Tutorial solutions – Lecture 9

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Tutorial solutions – Lecture 9
  Tutorial solutions  –   Lecture 9 1. The dealer’s demand and supply functions are:  where and are the quantities supplied and demanded by dealers. The customer’s demand and supply functions are: Calculate the bid  –  offer spread. Solution   The bid rate is calculated from the dealer’s demand function and the customer’s supply function. By equating supply and demand we obtain: bb  S S   2.425.210    which can be solved to obtain: 1940.17.68  b S    Similarly, the offer rate is calculated from the customer’s demand function and the dealer’s supply function. By equating supply and demand we obtain: aa  S S   5.353.212    which can be solved to obtain: 2069.18.57  a S   Therefore, the bid  –  offer spread is: 0129.01940.12069.1    or 129 points 2. The spot exchange rate between the Australian dollar and the Swiss franc (CHF/AUD) is 0.8500  –  0.8580. A speculator believes that the Swiss franc will appreciate, and so buys CHF1 000 000. Two days later, the exchange rate turns out to be 0.8200  –  0.8280. Ignoring the interest rate factor, answer the following questions: (a) What will the speculator do? Qd S  b   10 2 5. Qs S  a   5 35. Qd   Qs Qd S  a   12 2 3. Qs S  b   2 4 2.  (b) How much profit will the speculator make? (c) Assuming that the speculator could buy and sell at the mid-rates, calculate the profit/loss in this case. Comment on your results. Solution (a) The corresponding AUD/CHF exchange rates are 1.1655  –  1.1765 and 1.2077  –  1.2195, respectively. The speculator buys the Swiss franc at the offer rate of 1.1765. Two days later the speculator can sell at the bid rate of 1.2077. Assuming that the speculator wants to realise profit, the franc will be sold at 1.2077. (b) The profit realised by buying and selling CHF1 000 000 is: 20031)1765.12077.1(0000001  AUD   (c) The mid-rates for buying and selling are 1.1710 and 1.2136. If the speculator can act on these rates, the profit realised will be: 60042)1710.12136.1(0000001  AUD   It is obvious that the profit realised is lower in the presence of the bid  –  offer spread. 3. The exchange rate between the Australian dollar and US dollar is currently 0.6925  –  0.6975. A speculator takes a short position on the Australian dollar, and this position is squared two months later when the exchange rate is 0.6526  –  0.6575. (a) Calculate the mid-rates when the short position is taken and when it is squared. (b) Calculate the profit (in points) realised from this operation if the speculator buys and sells at the mid-rates. (c) Calculate the profit (in points) realised from this operation if the bid  –  offer spread is   taken into account. (d) Comment on your results. Solution (a) The mid-rates when the position is taken and squared (selling and buying rates, respectively) are:  6551026575065260 6950026975069250 ......   (b) If the speculator buys and sells the AUD at the mid-rates, the profit will be: 0399.06551.06950.0    which means that the speculator makes a profit of 399 points. This is because when a currency depreciates, a short position on that currency becomes profitable. (c) The speculator sells the Australian dollar at 0.6925 and buys it at 0.6575, earning a profit of 0.035, or 350 points. (d) The loss is greater when the bid  –  offer spread is taken into account because it represents a transaction cost.
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