Question

2.       Suppose a Canadian agent (investor) with C$1.0 million is choosing between bank deposits denominated in either euro or Canadian dollars.  Also suppose that the (one-year) interest rate paid on the C$ deposits is 1% (0.01) and on the euro deposit is 2% (0.02), the (one-year) forward C$-EURO exchange rate (F_C$/€ ) is 1.60 and the current spot rate (E_C$/€ ) is 1.65.  Based on this information, answer the following questions.

      

(a)     What is the forward spread? Is the Canadian dollar at forward premium or discount? And by how much (%)?

      

(b)   What is the (hedged = riskless) rate of return on the euro deposits?

 

(c)   Based on your answer above, is there an arbitrage opportunity between the two deposits?  Explain why or why not. 

 

(d)   If the spot rate of exchange as well as the interest rates are kept at their current levels (stated above), what will be equilibrium forward rate as implied by the covered interest parity theory (CIP)?

Answer 1

a) The forward for CAD/EUR is 1.60 while the spot rate is 1.65.
1.65 - 1.60 = 0.05
The forward exchange rate for CAD/EUR is at the premium by 0.05.
(0.05 / 1.65) * 100 = 3.03%

b) The return in CAD
1000000 * 0.01 = 10000 CAD

Return on EUR is 2%
1000000 / 1.65 = 606060.61
606060.61 * 0.02 = 12121.21

c) The arbitrage opportunity is possible if the exchange rate deviates from the interest rate parity condition.
(Forward Rate / Spot Rate ) = (1+Interest Rate in EUR) / (1+Interest Rate in CAD)

(Forward Rate / Spot Rate ) = 1.6 / 1.65 = 0.9697
(1+Interest Rate in EUR) / (1+Interest Rate in CAD) = (1.02 / 1.01) = 1.0099

Since these two values are not equal so there is an opportunity for arbitrage.

d) If there is any discrepancy in the spot rate of forward rate so that the interest rate parity condition is being violated then arbitrage trade is possible and will result in risk less profit.
However, the market forces will quickly negate that situation.

(Forward Rate / Spot Rate ) = (1+Interest Rate in EUR) / (1+Interest Rate in CAD)
Forward Rate = Spot Rate * (1+Interest Rate in EUR) / (1+Interest Rate in CAD)
1.65 * (1.02 / 1.01) = 1.65 * 1.0099
Forward Rate = 1.6663

Answer 2

Total Amoun of Investment in US $ Million Amount = 1.00
(one-year) interest rate paid on the $ deposits RUSD =   1.00%
(one-year) interest rate paid on euro deposit is REURO =  2.00%
forward $-EURO exchange rate (F$/€ ) is FR = 1.60
current spot rate (E$/€ ) SR = 1.65

Ans (a)

forward spread = Forward Price - Spot Price = FR - SR = 1.60 - 1.65 = ( 0.05)

As FR < SR, forward Dollar Rate is lower than the spot rate, So the Dollar is at Discount..

% of Discount = spread /  Spot Price = 0.05 / 1.60 = 3.030%

Ans (b)

the (hedged = riskless) rate of return on the euro deposits

What is the (hedged = riskless) return on the euro deposits

=   Amoun of Investment in US $ * ( Current Spot Rate / Forward Rate) * ( 1+ Euro Int Rate)

= Amnt * ( SR / FR) * ( 1+ REURO )

= 1 * (1.65/1.60) * (1 + 2%)

= 1.0518750

Here The Steps as follow :

Step 01: Convert the USD in EURO in Current Spot Rate = Amnt * SR

Step 02 : Invest this Amount in EURO Market for 01 Year = Amnt * SR * ( 1 + REURO )

Step 03 : Convert the EURO Return as per determined future rate =  Amnt * SR * ( 1 + REURO ) / FR

rate of return on the euro deposits = ( return on the euro deposits - Amoun of Investment ) / Amoun of Investment  

= ( 1.0518750 - 1) / 1 = 5.18%

the (hedged = riskless) rate of return on the euro deposits = 5.18% (Ans)

Ans c :

Riskless Return in EURO Deposit is 5.18% which is much higher than current prevailing Deposit rate in US Market is 01%.

So There is a Arbitrage Opportunity. (Ans)

Ans d.

according to covered interest parity (CIP) equilibrium Forward Rate

FR = SR * (1 +  REURO ) / (1 + RUSD) =  1.65 * ( 1 + 2%) / (1 + 1%) =  1.666

so, equilibrium Forward Rate  1.666  E$/€ (Ans)

B Now Total Amoun of Investment in US $ Million (one-year) interest rate paid on the $ deposits (one-year) interest rate paid on euro deposit is forward $-EURO exchange rate (F$1€ ) is current spot rate (E$/€) 1.00 1.00% 2.00% 1.60 1.65 Spread -0.05 Spread of Percentage 3.030% What is the hedged = riskless rate of return on the euro deposits 1.0518750 according to covered interest parity (CIP) Forward Rate 1.666 12 13

MON 0 Total Amoun of Investment in US $ Million (one-year) interest rate paid on the $ deposits (one-year) interest rate paid on euro deposit is forward $-EURO exchange rate (F$/€ ) is current spot rate (E$/€ ) 1.00 1.00% 2.00% 1.60 1.65 Spread Spread of Percentage =B5-B6 -B9/B6 10 12 What is the (hedged = riskless rate of return on the euro deposits =B2*(B6/B5)*(1+B4) according to covered interest parity (CIP) Forward Rate =B6*(1+B4)/(1+B3) 13 15