Reading 39: Risk Management App....tion Strategies－LOS c interest

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CFA Institute Area 8-11, 13: Asset Valuation
Session 13: Risk Management Applications of Derivatives
Reading 39: Risk Management Applications of Option Strategies
LOS c: Determine the payoffs for a series of interest rate outcomes when a floating rate loan is combined with (1) an interest rate cap, (2) an interest rate floor, or (3) an interest rate collar.

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A firm purchases a one-year cap with a strike rate of 4 percent, a notional principal of $3 million, and semiannual settlement. The reference rate at the initiation of the cap is 5 percent, falls to 4.5 percent at the next settlement and then to 4 percent one year after the caps initiation. The total payoffs (without discounting) over the maturity of the swap would be:

A) $25,500.

B) $22,792.

C) $15,167.

D) $7,583.

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Answer and Explanation

Since the number of days is not given for each period, approximate it with 182 in the first period and 183 in the second period. Remember that payments are made in arrears.

First payoff = $ 15,167 = $3,000,000 × max(0, 0.05 0.04) × (182/360).
Second payoff = $7,625 = $3,000,000 × max(0, 0.045 0.04) × (183/360)
Total = $22,792 = $7,625 + $ 15,167

First payoff = $ 15,167 = $3,000,000 × max(0, 0.05 0.04) × (182/360).
Second payoff = $7,625 = $3,000,000 × max(0, 0.045 0.04) × (183/360)
Total = $22,792 = $7,625 + $ 15,167

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A firm purchases a collar with floor rate of 3 percent and a cap rate of 4.4 percent. The cap and floor have quarterly settlement and a notional principal of $10 million. The maximum outflow and inflow the buyer can expect on a given settlement is (assume equal settlement periods):

A) $300,000 and maximum inflow = $110,000.

B) $75,000 and maximum inflow = $140,000.

C) $110,000 and maximum inflow = $140,000.

D) $75,000 and maximum inflow = infinite.

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Answer and Explanation

Given the possible answers, this must be a collar consisting of a short floor and long cap. The firms maximum outflow would occur from the floor when the reference rate is zero: $10,000,000 × (0.03-0)/4 = $75,000. Although interest rates cannot go to infinity, there is no upper limit on what the owner can expect from the cap. Thus infinite is the best answer.

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Which of the following is equivalent to a pay-fixed interest rate swap?

A) Selling a cap and buying a floor.

B) Buying a cap and selling a floor.

C) Buying a cap and selling an interest rate collar.

D) Selling a cap and buying an interest rate collar.

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Answer and Explanation

A pay-fixed interest rate swap has the same payoffs as a long position in the corresponding interest rate collar (with the strike rate equal to the swap fixed rate).