Question

In: Finance

Suppose an agent (investor) from the U.S. with $1.0 million is choosing between bank deposits denominated...

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

(a) What is the forward spread? Is the 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 the equilibrium forward rate as implied by the covered interest parity theory (CIP)?

Expert Solution

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)

jeff jeffy answered 1 year ago

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