Problem 1

Spot exchange rate is $1.3148 = 1 Euro. Interest rates are 1% in the U.S. and 3% in the Euro zone. One year futures contract on one million Euros is currently trading at $1.3200 per Euro.

a. Using the interest parity, show that the futures price is too high.

b. Suppose your bank enters a contract to sell 1,000,000 Euros at $1.32 in one year to a corporate client. What spot exchange rate movement would reduce the value of the deal to the bank?

c. Find the delta of the bank's position.

d. To protect the profit from the deal, should the bank borrow or invest in Euro today? What's the needed amount in Euro?

Problem 2

Analyze a two-year swap agreement to exchange LIBOR for fixed-rate payments on a $100 million notional principal. The first payment will be made in one year; the second in two years. You have the following information on LIBOR rates: One-year spot rate s1=3% per year. Two-year spot rate s2=4%. Annual compounding applies.

a) Find the forward rate f for the second year

b) Find the floating-rate payments to be made.

c) Find the present value of the floating-rate payments.

d) Find the fixed rate that would price the swap correctly.

Problem 3

You are a consumer of crude oil. A December light sweet crude futures settled at $60 a barrel. The contracts are for 1000 barrels each. You decide to hedge 100,000 barrels of your reserves with this futures contract.

a. Under each of the following scenarios, show the value of your futures position, the value of your physical crude oil position, and the total portfolio value on the maturity day. Please analyze each of your positions in this problem individually, i.e. as if the other position did not exist; and then simply add up the values of the two positions to get the total value under each scenario.

Maturity Day Spot Oil Price, $$ per bbl

50

60

70

Value of your position in the futures

Value of your physical position in crude oil

TOTAL

Multiple Choice

1. Cash-settled futures positions are marked to market daily but physically delivered futures positions are not. (True / False)

2. An electric power producer (e.g., a utility company) uses natural gas as fuel. It hedges with natural gas futures. So it has a _______ exposure to the price of natural gas through its physical position, and a ________ exposure to the price of natural gas through its futures position.

a. long; long

b. long; short

c. short; long

d. short; short

3. Convergence property implies that the futures price and the spot price change by the same amount from the day one enters the contract to the maturity day. That is, convergence property implies (ST - S0) = (FT - F0). (True / False)

4. When the term structure of interest rates is upward-sloping (yields are increasing with maturities), this can be if:

a. Forward rate is higher than expected future spot rate

b. Forward rate is equal to the expected future spot rate

c. Either a or b

5. 5-year CDX NA IG index is quoted by a market maker as bid 165 bp, ask (offer) 166 bp. This index includes 125 North American investment-grade companies. Suppose you want $800,000 of protection for each company. When one of the 125 companies defaults, your annual premium payment will be reduced by how much?

a. $800,000

b. $6,400

c. $13,200

d. $13,280

6. The LIBOR rate is which of the following?

a. Overnight borrowing/lending rate between banks and the Central Bank

b. Unsecured short-term borrowing rate between banks

c. Secured borrowing rate between banks

7. A speculator who has a _______position in foreign currency futures wants the foreign currency to _______ against the domestic currency in the future.

e. long; appreciate

f. long; depreciate

g. short; appreciate

h. long; stay the same

i. short; stay the same

8. For commodity futures, when convenience yield is smaller than the carrying cost, F > S (contango). (True / False)

9. A CDS is an instrument that provides insurance against default by a particular company. This company is known as

1. Reference entity
2. Cheapest to deliver bond

10. Risk-neutral probability of default:

a. Prices the credit default swap at its current value using the risk-free rate

b. Is lower than the physical probability of default

c. Both of the above