There are three currencies: alpha (a), beta (b) and gamma (c). The three exchange rates are as follows: 1 alpha buys you 5 betas; 1 beta buys you one half of one gamma; 1 gamma buys you one third of one alpha. That is, Xb/a = 5, Xc/b = 1/2 , Xa/c = 1/3 . There is no bid-ask spread, so that Xa/b = 1/Xb/a etc. There are six specialist traders, AB, BA, BC. CB, CA and AC who trade the six possible pairs of currencies: trader AB lives in Alpha-land and wants to sell alphas for betas; trader BA lives in Beta-land and wants to sell betas for alphas; and so on. All of these traders are willing to trade at the current market exchange rates, as quoted above. Suppose you are an arbitrage trader located in Alpha-land. Is there an arbitrage opportunity? What strategy would you adopt to exploit it and with whom do you trade?
There are three currencies: alpha (a), beta (b) and gamma (c). The three exchange
rates are as follows: 1 alpha buys you 5 betas; 1 beta buys you one half of one
gamma; 1 gamma buys you one third of one alpha. That is,
Xb/a = 5, Xc/b = 1/2
, Xa/c = 1/3
.
There is no bid-ask spread, so that Xa/b = 1/Xb/a etc. There are six specialist
traders, AB, BA, BC. CB, CA and AC who trade the six possible pairs of currencies:
trader AB lives in Alpha-land and wants to sell alphas for betas; trader BA lives
in Beta-land and wants to sell betas for alphas; and so on. All of these traders are
willing to trade at the current market exchange rates, as quoted above.
Suppose you are an arbitrage trader located in Alpha-land. Is there an arbitrage
opportunity? What strategy would you adopt to exploit it and with whom do
you trade?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
