Deck 21: Swaps and Floating Rate Products

Question 1

The main difference between the "short-form" and "forward" methods of pricing a floating-rate note is:
(a) The short-form method gives lower prices than the forward method.
(b) The short-form method gives higher prices than the forward method.
(c) The short-form method does not require knowledge of the entire forward term structure of interest rates.
(d) The short-form method does not use the entire forward term structure of interest rates and hence results in less accurate prices.

Answer 1

C.

Question 2

A bank makes long-term fixed-rate loans, and funds itself with short-term deposits. It can best manage its vulnerability to interest rate changes by
(a) Entering into a basis (floating-floating) swap.
(b) Entering into a pay-floating/receive-fixed interest rate swap.
(c) Entering into a pay-fixed/receive-floating interest rate swap.
(d) Entering into a fixed-fixed swap where the two legs have different payment frequencies.

Answer 2

C.

Question 3

A plain vanilla interest-rate swap is an agreement to exchange a series of periodic payments, one computed at a fixed rate and the other at
(a) A floating rate indexed to a money-market rate in the same currency (e.g., Libor).
(b) A floating rate linked to the return on any financial index, e.g., an equity index.
(c) A floating rate indexed to a money-market rate in the same or a different currency.
(d) A floating rate indexed to a commodity (e.g., gold) price.

Answer 3

A.

Question 4

Which of the following is not true of a standard floating-rate note on a coupon reset date?
(a) The next coupon payment is set based on prevailing market rates.
(b) The principal is unchanged.
(c) The ex-coupon price (the price of the note not including the coupon immediately due) of the note is par.
(d) The cum-coupon price (the price of the note including the coupon immediately due) is par.

Question 5

An important difference between a floating-rate note and a fixed-rate note indexed to Libor is that

A) The return from holding a fixed-rate note over any holding period is deterministic and known because of the fixed coupon payments, whereas the similar return on a floating rate note is unknown because the coupon "floats."'
B) The price of the floating-rate note resets to par on each coupon/reset rate, whereas that of the fixed-rate note does not necessarily do so.
C) The price of the fixed-rate note is deterministic and known because the bond pays fixed coupons whereas the floating-rate note has a fluctuating price because it pays floating interest rates.
D) A fixed-rate note is always worth par at issue whereas the floating-rate note may not be.

Question 6

The main difference between the "short-form" and "forward" methods of pricing a floating-rate note is:
(a) The short-form method is a computational short cut that is correct on average but may yield higher or lower prices than the forward method.
(b) The short-form method always works well whereas the forward method works well if interest rates are deterministic but not if they are stochastic.
(c) The short-form method requires knowledge of the term-structure of interest rates only out to the next coupon payment whereas the forward method requires knowledge of the entire interest-rate curve out to the maturity of the bond.
(d) The short-form method results in too high a price (relative to the forward method) if the term-structure of interest rates is downward sloping, and too low a price if it is downward sloping.

Question 7

Choose the most appropriate of the following alternatives: an off-market swap is one where the fixed rate in the swap is
(a) Higher than the prevailing swap rate.
(b) Lower than the prevailing swap rate.
(c) Equal to the prevailing swap rate.
(d) Different from the prevailing swap rate.

Question 8

An amortizing interest-rate swap is one in which
(a) The fixed interest rate in the swap declines in a specified manner over the life of the swap.
(b) The floating interest rate in the swap declines in a specified manner over the life of the swap.
(c) The notional principal amount in the swap declines in a specified manner over the life of the swap.
(d) The time-period between payments in the swap gets shorter in a specified manner.

Question 9

You enter into a $100 million notional swap to pay six-month Libor and receive 8%. Payment dates are semi-annual on both legs. The last payment date was March 25 and the next payment date is September 25. Floating payments are based on the USD money-market convention, and fixed payments are based on the 30/360 convention. If the net payment you will receive on September 25 is zero, what must have been the Libor reset on march 25?
(a) 6%.
(b) Higher than 6%.
(c) Lower than 6%.
(d) Cannot be calculated from the given information.

Question 10

In a plain vanilla fixed-for-floating swap,
(a) Fixed payments and floating payments must be made on the same date.
(b) Fixed payments and floating payments may follow different payment cycles.
(c) Fixed payments are made semi-annually while floating payments are quarterly.
(d) Fixed payments are known ahead of time while the floating payment due on a particular date gets to be known only on that date.

Question 11

Firm A can borrow at 4% fixed or in the floating-rate market at Libor flat. Firm B can borrow at 7% fixed or at Libor $+ 100$ bps. A wants to borrow floating and B fixed. Suppose that to reduce financing costs, A borrows fixed, B borrows floating, and they enter into an interest-rate swap. Which of the following statements is valid?

