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. In the absence of arbitrage opportunities, what will be the relationship between the three exchange rates Xb/a, Xc/b and Xa/c. Compare the relative importance of least cost dealing and arbitrage in determining the relative equilibrium exchange rates.
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.
In the absence of arbitrage opportunities, what will be the relationship between
the three exchange rates Xb/a, Xc/b and Xa/c. Compare the relative importance
of least cost dealing and arbitrage in determining the relative equilibrium
exchange rates.
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