CFA Practice Question

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CFA Practice Question

An analyst is reviewing the following quotes from around the world:

In New York: $1 = 120 Yen.
In Tokyo: 1 AUD (Australian Dollar) = 60 Yen.
In Sidney: $1 = 2.3 AUD.

What would be the analyst's profit if she were to exploit the inherent triangular arbitrage opportunity with just $1,000?
A. $68.50
B. $150.00
C. $225.00
Explanation: Step 1. Determine which currency is overvalued or undervalued.
The true cross rate in Tokyo should be (120Yen/$) / (2.3AUD/$) = 52.174Yen/AUD. The actual rate being quoted in Tokyo is 60 Yen/AUD. Therefore, quoted rate in Tokyo is overvaluing the AUD. We should sell AUD to the dealer in Tokyo.

Step 2. The trades.
i. convert $1,000 into AUD: $1,000 x 2.3AUD/$ = 2,300 AUD.
ii. sell the AUDs to the Tokyo dealer: 2,300 AUD x 60 Yen/AUD = 138,000 Yen.
iii. convert the Yen back to dollars: 138,000 Yen x $1/120Yen = $1,150.

Step 3. Profit: 1,150 - 1,000 = $150.

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