Question

For all questions, interest (r) and dividend (d) rates are continuously compounded unless specified otherwise.

Q2) CAD interest rate rd = 1.75% (c.c.), USD interest rate rf = 2.75% (c.c.). The spot USD/CAD exchange rate is $1.32.

a) What is the one year forward USD/CAD exchange rate F0,1? Does this mean a stronger or a weaker Canadian dollar (relative to the US dollar)?

b) Suppose someone offers to sell you $1,000,000 U.S. dollars for $1,310,000 Canadian dollars in one year’s time. If you agree to this trade, what is the future value (in 1 year) of your expected profit/loss?

c) Suppose instead they offer to buy $1 million USD from you for $1.31 million CAD in one year’s time. Construct an arbitrage portfolio (of some amount of USD and some amount of CAD) that will guarantee you a profit.

Answer 1

a) Calculating one-year forward rate:

Forward exchange rate = Spot rate X [(1+ domestic interest rate)/(1+ foreign interest rate)]

USD/CAD spot Exchange rate= $ 1.32

CAD Interet rate = 1.75% (continuous compounding)(rd)

USD Interest Rate = 2.75% (continuous compounding)(rf)

Since interest is continuous compounding:

Forward exchange rate = spot rate X (e(rdt))/erft) (note standard value of e= 2.718218)

=(1.32)*[ (e^(0.0175)/e^(0.0275)] = 1.31 (lower than current rate)

This means a stronger Canadian dollar ( relative to the US Dollar)

To get an arbitrage Dollars Let us booson in the Canadian mosteet since it has a lower interest rate and deposit in USB CAD interest rate rd = 1.75% USD interest rate of = 2.75 % Since we need to sell $ 1 million USD in one year's do to get 1 million after one time year. we need to invest an amount that would earn 48 USD 1 million 8 x keep the deposit amount a to day @ 10.0275) a = 1000 000 2= 1 000 000 = 1000000=972767 e 10.0275 1.028 - 972762 Multiply it with current exchange rate 972762 X 1.32 -


If someone offers to sell $1000000 U.S. dollars for $1310000 Canadian dollars in one year's time the in the forward rate computed previous cas part is $ 1:31 & no poofet one I rate year from now will be earned will then be as enchange $ 1.31 CAD = 1 USD Answes $0 profit