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. What is the cost of one beta in terms of alpha when trading indirectly using the currency gamma? When buying betas with alphas, is the direct route or the indirect route the method of least cost dealing?
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.
What is the cost of one beta in terms of alpha when trading indirectly using
the currency gamma? When buying betas with alphas, is the direct route or
the indirect route the method of least cost dealing?
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