Suppose the spot exchange rate for the Canadian dollar is Can$1.12 and the six-m

Question

Suppose the spot exchange rate for the Canadian dollar is Can$1.12 and the six-month forward rate is Can$1.14.

  

Which is worth more, a U.S. dollar or a Canadian dollar?

Assuming absolute PPP holds, what is the cost in the United States of an Elkhead beer if the price in Canada is Can$2.85? (Round your answer to 3 decimal places, e.g., 32.161.)

  

  

  

  

Suppose the spot exchange rate for the Canadian dollar is Can$1.12 and the six-month forward rate is Can$1.14.

Explanation / Answer

a> $1 = C$1.12 so US is worth more b> Purchasing Power Parity implies consumers can buy the same goods irrespective of currency (it's sometimes illustrated by the Big Mac index..ie the price of a Big Mac in diferent currencies reflects the long term equilibrium relationship between those currencies). So C$2.85/1.12 or US$2.54 is the implied PPP price. But this is a theoretical equivalence - the fact that (presumably) Elkhead beer is brewed in Canada implies a comparative advantage for Canadian consumers. Transportation costs would increase the price in the US. In practice there are many other factors eg different size of market, competitive conditions that also would need to be taken into account. c> US dollars are trading at a premium to Canadian dollars in the forward market. In other words it takes more Can$ (1.14) to buy US$1 d> Although the Can$ is trading at a discount in the forward FX market this does not imply that the US$ is expected to appreciate in value. All future expectations about the relative strength/weakness of US$ versus C$ are in fact contained within the current spot rate. To understand why this is consider an alternative way of paying out Can$ and receiving US$ in 6 months. If I want to sell C$ in 6 months there are two basic ways to do it. I can either use the forward market or by selling C$ / buying US$ in the spot market and simultaneously borrowing C$ and lending US$ in the equivalent amounts for the 6 month period. I'm left with net cashflows of zero on the spot date and an outflow of C$/inflow of US$ in 6 months time. The actual amouts will depend on how much interest I have to pay and receive in each of the two currencies. The implied FX rate is merely the Can$ amount divided by the US$ amount. The fact that this alternative exists means that if the forward FX rate did not reflect the interest rate differential between the two currencies arbitrage would be possible. People would do equal and opposite transactions two lock in profit by eg selling Can$/ buying US$ spot and simultaneously borrowing Can$ and lending US$ for 6 months on the one hand, which would create a - Can$/+US$ position in 6 months time. At the same time they would use the forward FX (or indeed the currency futures market) to buy Can$ and sell US$ in 6 months. As the arbitrage is spotted and acted on the price differential is eliminated by supply and demand pressures. Because this arbitrage is already widely understood it is automatically incorporated into the way forward FX is priced. e> See for a fuller explanation, but the answer here is that Canada has higher interest rates. The actual interest differential is a time value of money calculation. To find the precise mathematical differential you need to know one or other country's 6 month interest rate, but you can get a good approximation via the following formula...( Fwd/Spot - 1) / n , where n is the number of years. So in this case:- (1.14/1.12)- 1)/0.5 = 3.57%

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