Deck 6: Interest-Rate Forwards Futures

Question 1

Eurodollar deposits are
(a) Deposits that may be made in euros or dollars.
(b) Euro denominated deposits that are redeemable in dollars.
(c) Dollar denominated deposits made in banks in Europe.
(d) Euro denominated deposits made in the US.

Answer 1

C.

Question 2

Consider a 6×12 FRA where the underlying six-month period is 183 days and the notional is $100. The FRA fixed rate is 5%. At maturity of the contract the underlying Libor for six months is 7%. What is the settlement amount on the FRA? Assume the Actual/360 convention.
(a) 0.9683
(b) 0.9687
(c) 0.9817
(d) 1.0167

Answer 2

C.

Question 3

The convexity bias between FRAs and eurodollar futures implies that
(a) The futures results in greater cash outflows or smaller cash inflows than the FRA.
(b) The futures settlement amount is convex in Libor rates.
(c) The futures results in greater cash inflows or lower cash outflows than the FRA.
(d) The FRA payoff minus the futures payoff is convex in Libor rates.

Answer 3

C

Question 4

A $100 notional 6×12 FRA has the following features at inception. The first six month period is 182 days and the second is 183 days. The locked-in rate on the FRA is 6%. After one month the 5×11 FRA is trading at a fair strike of 6.2% with 151 days in the first five month period. What is the value of the FRA to the buyer if the five-month Libor rate at this point is is 5%?

A) (+0.0965)
B) (?0.0965)
C) $+ 0.0986$
D)( -0.0986)

Question 5

You borrow money at Libor with a floating-rate note for one year with two semi-annual payments. What position do you need to add to this note to fix the cost of borrowing for the entire year?

A) Sell a $6 \times 12$ FRA.
B) Buy a $6 \times 12$ FRA.
C) Buy a one-year zero-coupon bond and short a 1.5-year zero-coupon bond.
D) Buy a six-month zero-coupon bond and short a one-year zero-coupon bond.

Question 6

A $100,000,000 $3 \times 6$ FRA has a fixed rate of 4%. The first three-month period is for 91 days and the second one for 92 days. The 91-day Libor rate is 3% and the 183-day Libor rate is 3.5%. The value of this contract to the buyer of the FRA is

A) $- \$ 8913$
B) $- \$ 4822$
C) $+ \$ 3289$
D) $+ \$ 5433$

Question 7

Your bond portfolio has a value of $10,600,000 with a duration of 2.2 years. How many 90-day US Treasury bill futures contracts do you need to hedge this exposure if the futures contract is priced at $995,000? Assume you are carrying out duration-based hedging.
(a) 1.21
(b) 5.86
(c) 10.65
(d) 93.75

Question 8

Bonds A and B both have a duration of exactly one year. An equally-weighted portfolio of these bonds will have a duration of
(a) Greater than 1 year because duration is additive.
(b) Equal to one year because the average duration is still one year.
(c) Less than one year, because duration is a measure of risk, and combining two bonds into a portfolio diversifies away risk.
(d) Cannot say because the outcome depends on the interaction of specific cash flows of both bonds.

Question 9

You plan to borrow $1,000,000 for six months (183 days) in six months' time (182 days). The current Libor rate for six months is 6%. You want to hedge your interest-rate exposure by using 90-day eurodollar futures contracts that mature in six months. Using PVBP analysis, how 90-day eurodollar futures contracts are needed for this hedge?
(a) 1.79
(b) 1.85
(c) 1.92
(d) 2.00

Question 10

When you are short a position in a $3 \times 6$ FRA, you are effectively

A) Long the three-month zero-coupon bond, and long the six-month zero-coupon bond.
B) Long the three-month zero-coupon bond, and short the six-month zero-coupon bond.
C) Short the three-month zero-coupon bond, and long the six-month zero-coupon bond.
D) Short the three-month zero-coupon bond, and short the six-month zero-coupon bond.

Question 11

You are given the following data concerning a 6×12 FRA. The first six-month period is 182 days and the second is 183 days. The Libor rate for six months is 5% and for one year is 6%. The arbitrage-free price of the 6×12 FRA, assuming the Actual/360 day-count convention, is
(a) 5.50%
(b) 6.22%
(c) 6.55%
(d) 6.82%

Question 12

All else being equal, a bond with a higher coupon has a duration that is ________ than that of a bond with a lower coupon.
(a) greater than.
(b) less than.
(c) equal to.
(d) undetermined in relation to.

