3.4 Swaps

3.4 Swaps

Question 1

Two companies, C and D, have the borrowing rates shown in the following table.

According to the comparative advantage argument, what is the total potential savings for C and D if they enter into an interest rate swap?

A. $0.5\%$
B. $1.0\%$
C. $1.5\%$
D. $2.0\%$

Answer: C
The difference of the differences is (12% - 10%) - [LIBOR + 1% - (LIBOR + 0.5%)] = 1.5%.

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Question 2

PE2018Q60 / PE2019Q60 / PE2020Q60 / PE2021Q60 / PE2022Q60
An oil driller recently issued USD $250$ million of fixed-rate debt at $4.0\%$ per year to help fund a new project. It now wants to convert this debt to a floating-rate obligation using a swap. A swap desk analyst for a large investment bank that is a market maker in swaps has identified four firms interested in swapping their debt from floating-rate to fixed-rate. The following table quotes available loan rates for the oil driller and each firm:

A swap between the oil driller and which firm offers the greatest possible combined benefit?

A. Firm A
B. Firm B
C. Firm C
D. Firm D

Answer: C
Learning Objective: Describe the comparative advantage argument for the existence of interest rate swaps and evaluate some of the criticisms of this argument.

Since the oil driller is swapping out of a fixed-rate and into a floating-rate, the larger the difference between the fixed spread and the floating spread the greater the combined benefit.

See table below:

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Question 3

Firm X wants to borrow GBP at a floating interest rate, and Firm ‘I’ wants to borrow GBP at a fixed annual interest rate. The interest rates that they face are shown in the table below. What is the maximum spread a financial intermediary could get if it designs a swap making firms X and Y each better off by $20$ basis points?

A. $5$ basis points
B. $10$ basis points
C. $15$ basis points
D. $20$ basis mints

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Question 4

PE2018Q78 / PE2019Q78 / PE2020Q78 / PE2021Q78 / PE2022Q78
A financial institution entered into a 4-year currency swap contract with a French industrial company. Under the terms of the swap, the financial institution receives interest at $3\%$ per year in EUR and pays interest at $2\%$ per year in USD. The principal amounts are EUR $50$ million and USD $60$ million, and interest payments are exchanged once a year. Suppose that it is exactly one year before expiration of the swap contract and just in time for the year $3$ cash flow payments and receipts when the exchange rate is USD $1.044$ per EUR $1$, the 1-year French risk-free rate is $3.0\%$ and the 1-year US Treasury rate is $2.0\%$. Assuming continuous compounding, what is the value of the swap to the financial institution at the end of year $3$?

A. USD $-7.603$ million
B. USD $-7.456$ million
C. USD $-7.068$ million
D. USD $-6.921$ million

Answer: B
Learning Objective: Explain the mechanics of a currency swap and compute its cash flows.

Step 1: calculate the forward exchange rates as at the end of year $3$:

1 year forward exchange rate (USD per EUR):
$F=S\times e^{(r_{usd}–r_{eur})\times T}=1.044\times e^{(0.02–0.03)\times 1}=1.0336$

Step 2: calculate the expected cash flows as at year 3:
Receipts:
Year 3: EUR $50\times 0.03=1.5\text{million}$
Year 4: EUR $50\times 0.03+50=51.5\text{million}$
Payments:
Year 3: USD $60\times 0.02=1.2\text{million}$
Year 4: USD $60\times 0.02+60=61.2\text{million}$

Step 3: convert the EUR cash flows into base currency, i.e. USD:
Receipts:
Year 3: USD $1.5\times 1.0440=1.566\text{million}$
Year 4: USD $51.5\times 1.0336=53.2304\text{million}$

Step 4: Net the cash flows per year:
Year 3: USD $1.566-1.2=0.366\text{million}$
Year 4: USD $53.230-61.2=-7.969\text{million}$

Step 5: discount to year 3 and sum the cash flows in USD:
Year 3: Present value USD $0.366\text{million}$
Year 4: Present value USD $-7.969\times e^{-0.02\times 1}=-7.811\text{million}$

Net value to the financial institution $0.366-7.811=-7.456\text{million}$

A is incorrect. USD $-7.603$ million uses the appropriate exchange rates but does not discount back to year $3$.

C is incorrect. USD $-7.068$ million uses the current USD per EUR rate (USD $1.044$) to convert the EUR cash flows and does not discount back to year $3$.

D is incorrect. USD $-6.921$ million uses the current USD per EUR rate (USD $1.044$) to convert the EUR cash flows; however, it does discount back to year $3$.

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Question 5

PE2018Q34 / PE2019Q34 / PE2020Q34 / PE2022Q34 / PE2022PSQ24 / PE2022Q34
Savers Bancorp entered into a 2-year interest rate swap on August 9, 2014, in which it received a $4.00\%$ fixed rate and paid LIBOR plus $1.20\%$ on a notional amount of USD $6.5$ million. Payments were to be made every 6 months. The table below displays the actual annual 6-month LIBOR rates over the 2-year period:

Assuming no default, how much did Savers Bancorp receive on August 9, 2016?

A. USD 72,150
B. USD 78,325
C. USD 117,325
D. USD 156,650

Answer: B
Learning Objective: Explain the mechanics of a plain vanilla interest rate swap and compute its cash flows.

The proper interest rate to use is the 6-month LIBOR rate at February 9, 2016, since it is the 6-month LIBOR that will yield the payoff on August 9, 2016.

Therefore, the net settlement amount on August 9, 2016 is as follows:
Savers Bancorp receives: $6,500,000\times 4.00\%\times 0.5$, or USD $130,000$
Savers Bancorp pays: $6,500,000\times (0.39\%+1.20\%)\times 0.5$, or USD $51,675$

Therefore, Savers Bancorp would receive the difference of USD 78,325,

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Question 6

Consider a USD $1$ million notional swap that pays a floating rate based on $6$-month LIBOR and receives a $6\%$ fixed rate semiannually. The swap has a remaining life of $15$ months with pay dates at $3$, $9$ and $15$ months. Spot LIBOR rates are as following: $3$ months at $5.4\%$; $9$ months at $5.6\%$; and $15$ months at $5.8\%$. The LIBOR at the last payment date was $5.0\%$. Calculate the value of the swap to the fixed-rate receiver using the bond methodology.

A. USD $6,077$
B. USD $-6,077$
C. USD $-5,077$
D. USD $5,077$

Answer：D

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