Derivatives【 Reading 38】习题精选 2012

optiix

Which of the following positions results in synthetic fixed-rate debt?

A) A long position in a floating-rate note combined with a pay-fixed interest rate swap.

B) A short position in a floating-rate note combined with a pay-fixed interest rate swap.

C) A long position in a floating-rate note combined with a receive-fixed interest rate swap.

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The receive-floating part of the interest rate swap offsets the floating rate payments the short-bond position requires. Therefore, a synthetic fixed-rate debt position is created.

optiix

A borrower with a $4 million floating rate loan pays LIBOR plus 200 basis points on the loan. Payments are semiannual. The borrower wishes to convert this obligation to a fixed-rate loan. The borrower uses a swap with a fixed rate equal to 5.6%, floating rate equal to LIBOR, and notional principal equal to $4 million. Which of the following most closely approximates the semiannual payments made by the borrower on the loan and the swap?

A) $76,000.

B) $72,000.

C) $152,000.

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The borrower will enter into the swap to receive LIBOR and pay 5.6%. The LIBOR payment effectively passes from the counterparty through to the lender while the 200 basis point spread remains an obligation of the borrower. Thus, the borrower pays (0.056 + 0.02) / 2 on $4 million each six months = $152,000.

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Which of the following statements about debt is least accurate?

A) To create synthetic dual currency debt, the portfolio manager can issue domestic debt and enter into a fixed-for-fixed currency swap where notional principal is swapped at origination.

B) To create synthetic callable debt from existing noncallable debt, the portfolio manager can enter into a receiver's swaption.

C) The all-in-cost is another way of saying "the internal rate of return of a financing alternative."

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To create synthetic dual currency debt, the portfolio manager can issue domestic debt and enter into a fixed-for-fixed currency swap where notional principal is NOT swapped at origination.

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To create synthetic fixed-rate debt from a floating-rate obligation, a portfolio manager can do which of the following?

A) Pay variable and receive fixed in a swap.

B) Sell interest rate caps.

C) Pay fixed and receive variable in a swap.

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To create synthetic fixed-rate debt, a portfolio manager can pay fixed and receive variable in a swap.

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A firm has most of its liabilities in the form of floating-rate notes with a maturity of two years and quarterly reset. The firm is concerned with interest rate movements over the next eight quarters but is not concerned with potential movements after that. Which of the following strategies will allow the firm to hedge the expected change in interest rates?

A) Enter into a 2-year, quarterly pay-floating, receive-fixed swap.

B) Enter into a 2-year, quarterly pay-fixed, receive-floating swap.

C) Buy a swaption that allows the firm to be the fixed-rate payer upon exercise. In other words, go long a payer’s swaption with a 2-year maturity.

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The firm should receive floating to offset the floating-rate obligation. Given its goals, the firm should enter into the swap to hedge the immediate risk and not the future risk offered by the swaption.

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Jane Hiatt and Penny Hoskins have responsibility for interest rate and currency risk management for the Rensselaer Corporation, a large multinational firm based in the Midwestern United States.
Due to an increase in global economic growth, Rensselaer has seen its sales increase and is planning to expand its U.S. factory at a cost of $30,000,000. The factory expansion will be financed at a floating interest rate of LIBOR plus 200 basis points, with payments made quarterly over seven years. Hiatt expects that Rensselaer will begin the expansion in six months and will receive the $30,000,000 in financing at that point in time. She is concerned, however, that global interest rates will increase in the interim and would like to have the option to convert the loan’s interest rate to a fixed rate in six months. Hiatt evaluates the forecasts for future swap fixed rates as well as the current terms of various swaptions, provided in the following table. The swaptions are for a 7-year swap where the floating interest rate is LIBOR flat.

Fixed rate for payer's swaption that matures in six months	7.00%
Fixed rate for receiver's swaption that matures in six months	7.10%
Projected Swap Fixed Rate in six months	7.20%
Fixed rate for payer's swaption that matures in seven years	8.40%
Fixed rate for receiver's swaption that matures in seven years	8.50%
Projected Swap Fixed Rate in seven years	9.20%

Rensselaer has just opened a factory in Germany that will sell products locally, earning projected cash flows of €10,000,000 on a quarterly basis. In order to convert these cash flows into dollars, Hoskins suggests that Rensselaer enter into a currency swap without an exchange of notional principal where euros will be exchanged for dollars. Hoskins contacts a currency swap dealer and reports the following exchange rate and annual swap fixed interest rates. These rates are for an exchange of cash flows starting in three months, which is approximately when Rensselaer will receive its next euro cash flow from its German operation. The maturity of the swap will be two years, because Hoskins does not feel comfortable projecting cash flows from the German factory beyond the next two years.

Exchange rate (EUR per dollar)	0.72
Swap interest rate in U.S. dollars	3.40%
Swap interest rate in euros	5.80%

Given her interest rate forecasts, which of the following is the most likely position Hiatt should recommend Rensselaer take to hedge the financing of the factory expansion?

A) Buy a seven year maturity payer swaption.

B) Buy a six month maturity payer swaption.

C) Buy a six month maturity receiver swaption.

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If LIBOR increases as she expects, the cost of Rensselaer’s floating rate loan will increase. In this case the firm will want to pay a fixed rate and receive a floating rate in a swap. The payer’s swaption will allow them to pay a predetermined fixed rate in a swap. The maturity of the swaption should coincide with the initiation of the loan. (Study Session 15, LOS 38.h)

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Assume the firm buys the appropriate swaption and Hiatt’s interest rate forecasts prove correct. Determine which of the following is closest to the net interest payment Rensselaer will make on the factory expansion loan in six months.

A) $675,000.

B) $682,500.