A) The combined improvement in cost of financing to A and B with the swap is always equal to the difference between the fixed rate differential (between A and B) and the floating rate differential which in this case is 200 basis points.
B) The combined improvement in cost of financing to A and B with the swap is always equal to the floating rate differential, which in this case is 100 basis points.
C) The combined improvement in cost of financing to A and B with the swap depends on the negotiated fixed rate on the swap between the two counterparties.
D) No improvement in combined financing costs is possible-what one party gains in financing costs, the other party loses.

Question 12

The UK money-market day-count convention is
(a) Actual/365.
(b) Actual/360.
(c) Actual/Actual.
(d) 30/360.

Question 13

Firm A can borrow at 4% fixed or at Libor flat in the fixed and floating rate markets, respectively. Firm B can borrow at 7% fixed or Libor plus 100 bps in the fixed and floating rate markets, respectively. A wants to borrow floating and B wants to borrow fixed. If A borrows fixed and B borrows floating and they enter into a fixed-for-Libor interest-rate swap in which A pays Libor flat, what is the range of fixed rates for B that enables each firm to improve its financing costs (compared to accessing financing in the market directly)?
(a) 4%-7%
(b) 4%-6%
(c) 5%-6%
(d) 5%-7%

Question 14

Your firm can borrow fixed at 8% and floating at Libor+1%. You can also enter into a fixed-for-Libor swap where the fixed rate is 7.5% (and the swap has the same maturity as the borrowing). What is the cheapest way for the firm to obtain fixed rate financing?
(a) Borrow at the fixed rate.
(b) Borrow at the fixed rate and then swap into floating rate using the swap.
(c) Borrow floating rate and then swap into fixed rate using the swap.
(d) Both (a) and (b).

Question 15

You enter into a $100 million notional swap to pay six-month Libor and receive 8%. Payment dates are semi-annual on both legs. The last payment date was March 25 and the next payment date is September 25. Floating payments are based on the USD money-market convention, and fixed payments are based on the 30/360 convention. If the floating rate was reset to 6% on March 25, what is the net amount you will receive on September 25?
(a) $933,333
(b) $966,667
(c) $1,000,000
(d) $1,066,667

Question 16

Which of the following is not an interest-rate swap?
(a) A fixed-for-floating swap involving exchange of fixed interest rate payments in one currency for floating payments in the same currency but in which the swap NPV at inception is non-zero.
(b) A floating-for-floating swap in which one floating rate in a currency is exchanged for another floating rate in the same currency.
(c) A fixed-for-floating swap in which a fixed interest rate payment in one currency is exchanged for floating interest-rate payments in another currency.
(d) A fixed-for-floating swap involving exchange of fixed interest rate payments in one currency for floating payments in the same currency but in which the payments are computed on principal that is reduced in a pre-specified manner during the life of the swap.

Question 17

The US swap market convention, that is used to compute the fixed payments in a USD swap, is
(a) Actual/365.
(b) Actual/360.
(c) Actual/Actual.
(d) 30/360.

Question 18

The US and euro-zone day-count convention for a floating-rate note (based on Libor and Euribor, respectively) is
(a) Actual/365.
(b) Actual/360.
(c) Actual/Actual.
(d) 30/360.

Question 19

The US Treasury market day-count convention is
(a) Actual/365.
(b) Actual/360.
(c) Actual/Actual.
(d) 30/360.

Question 20

You enter into a $100 million notional swap to pay six-month Libor and receive 6%. Payment dates are semi-annual on both legs. The last payment date was March 25 and the next payment date is September 25. Floating payments are based on the USD money-market convention, and fixed payments are based on the 30/360 convention. If the floating rate was reset to 6% on March 25, what is the net amount you will receive on September 25?
(a) 0.
(b) -$66,667.
(c) +$66,667
(d) +133,333

Question 21

Consider a one-year caplet on underlying six-month Libor at a strike rate of 6%. If the corresponding floorlet is equal to the caplet in price, what is the current forward rate for the period (1,1.5) years?

A) $< 6 \%$
B) $= 6 \%$
C) $> 6 \%$
D) Cannot be determined from the given information.

Question 22

Consider a one-year maturity caplet on underlying six-month Libor at a strike rate of 6%. If the forward rate is lognormal with volatility $\sigma = 0.10$ , and the one-year spot rate is 5%, what is the price of a $100,000-notional caplet if the (1,1.5)-year forward rate is 6%?

A) $113.80
B) $139.34
C) $160.96
D) $227.59

Question 23

An equivalent description of the holding of a receive-floating pay-fixed swap is as follows:
(a) An exchange of a long position in a fixed-rate bond for a short position in a floating-rate note.
(b) A portfolio of long positions in forward-rate agreements (FRAs) for each swap payment date, all at the same fixed rate as the swap.
(c) A bond that pays the fixed rate minus the floating rate each period.
(d) All of the above.

Question 24

You have sold a $10,000 notional cap consisting of a single caplet with a strike of 6% for a six-month underlying period. All interest rates are computed based on the 30/360 convention. At maturity of the cap period, the underlying interest rate is 7%. What is the net cash flow to you on maturity?

