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.

jawz

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

A) Go long a payer’s swaption with a 1-year maturity.

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

C) Go short a payer’s swaption with a 2-year maturity.

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The firm will want to receive floating payments to offset the volatility of its floating-rate obligations. A payer’s swaption allows the firm to become a fixed-rate payer/floating-rate receiver in a swap. The one-year maturity corresponds to the start of the period of concern.

jawz

A firm contracts to borrow $5 million in one year. The firm enters into a one-year swaption where the swap maturity and notional principal match that of the planned loan. The swaption gives the firm the right to be a floating-rate payer. This hedging strategy would be most effective if the loan contract specifies a:

A) variable rate and interest rates decline.

B) variable rate and interest rates increase.

C) fixed rate and interest rates decline.

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A firm that has contracted to borrow at a fixed rate in the future would want a hedge against interest rates falling and being stuck paying a higher-than-market rate. A swaption to become a floating-rate payer benefits the owner when interest rates decline. The firm will receive a “high” fixed rate and pay “low” variable rates, and this will offset the higher-than-market rate in the contract.

jawz

A borrower who is also the owner of a swaption that gives the holder the right to become a fixed-rate payer and floating-rate receiver would most likely do which of the following? Exercise the swaption when interest rates:

A) increase to convert a fixed-rate loan to a floating-rate loan.

B) increase to convert a floating-rate loan to a fixed-rate loan.

C) decrease to convert a floating-rate loan to a fixed-rate loan.

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The owner will benefit when interest rates increase because the owner has the right to pay a fixed rate and receive the floating rate, which will be higher with the increase in interest rates. Receiving the floating rate and paying the fixed rate can turn a floating-rate loan to a fixed-rate loan.

jawz

An investor has a $5,000,000 investment in small-cap stocks. The investor enters into an equity index swap where the investor pays the return on the Russell 2000 and receives the return on the Dow Jones Industrial Average. The notional principal of the swap is $1 million. The resulting position is a synthetic mix of:

A) 16.67% large stocks and 83.33% small stocks.

B) 20% large stocks and 80% small stocks.

C) 25% large stocks and 75% small stocks.

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After the swap, $1 million, or 20% of the portfolio’s exposure will be invested in the Dow Jones Industrial Average index of large stocks. $4 million, or 80% of the portfolio will remain invested in small stocks. The $1 million notional principal represents 20% of the position. That is the amount that has been synthetically transferred from one class of assets to the other.

jawz

An investor who enters into a swap to exchange half the return on her 100,000 share position in a stock for the return on an equal value of the S&P 500 would most likely be trying to:

A) reduce systematic risk in the portfolio.

B) diversify her portfolio.

C) increase the risk and return of her position.

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Entering into a swap to exchange the returns on the stock for those of the index would be way to create synthetic diversification in a portfolio. Note that the added diversification as a result of the swap would reduce unsystematic risk, but systematic risk will still exist.

optiix

A manager of a $300 million bond portfolio consisting of $50 million in investment-grade corporate bonds and $250 million in U.S. Treasuries wants to re-weight to a 50/50 mix. This can be done with a bond-index swap with a notional principal of:

A) $100 million.

B) $275 million.

C) $250 million.

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The swap would exchange the return on $100 million in U.S. Treasuries for the return on $100 million of the corporate bonds. This would create a synthetic mix of $150 million in each position.

optiix

A U.S. firm that wishes to convert its annual cash flows of €10 million each to US$ upon receipt. The exchange rate is currently 0.9€/$, and the swap rates in the U.S. and Europe are 5.4% and 5% respectively. Appropriately using a fixed-for-fixed currency swap that does not exchange principal, what would be the annual dollar cash flow to the firm?

A) $22,222,222.

B) $11,111,111.

C) $12,000,000.

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At current interest rates, the €10 million per year translates to a notional principal of:

NP = 10,000,000 / 0.05
NP = €200,000,000

The corresponding dollar amount is $222,222,222 = €200,000,000 / (0.9€/$). The annual interest payments on this amount would be $12,000,000 = $222,222,222 × 0.054.

optiix

A U.S. firm that wishes to convert its quarterly cash flows of €7 million each to dollars upon receipt. The exchange rate is currently €0.8/US$, and the swap rates in the U.S. and Europe are 5.2 percent and 5.6 percent respectively. What should be the notional principal of a currency swap, where the principal is not exchanged and the rates are fixed, that will accomplish the goal?

A) $625,000,000.

B) €500,000,000.

C) $8,125,000.

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At current interest rates, the €7 million per quarter translates to a notional principal in the foreign currency of:

NP = 7,000,000 / (0.056 /4)
NP = €500,000,000

The notional principal in U.S. dollar terms is: €500,000,000 X US$/ €0.8 = $625,000,000
The quarterly cash flows on the swap would then be $625,000,000 X 0.52/4 = $8,125,000

optiix

A U.S. firm that wishes to convert its annual cash flows of €20 million each to dollars upon receipt. The exchange rate is currently €0.9/USD, and the swap rates in the U.S. and Europe are both 6.1 percent. Appropriately using a fixed-for-fixed currency swap that does not exchange principal, what would be the annual dollar cash flow to the firm?

A) $32,786,885.

B) $10,980,000.

C) $22,222,222.

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At current interest rates, the €20 million per year translates to a notional principal of:

NP = 20,000,000 / 0.061
NP = €327,868,852

The corresponding dollar amount is $364,298,725 = €327,868,852 / (€0.9/$). The annual interest payments on this amount would be $22,222,222 = $364,298,725 × 0.061.