C) $690,000.

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If interest rates increase and the fixed rate on swaps in six months (projected at 7.2%) exceeds the swaption fixed rate, the firm will exercise the swaption and pay 7.0%. They receive LIBOR from the swap in the swaption and pay in total 7.0% + 2.0% = 9% in the swap and the loan. The firm’s first quarterly payment in net will be 9% × $30,000,000 × 90/360 = $675,000.
Note that if swap fixed rates are less than 7.0% in six months, the firm would not exercise the swaption. The firm could either a) enter a swap at that time and pay the lower fixed rate or b) not enter a swap and just pay the floating rate in the loan. (Study Session 15, LOS 38.h)

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If Hiatt’s interest rate forecasts prove correct, and the appropriate hedge is enacted, which of the following best represents the changes in Rensselaer’s risk exposure? The firm’s cash flow risk:

A) decreases and its market value risk decreases.

B) decreases and its market value risk increases.

C) increases and its market value risk decreases.

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A floating-rate cash flow will have a very low duration which means that its market value is largely resistant to changing interest rates. If Rensselaer hedges its floating rate loan so that it becomes a synthetic fixed rate loan, they have increased its duration and increased its sensitivity to changes in interest rates. So the loan’s market value risk increases.
However, they will have decreased the sensitivity of the cash flows in the loan to changes in interest rates, so cash flow risk declines. (Study Session 15, LOS 38.c)

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What are the periodic cash flows resulting from Rensselaer’s hedge of the German factory sales?

A) $4,264,706.

B) $8,141,762.

C) $13,888,889.

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In order to calculate how much Rensselaer will receive in dollars as a result of the swap, first calculate the implied notional principal (NP) from the quarterly cash flows of EUR 10,000,000, using the quarterly euro interest rate:
Next, calculate the dollar implied principal at the current exchange rate: EUR 689,655,172.41/0.72 = $957,854,406.13. Lastly, calculate a dollar cash flow using the quarterly dollar interest rate:
$957,854,406.13 × 0.034/4 = $8,141,762. (Study Session 15, LOS 38.f)

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Suppose that Rensselaer’s currency swap can be structured with fixed or floating payments. If Hiatt’s interest rate concerns are correct, which of the following would be the ideal position for Rensselaer to take in the currency swap? From Rensselaer’s perspective, the swap should be structured with a:

A) fixed dollar interest rate and a floating euro interest rate.

B) floating dollar interest rate and a fixed euro interest rate.

C) floating dollar interest rate and a floating euro interest rate.

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Hiatt is concerned that global interest rates will increase. In the currency swap, Rensselaer will pay euros and receive dollars. They will therefore want to fix the euro interest rate and receive dollars at a floating interest rate, which is expected to be higher in the future. (Study Session 15, LOS 38.a)

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In the currency swap, Rensselaer is exposed to:

A) credit risk and economic risk.

B) credit risk.

C) neither credit risk nor economic risk.

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Rensselaer has credit risk because if the swap counterparty defaults on the contract, Rensselaer will not have hedged its dollar cash flows. Rensselaer is also exposed to the type of currency risk referred to as economic risk to the extent that local asset and currency movements are correlated. Economic risk refers to longer term noncontractual exchange rate risk and the amount to hedge is not readily determined. Hoskins states that she does not feel comfortable projecting cash flows from the German factory beyond the next two years. She therefore is uncertain how much to hedge in the future and Rensselaer has economic risk. (Study Session 15, LOS 38.a)

optiix

For a plain-vanilla interest-rate swap with annual reset and one year to maturity, which of the following is closed to the duration for the floating side of the swap?

A) 0.50.

B) 1.00.

C) 0.75.

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The duration of the floating side is 1/2 the time until the next reset date. Since this is an annual pay swap with 1 year left the duration of the floating side is 1 x .5 = .5 or 1 divided by 2 = .5. The duration of the fixed side of a swap is approximately .75 to the time until maturity. If we take a different example of a 4 year swap with semi-annual payments the duration of the fixed side would be .75 x 4 = 3 and the duration of the floating side is .5 / 2 = .25.

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For a pay-fixed counterparty, the duration of the swap will generally be (in absolute value terms):

A) greater than the duration of the fixed-rate payments.

B) less than the duration of the fixed-rate payments.

C) equal to the duration of the fixed-rate payments.

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Since the problem asks only about the absolute value, we can ignore the fact that the duration for this position will be opposite in sign to that we usually calculate. Although most of the duration is associated with the fixed payments, the next “floating” payment is predetermined. Therefore, for example, the duration of a quarterly-reset swap might be duration of fixed payments minus 0.25. Because she receives floating-rate cash flows, taking the pay–fixed/receive–floating position in a swap decreases the dollar duration of a fixed income portfolio.

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The duration of a pay-floating swap is obtained by:

A) adding the duration of the floating-rate payments to the duration of the fixed-rate payments.

B) dividing the duration of the floating-rate payments by the duration of the fixed-rate payments.

C) subtracting the duration of the floating-rate payments from the duration of the fixed-rate payments.

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The duration of a pay-floating swap is the difference between the duration of the payments. Expressed as the formula: DPay-floating = DFixed-rate payments – DFloating-rate payments.

optiix

Which of the following positions results in synthetically issuing floating-rate debt?

A) A long position in a fixed-rate bond combined with a receive-fixed interest rate swap.

B) A short position in a fixed-rate bond combined with a receive-fixed interest rate swap.

C) A long position in a fixed-rate bond combined with a pay-fixed interest rate swap.

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The receive-fixed part of the interest rate swap offsets the fixed rate payments the short bond position requires. Therefore, a synthetic floating-rate debt position is created.