A) $- \$ 50.00$
B) $+ \$ 48.31$
C) $- \$ 48.31$
D) $+ \$ 46.73$

Question 25

You have the view that rates will be rising over time. What is thebest kind of swap to exploit this view from among the following alternatives?
(a) Pay fixed, receive floating.
(b) Pay floating, receive fixed.
(c) A maturity-mismatch basis swap in which you pay floating indexed to three-month Libor and receive fixed indexed to six-month Libor.
(d) Pay fixed, receive floating on a reverse-amortization swap.

Question 26

You have entered into a swap where you receive the fixed rate and pay the floating rate. What is the best way to hedge interest-rate risk in this swap from among the following choices?
(a) Add a long position in fixed rate bonds.
(b) Add a short position in interest-rate futures.
(c) Add a basis (i.e., floating-floating) swap.
(d) Add a short position in FRAs.

Question 27

You enter into a $100 million notional swap to pay six-month Libor and receive $x$ %. Payment dates are semi-annual on both legs. The last payment date was March 25 and the next payment date is September 25. Floating payments are based on the USD money-market convention, and fixed payments are based on the 30/360 convention. If the floating rate was reset to 6% on March 25, what must be the minimum value of $x$ that ensures you will receive a positive net payment on September 25?

A) 5.87%
B) 5.95%
C) 6.00%
D) 6.01%

Question 28

If the (1,1.5)-year forward rate is lognormal with volatility $\sigma = 0.15$ , and the one-year spot rate is 4%, what is the NPV of a $100,000-notional $12 \times 18$ -FRA at a 5% strike rate if the (1,1.5)-year forward rate is 6%, as seen from the buyer's point of view? (Assume the Black model applies for interest-rate options.)

A) $- \$ 470.88$
B) $0
C) $475.61
D) $480.39

Question 29

The 4%-strike six-month Libor-based two-year cap and floor are trading at $2.30 and $2.55, respectively. Assume that the cap has 4 caplets maturing in 6 months, 1 year, 18 months, and 24 months, respectively, and that the floor similarly has 4 floorlets. What is the NPV at inception of a two-year swap in which you are paying Libor versus receiving 4%?

A) $- \$ 0.25$
B) $0
C) $0.25
D) There is not enough information to determine the price of the swap.

Question 30

Consider a $100 five-year zero-coupon swap to pay fixed and receive floating. The five-year spot rate is 5% expressed with semi-annual compounding. The floating leg makes payments every six months indexed to Libor. What is the final payment on the fixed leg of this swap?
(a) $78
(b) $100
(c) $125
(d) $128

Question 31

Suppose Libor caps and floors at the same strike rate are unequal in price. Suppose that, ceteris paribus, there is a sudden increase in interest-rate volatility. Which of the following statements is valid?
(a) Caps and floors will increase in value, but caps will increase by more than floors.
(b) Caps and floors will increase by the same amount.
(c) Caps and floors will increase in value, but caps will increase by less than floors.
(d) There is insufficient information to determine the answer.

Question 32

Which of the following isnot true of a swaption, i.e., an option on a swap?
(a) A swaption is always less valuable than the underlying swap.
(b) A swaption's value is always non-negative.
(c) A payer swaption is worth less than a cap with caplets on the same dates as the swap underlying the swaption.
(d) A swaption's value increases with interest rate volatility irrespective of which side of the underlying swap one may be on.

Question 33

Consider the following table of prices of five-year semi-annual pay caps and floors: $$\begin{array} { | c | c | c | } \hline \text { Strike (\%/) } & \text { Cap price } & \text { Floor price } \\\hline 4 \% & 2.50 & 0.50 \\\hline 5 \% & 1.50 & 1.50 \\\hline 6 \% / & 0.50 & 2.50 \\\hline\end{array}$$ Assume that the caps and floors also include the first payment in 6 months, so there are 10 payment dates in each instrument. The quoted prices of the caps and floors includes this first payment for which the floating leg has already been set. What is the fixed-rate on a five-year fairly priced swap?

A) 4%
B) 5%
C) 6%
D) Not possible to determine from the available information.

Question 34

You have a $50 cash flow that is to be received 1.3 years from now. The one-year zero-coupon rate is 6% and the one-and-a-half-year zero-coupon rate is 7%, both in continuously-compounded and annualized terms. If you preserve net present value and duration risk, how would you allocate the cash flow into two equivalent cash flows in the one-year and one-and-a-half-year buckets?
(a) 18.23 and 32.01
(b) 19.47 and 30.54
(c) 19.54 and 30.46
(d) 20.00 and 30.00

Question 35

Who is likely to bear the greater counterparty risk in a swap where A pays fixed and B pays floating if interest rates are expected to rise over the life of the swap?
(a) A.
(b) B.
(c) Both A and B.
(d) There is not enough information to determine the correct answer.