Answer to Question #250876 in Macroeconomics for Comfort

Question

a) you are given the following exchange rates
SF in Zurich: 1.6000-35 SF/1$
£ in NY: 1.9810-50 $/1 £
I) as a banker in London you would like to quote a £ cross-rate for the SF (i.e, £/1SF). If you anticipate to be the sole banker in the world quoting this cross-rate, what is your quote going to be? Explain

ii) Now suppose that you have operating cost of 0.05% of volume. Would this affect your answer? Show your work

iii) suppose one of your competitors in London quotes the following: 0.3160-80 £/1SF. Assume that you can trade with him up to a maximum of $2,000,000. Could you take advantage of that competition? Is there any risk of doing so?

Answer 1

(1)

a)

As a banker in London, your bid will be the price at which you will buy customers' SF. It is the # of € that you will give them for 1SF.

Even though the question states that you have no competition in the cross rate business, your customers can always obtain their € by changing their SF into $, then their $ into € as follows:

$1SF\to 1/1.6035=0.6236$$$\to0.6236/1.9850=0.3142€$

$\therefore$ the lowest price at which you can propose to buy their SF in exchange for € and still get their business is 0.3142€/1SF.

b)

As a banker in London, your asked price is the € price at which you will sell 1SF to your customers.

Even though you have no competition in the cross rate business, your customers can always obtain their SF by selling their € for $, then selling these $ for SF.

If they do so, they need the following # of € to get 1SF:

$1€\to1*1.9810=$ $$1.981\to1.9810*1.6000=3.1696 SF$

$\therefore$ the highest price at which you can propose to sell them 1SF in exchange for € and still get their business is given by 0.3155€/1SF.

The answer is 0.3142$\to$ 0.3155€/1SF.

(2)

Here, we have competition in the cross rate sector. Competition in the cross rate market will ensure that B is strictly greater than 0.3142€/1SF and that A is strictly lower than 0.3155€/1SF.

Since we have costs equal to approximately 0.05% of your transactions volume, you must find a bid- asked spread which is high enough to cover those costs, yet still attract customers.

(3)

The bid of that guy is higher than 0.3155€/1SF, which is the price that 1SF will cost you if you do 2 transactions via the $. In other words, he is willing to pay too much for SF, which means that you need to sell him SF in order to exploit his mistake.

Assuming you have $2m,

Sell $2m for SF in Zurich at a bid of 1.6000SF/1$, this gives you SF 3.2m.

Now resell these SF3.2m to that competitor in London, at his bid of 0.3160€/1SF: you get 1011200€.

Finally, exchange those € for $ in NY the bid of 1.9810: this gives you 2,003,187$.

Your profit is $3.187. You must be fast to take this advantage because a lot of people will notice it and it will not last for long.

There is no risk in doing this.