.25 francs to obtain 107.35 million marks for a profit of a bit over 7 million marks.
A key purpose of the question was to make sure that you understand the difference between arbitrage and speculation. Arbitrage involves a sure profit at the existing exchange rates and a realized profit if the exchange rates do not move unfavorably by a sufficient amount while the necessary transactions are being made. Speculation involves an attempt to profit from an expected movement of the exchange rate. A profit will be earned if the exchange rate moves as expected and a loss will result if the exchange rate moves in the opposite direction to what was expected.