Question 13

The quoted price on a 91-day Treasury bill is 5. What is the cash price of the bill?
(a) 95.00
(b) 98.50
(c) 98.74
(d) 98.75

Question 14

Ceteris paribus, as interest rates rise, which of these statements is most likely to be true?
(a) The duration of bonds rises.
(b) The duration of bonds falls.
(c) Newly issued bonds have a higher duration than bonds issued some time ago.
(d) The volatility of bonds increases.

Question 15

You are long 5 eurodollar futures contracts. If the Libor rate underlying the contract increases by 5 basis points, your position gains the following value:
(a) ?$25
(b) +$25
(c) ?$125
(d) +$125

Question 16

ABC Inc. has to borrow money to undertake a seasonal business expansion in six months time. They will need additional working capital funding for six months and wish to hedge themselves against a rise in interest rates in six month's time. They should
(a) Take a short position in a 6×12 FRA.
(b) Take a long position in a 6×12 FRA.
(c) Lend the notional amount for one year and borrow the same amount for six months, both at the spot rates prevailing today.
(d) Lend the notional for one year, wait six months, and borrow the same amount for six months at the spot rate prevailing then.

Question 17

Eurodollar deposits follow the money-market day-count convention. Suppose a deposit is made for 92 days at a Libor rate of 4% on a notional amount of $100. The interest amount is
(a) 1.0082
(b) 1.0099
(c) 1.0101
(d) 1.0222

Question 18

The payoff of the FRA has the following property
(a) It is convex in the Libor rate.
(b) It is linear in the Libor rate.
(c) It is concave in the Libor rate.
(d) None of the above.

Question 19

The September eurodollar contract is trading at 95. You have a 90-day borrowing commencing in September for $500,000,000 that you wish to hedge using futures. How many eurodollar futures contracts should you buy (rounded off to the nearest integer)?
(a) 490
(b) 492
(c) 494
(d) 500

Question 20

In satisfaction of a US Treasury bond futures contract, the short position delivers a 15-year 9% bond instead of the standard bond. What is the conversion factor on this delivery? Assume the last coupon on the bond was just paid.
(a) 1.255
(b) 1.294
(c) 1.354
(d) 1.446

Question 21

You are long an $3 \times 6$ FRA and long a eurodollar futures contract expiring in 3 months. Assume the fixed rate in the FRA is the same as the rate locked-in via the eurodollar futures contract. If interest rates jump down by 100 basis points,

A) There is no net cash flow consequence because you are perfectly hedged.
B) You will lose more on the FRA than you will make on the eurodollar futures.
C) You will make more on the FRA than you will lose on the eurodollar futures.
D) You will lose less on the FRA than you will make on the eurodollar futures.

Question 22

You are short an $3 \times 6$ FRA and short a eurodollar futures contract expiring in 3 months. Assume the fixed rate in the FRA is the same as the rate locked in via the eurodollar futures contract. If interest rates jump up by 100 basis points,

A) You will lose money on both the FRA and the eurodollar futures.
B) You make money on the FRA but lose on the eurodollar futures.
C) You make money on both the FRA and the eurodollar futures.
D) You lose money on the FRA but make money on the eurodollar futures.

Question 23

Suppose the duration of a bond portfolio is 2. This means
(a) The final cash flow from the portfolio will occur in two years.
(b) The weighted-average maturity of the portfolio's cash flows is 2 years.
(c) The portfolio is fully equivalent to a 2-year zero-coupon bond.
(d) The portfolio is fully equivalent to a 2-year par-coupon bond.

Question 24

You anticipate a three-month borrowing in 6 months' time. To hedge the interest-rate exposure you can go either

A) Long a $6 \times 9$ FRA or long a eurodollar futures contract maturing in 6 months.
B) Short a $6 \times 9$ FRA or long a eurodollar futures contract maturing in 6 months.
C) Long a $6 \times 9$ FRA or short a eurodollar futures contract maturing in 6 months.
D) Short a $6 \times 9$ FRA or short a eurodollar futures contract maturing in 6 months.

Question 25

A long position in a $6 \times 9$ FRA can be replicated using

A) A six-month borrowing combined with a 9-month investment.
B) A six-month investment combined with a 9-month borrowing.
C) A six-month investment combined with a 3-month borrowing.
D) A six-month borrowing combined with a 3-month investment.

Question 26

A long position in a eurodollar futures contracts expiring in June may be used to hedge interest-rate exposure resulting from a planned
(a) 90-day borrowing ending in June.
(b) 90-day borrowing beginning in June.
(c) 90-day investment ending in June.
(d) 90-day investment beginning in June.