Question

3. QRS, a German (currency EUR) corporation, will pay GBP 1,000,000 after one year to its supplier in the UK. The following quotes are current in the market:

One-year UK interest rate 2.25 percent

One-year Germany interest rate 1.75 percent

Spot exchange rate 1.2491 EUR/GBP

One-year forward exchange rate 1.2400 EUR/GBP

Assume the spot rate after one year can be 1.2000 EUR/GBP, 1.2400 EUR/GBP, or 1.2800 EUR/GBP.

(i) If QRS wanted to hedge this cash flow in the forward market, what contract would it need to enter into? Show the end-of-period cash flows in Euros for the possible future spot rates if QRS enters into this forward market hedge.

(ii) If QRS wanted to hedge this cash flow in the options market, what would it need to do? Suppose that the option premium is 3% of the exercise price, and the option is at the forward. Show the end-of-period cash flows in Euros for the possible future spot rates if QRS enters into this option market hedge (and include the option premium).

(iii) If QRS wanted to hedge this cash flow in the money market, what transactions would it need to enter into? Show the end-of-period cash flows in Euros for the possible future spot rates if QRS enters into this money market hedge.

(iv) Which of the above hedging possibilities should QRS choose and why?

(v) Does covered interest rate parity hold in this problem? If not, what should the UK interest rate be in order for covered interest rate parity to hold?

Answer 1

Part 1- Outflow int he forward market:

GBP 1000000 Payable, therefore- buy GBP forward at 1 year forward rate.

Amount payable= GBP1,000,000*1.24 EUR/GBP= EUR 1,240,000

Part 2- Outflow in the options market:

Since QRS has GBP payable, it should enter into C+ or P-

Steps to be followed for C+:

Step i): strategy: should be [email protected] EUR/GBP outflow

Step ii): Expected spot rate assuming equal probabilty of the spot rates= (1.2/3)+(1.24/3)+(1.28/3) = 1.24 EUR/GBP

Step iii) Expected payoff:

Spot rates- Eur/GBP	Call( Exercised/ lapsed)	Payoff	Probability	Net
1.2	Lapsed	0	0.3333	-
1.24	Lapsed	0	0.3333	-
1.28	Exercised	0.04	0.3333	0.0133
				0.0133	Inflow

Net cash outflow= GBP 1000000* (Premium + expected spot rate at end of year 1 - Net inflow in step 3)

= 1000000* (0.0372+1.24-0.01333)= EUR1,263,900

Part 3- Outflow if cash flow hedged in money market:

To hedge the cash flow in money market: Cut the exposure, so create GBP receivable as follows:

Steps:

a) Invest GBP today such that GBP reveiable after 1 year equals 1,000,000= 1000000/1.0225= GBP 977995.11

b) Euro needed to buy GBP= GBP 977995.1*1.2491EUR/GBP = 1,221,613.679

c) Borrow Euro at 1.75% per annum,

Amount payable after 1 year= EUR1221614*1.0175 = EUR1,242,992.245

Part 4- QRS should choose to hedge in the forward market as the outflow of EUR 1,240,000 is least under that option.