Find Arbitrage

A first interview round Finance question asked in Flow Traders

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You are a forex trader analysing the markets and think you have spotted an arbitrage opportunity. You have $1000 USD to start with, and can trade the following exchanges at the following rates. How much profit can you generate?

\(\begin{align*} \text{EUR/USD} &= 0.85 \\ \text{EUR/GBP} &= 1.5 \\ \text{USD/GBP} &= 1.8 \end{align*}\)

Bonus problem: if we expand it to n currencies with their conversion rates given, can you find a optimum algorithm to find the arbitrage opportunity ?

Hint: Think in terms of cycles and graphs !

Try to solve this problem yourself before moving on to the solution below

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Solution

First you must sell Dollars for Euros,

\( $1000 \cdot 0.85 = \$850$.\)

You then exchange your Euros for Pounds,

\( $\frac{\$850}{1.5} \approx \$566.667$\)

And finally, Pounds for Dollars,

\( $566.667 \cdot 1.8 = \$1020$\)

Which yields $20 in profit.

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😃 Over to you: Were you able to solve this?

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