Risk Management

Exercise 1

You are the finance director of CR7, a US based manufacturer of luxury products.

The CEO has just signed a large contract with ‘Hotel de Paris’ from Monaco for a

large delivery of accessories, worth € 1 million. Both delivery and payment are

due in 7 months from now. At the current exchange rate of about 1.25 $ per €, this

contract is worth about $ 1.25 million.

a. Represent graphically the cash flow (in $) of CR7 in six months on a figure as a function of the $/€ exchange rate, supposing that CR7 remains long in €, i.e. if it does not hedge.

b. The current US interest rate is 3%, the euro area interest rate is 1%. Calculate the arbitrage-free 7-month forward price for the $/€ exchange rate. Show how this currency forward contract can be replicated by buying / lending $ and/or €’s.

The formula to calculate arbitrage-free 7-month forward price is: F = S0*e^(r$ – r €)t. With S0= spot price of exchange rate, r$ = US $ interest rate, r € = euro € interest rate, t= time in years.

F = 1,25 * e(0,03 – 0,01)*(7/12)

F = 1,2647 $/€

To receive at t=1: $ 1.264.668,735

Replicating strategy:

Buy: € 1.000.000 * e-0,01*(7/12). The cost in $ is then equal to €1.000.000 * e-0,01*(7/12) * $1,25/€.

This is $1.242.729,559.

Borrow: PV(F) = €1.000.000 * F * e-0,038(7/12) = €1.242.729,559

Calculate F in such a way that this portfolio has zero cost:

€1.000.000 * F * e-0.03*(7/12) = 1.25 * e-0.01*(7/12)

€1.000.000 * F * e-0.03*(7/12) = 1.242.729,559

€1.000.000 * e-0.03*(7/12) = 982.652,236

F = 1.242.729,559/982.652,236 = 1,2647

Result of the replicating strategy:

Buy: St*e-RfT = 1.25 * e-0,01*(7/12) = 1.242.729,559

Borrowing: F*e-RhT = F * e-0,03*(7/12) = 1.242.729,559

Net cash flow: = 0

Cash flow at time T:

Foreign deposit ST =1.250.000

Repay domestic loan F = 1.264.668,735

c. Describe the position in this forward contract if management of CR7 would decide to fully eliminate exchange rate...