Interest Parity and Exchange Rates.

1 Interest Parity: In Jan 2007, Canadian interest rates were 4.50% while US interest rates were 5.27%. The exchange rate was 1.1759 ($C per $US). (10 points) a. Using this information alone and the uncovered interest rate parity condition, make a rough prediction of the 90-day forward exchange rate. That is, would you expect the Canadian dollar to appreciate or depreciate over the next 90 days? Show your work and discuss the rationale. b. It turns out that, in fact, that the 90 day forward exchange rate was 1.1728. Does your prediction in (a) match the actual forward rate? If not, how might you explain the discrepancy between your rough calculation and the actual observed forward rate? c. Suppose you expect that in 1 year the U.S. dollar will be worth $C1.10 and are willing to commit $C100,000 to speculation on the Canadian dollar. What should you do given the interest rates above if it held for one year? Would you buy US bonds? Stay in Canadian bonds? Explain. d. How much profit (in Canadian dollars) will you make if the U.S. dollar turns out in fact to be equal to $1.10? What if it remains at its current value of $1.1759? What if it turns out to be worth its current 90 day forward value of $1.1728? e. From (d), discuss how expectations of the future spot rate, relative to the current forward rate, affects the flow of investments in bonds. Collect the data set on exchange and interest rates from the course website: (Please see attached data) 2 Canadian Exchange Rates (10 points) a. Plot the CAN-US exchange rate from Jan 1999 to 2013. Describe the changes in the exchange rate over this period. b. Can you identify specific events that may have driven the exchange rate up or down? Explain 3 Bilateral Exchange Arbitrage: (10 points) a. Calculate the bilateral exchange rates for all countries: That is, find the US-CAN, US-YEN, US-AUS, US-UK, US-EURO exchange rates. Pick Aug, 2011 to do this. CAN USD EUR GBP AUD JPY CHF CAN to 1.00 USD to 1.00 EUR to 1.00 GBP to 1.00 AUD to 1.00 JPY to 1.00 CHF to 1.00 b. Now do it again for Aug, 2012. Discuss relative changes over that time. Is Canada rising relative to all currencies, some? What about the Euro? c. Take Aug, 2011 again. Suppose you could buy also Canadian dollars in London with the following rates (I just made these up): USD EUR GBP AUD JPY CHF 1.01 0.80 0.62 0.95 78.06 0.99 Explain and show whether you can make arbitrage profits by buying/selling in Toronto (using data from (a)) then buying/selling in London. d. Explain whether such an arbitrage opportunity is likely to be exploitable. Ie, is my scenario plausible? 4 Forward Exchange Rates. We want to see whether today's 90-day forward rate is a good predictor of the spot rate three months from now. (10 points) You may need to review the relevant section in JSGS874. Or read a statistics book on “Linear Regressions”. a. Plot the spot and forward exchange rates together. Note: You have to manipulate the data so that the spot rate on Jan 1 is matched to the forward rate 3 months earlier. b. Run the OLS regression: et+1 = ßo + ß Ft + μt where et+1 is the spot rate 90 days after the forward Ft. c. Interpret your results. d. Why might the OLS results in (a) not be believable? Discuss. Hint: Read Polito’s article. 5 Does Interest Parity Hold? (10 points) a. Calculate and Plot the CAN-US interest differential b. Calculate and plot the monthly appreciation of the exchange rate (in percent) between Canada and the US. c. Plot them together. Does it appear to support the Uncovered Interest Rate Parity condition? That is, if Canadian interest rates rises vis-à-vis the US, do we see a proportionate change in the Canadian dollar: ? Discuss. d. Calculate and Plot the Forward Premium (in percent) between Canada and the US. e. Plot the Interest Differential and the Forward Premium together. Does it appear to support the Covered Interest Rate Parity equation? That is, does the following hold on average? Discuss.      

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