Chapter 2 Question 6

If the spot rate is 1.5 euros per pound, and interest rates are as stated previously, what is the equilibrium forward rate, according to CIP?

CIP implies: F€/£=E€/£ (1+i€)/(1+i£) =1.5x1.0404 / 1.02 =€1.53 per £.

Suppose the forward rate takes the value given by your answer to (d). Calculate the forward premium on the British pound for the Dutch investor (where ex- change rates are in euros per pound). Is it positive or negative? Why do investors require this premium/discount in equilibrium?

Forward premium (F€/£ / E€/£-1)=(1.53 / 1.50)-1 =0.02 =2%. The existence of a positive forward premium would imply that investors ex- pect the euro to depreciate relative to the British pound.Therefore, when estab- lishing forward contracts, the forward rate is higher than the current spot rate.

What is the (riskless) euro-denominated return on British deposits for this in- vestor using forward cover?

The euro-denominated return on British deposits using forward cover is equal to €1,071(=€1,000 x(1.575 / 1.5)x(1 +0.02)).

Consider a Dutch investor with 1,000 euros to place in a bank deposit in either the Netherlands or Great Britain.The (one-year) interest rate on bank deposits is 2% in Britain and 4.04% in the Netherlands.The (one-year) forward euro-pound exchange rate is 1.575 euros per pound and the spot rate is 1.5 euros per pound. Answer the following questions, using the exact equations for UIP and CIP as necessary. a. What is the euro-denominated return on Dutch deposits for this investor?

The investor's return on euro-denominated Dutch deposits is equal to €1,040.04(=€1,000x(1+ 0.0404)).

Based on your answer to (f), what is the expected euro-pound exchange rate one year ahead?

Using the exact UIP (not the approximation), we know that the following is true: Ee£/€=E£/€x(1+i€)/(1+i£) =1.5x1.0404/1.02 =€1.53 per £. Using the approximation, E£/€ decreases by 2.04% from 0.667 to 0.653.This implies the new spot rate, E€/£=1.53.

Is there an arbitrage opportunity here? Explain why or why not. Is this an equi- librium in the forward exchange rate market?

Yes, there is an arbitrage opportunity. The euro-denominated return on British deposits is higher than that on Dutch deposits.The net return on each euro deposit in a Dutch bank is equal to 4.04% versus 7.1% (=(1.575 / 1.5)x(1+0.02)) on a British deposit (using forward cover).

If UIP holds, what is the expected depreciation of the euro against the pound over one year?

According to the UIP approximation, Ee£/€ / E£/€=i£-i€=2.04%. Therefore, the euro is expected to depreciate by 2.04%. Using the exact UIP condition, we first need to convert the exchange rates into pound-euro terms to calculate the depreciation in the euro. From UIP: Ee£/€=E£/€X(1+i£)/(1+i€) =(1/1.5)x(1+0.02)/(1+0.0404) =£0.654 per €. Therefore, the depreciation in the euro is equal to 1.34% = (0.654-0.667).