Learn / Library / Market making

Currency loop

Market makingMedium

$3$ currencies X, Y and Z trade as follows with no fees: $1$ unit of X buys $0.9$ units of Y; $1$ unit of Y buys $130$ units of Z; $1$ unit of Z buys $0.0087$ units of X. A trader starts with $1000$ units of X and converts around the loop X to Y to Z to X once. How many units of X does the trader gain?

Checking an answer needs JavaScript. The hint and the solution open without it.

Hint

Multiply the conversion rates.

Solution

After the first trade the trader holds $1000 \times 0.9 = 900$ units of Y.
After the second trade the trader holds $900 \times 130 = 117000$ units of Z, and after the third $117000 \times 0.0087 = 1017.9$ units of X.
The gain is $1017.9 - 1000 = 17.9$ .

Answer: $17.9$

Next question Back to the library