Question

Suppose a Canadian bond portfolio manager wishes to enhance his yield on Canadian short-term bills. Current one-year Canadian T-Bills yield 13%. The current spot rate is C$ 1.40/$. The one-year forward rate is C$ 1.50/$. The US one-year T-Bill rate is 6%. What is the Canadian T-Bill rate implied by interest rate parity? What percentage yield could the portfolio manager obtain by exploiting the arbitrage opportunity? (Show your calculations!)

Answer 1

1 year interest rate in US =6%

Spot exchange rate $1 = 1.40 C$

Forward rate $1= 1.50 C$

Years (n)= 1

Forward rate as per Interest parity formula

Forward rate = spot rate * (1+ canada. T-bill interest rate)^n / (1+U.S interest rate)^n

1.50 = 1.40*(1+Canada interest yield)^1/ (1+6%)^1

1.5/1.40*1.06= (1+Canada t-bill yield)

Canada t-bill yield = 1.135714286-1

=0.135714286 or 13.57%

So Canada t-bill rate should be 13.57%

B.

Actual Canada rate = 13%

So it is lower compared to Interest rate parity rates. So Investment should be made in US Currency by borrowing from canada Currency

Arbitrage strategy:

Borrow Canadian dollar 1000000

Convert to US$ at current rate = 1000000/1.40

=714285.7143

Investment in US $ 714285.7143

Received interest 6%+ principal = (714285.7143*6%)+714285.7143

757142.8572

Conversion in Canadian dollar= 757142.8572*1.50

=1135714.286

Interest + principal repaid in C$ =(1000000*13%)+1000000

=1130000

Net gain =1135714.286-1130000

=5714.286

% of gain = 5714.286/1000000

=0.005714286 or 0.57%