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37#
发表于 2012-3-28 10:19
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Donna Ackerman, CFA, is an analyst in the currency trading department at State Bank. Ackerman is training a new hire, Fred Bos, a recent college graduate with a BA in economics.
Ackerman and Bos have the following information available to them:Spot Rates |
| Bid Price | Ask Price |
USD:EUR | €1.0000 | €1.0015 |
USD:GBP | ₤2.0000 | ₤2.0100 |
GBP:EUR | €0.3985 | €0.4000 |
Ackerman and Bos are interested in pursuing profitable arbitrage opportunities for State Bank. Using the appropriate bid or ask rates for the USD:EUR and the USD:GBP, what will be the profits from triangular arbitrage, starting with $1,000?
The USD:EUR and USD:GBP rates imply that the arbitrage free cross rates for the GBP:EUR are:bid = €1.000/₤2.0100 = €0.4975
ask = €1.0015/₤2.0000 = €0.5008
Since the cross rates given (€0.3985 − €0.4000) are outside of the arbitrage-free cross rates, profitable arbitrage is available. It takes too few euros to buy 1 pound, so we want our arbitrage trades to go in the direction that will cause us to sell overvalued euros for pounds at the ask rate of €0.4000.
Start with $1,000.
Use the $1,000 to buy euros ($1,000 × €1.000/$) = €1,000.
Use the €1,000 to buy sterling (€1,000 / €0.4000/₤) = ₤2,500. This step is the key.
Use the ₤2,500 to buy dollars (₤2,500 / ₤2.0100/$) = $1,243.78.
Arbitrage profit = $1,243.78 − $1,000 = $243.78.
Now, Ackerman and Bos note there is a larger observed spread for British pounds versus Euros in the spot market. Which of the following statements is least likely consistent with this situation? Consider each statement individually. A)
| The proportion of trading volume related to currency arbitrage is greater in the British pound than in the Euro. |
| B)
| The total volume of spot market transactions is higher in the Euro than in the British pound. |
| C)
| The British pound is more volatile than the Euro. |
|
If the proportion of trading volume related to currency arbitrage is greater in the pound than in the Euro, we might expect pound spreads to be narrower, all else equal, because arbitrage activity tends to reduce transaction costs and increase market efficiency. The other two effects are consistent with a larger spread on the pound.
Ackerman explains to Bos that a theoretical relationship exists between forward rates and future spot rates, called the foreign exchange expectation relation. This relation suggests that: A)
| the forward rate is a biased predictor of the expected future spot rate, and there is a foreign currency risk premium present. |
| B)
| the forward rate is an unbiased predictor of the expected future spot rate, and there is a foreign currency risk premium present. |
| C)
| the forward rate is an unbiased predictor of the expected future spot rate, and there is no foreign currency risk premium present. |
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The foreign exchange expectation relation is F = E(S1), meaning that the forward rate is an unbiased predictor of the expected future spot rate. If this is the case, there is no foreign currency risk premium present in the forward rate. When the forward rate is not an unbiased predictor, this implies that some investors are willing to pay a premium to hedge foreign currency exposure. |
|
KK bid-ask 2.4365 − 2.5843