Reading 28 Risk Management Applications of Swap Strategies

Question 1

Using Swaps to Adjust the Duration of a Fixed-Income Portfolio

Answer 1

In general, the notional principal of a swap necessary to change the duration of a bond portfolio worth B from MDUR_B to a target duration, MDUR_T, is

NP=B•(MDUR_T−MDUR_B)/MDUR_S

A $250 million bond portfolio has a duration of 5.50. The portfolio manager wants to reduce the duration to 4.50 by using a swap. Consider the possibility of using a one-year swap with monthly payments. Determine the durations of the swap under the assumption of paying fixed and receiving floating. Assume that the duration of a fixed-rate bond is 75 percent of its maturity.

The duration of a one-year pay-fixed, receive-floating swap with monthly payments is the duration of a one-year floating-rate bond with monthly payments minus the duration of a one-year fixed-rate bond with monthly payments. The duration of the former is about one-half of the length of the payment interval. That is 1/24 of a year, or 0.042. Because the duration of the one-year fixed-rate bond is 0.75 (75 percent of one year), the duration of the swap is 0.042 – 0.75 = –0.708.

Question 2

Using an Interest Rate Swaption to Terminate a Swap

Answer 2

When a company enters a swap, it knows it may need to terminate the swap before the expiration day. It can do so by either entering an offsetting swap or buying a swaption (American-style).

If a borrower feels that rates will fall, it would then want to convert its pay-fixed position to a pay-floating position.

If the market rate is more than the exercise rate, the borrower can do so by entering into a swap at the market rate. It can then receive more than the exercise rate, which more than offsets the rate it pays on the swap. The borrower would then effectively be paying less than Libor.

If the rate in the market is less than the exercise rate, the borrower can exercise the swaption, thereby receiving the exercise rate to offset the rate it pays on the swap. Alternatively, it can choose to continue paying a floating rate but can still exercise the swaption if doing so is optimal.

Consider this example. Internet Marketing Solutions (IMS) takes out a $20 million one-year loan with quarterly floating payments at Libor from a lender called Financial Solutions (FINSOLS). Fearing an increase in interest rates, IMS engages in a pay-fixed, receive-floating swap that converts the loan into a fixed-rate loan at 8 percent. IMS believes, however, that the interest rate outlook could change, and it would like the flexibility to terminate the swap, thereby returning to the status of a floating-rate payer. To give it this flexibility, IMS purchases an American-style receiver swaption for $515,000. The swaption allows it to enter into a receive-fixed, pay-floating swap at a fixed rate of 8 percent at the swaption expiration. The swap and swaption counterparty is Wheatstone Dealer (WHD).

Exhibit below illustrates this transaction. In Panel A, IMS takes out the loan from FINSOLS, receiving $20 million. It engages in the swap with WHD, thereby committing to pay fixed and receive Libor. There are no cash flows at the start of the swap contract, but IMS pays WHD $515,000 for the swaption. Now let us move to the expiration of the swaption, at which time we shall assume that IMS is no longer concerned about rising interest rates and would like to return to the status of a floating-rate borrower. In Panel B(i), at the expiration of the swaption, the market swap rate is greater than or equal to 8 percent. This panel shows the cash flows if the loan plus swap (note that the loan is floating rate) is converted to a fixed rate using the market fixed rate because the swaption is out-of-the-money. IMS makes interest payments of Libor(90/360)$20 million to FINSOLS. IMS makes a swap payment of 8 percent, which is $400,000, to WHD, which pays Libor.31 Thus, to offset the effect of the pay-fixed swap, IMS is better off entering a new swap rather than exercising its swaption. IMS then enters into a swap to receive the market fixed rate, FS, which is greater than or equal to 8 percent, and pay Libor. IMS is, in effect, paying a floating rate less than Libor (or equal to Libor if the market swap rate is exactly 8 percent).

In Panel B(ii), the market swap rate is less than 8 percent and the loan is converted back to a floating-rate loan by exercising the swaption. IMS makes loan interest payments at Libor to FINSOLS and swap payment of 8 percent or $400,000 to WHD, which pays LIBOR. Exercise of the swaption results in IMS entering into a swap to receive a fixed rate of 8 percent and pay a floating rate of Libor. The swap and swaption would probably be structured to offset and terminate both swaps. At the end of the transaction, the loan is paid off and there are no payments on the swap or swaption. If IMS wants to continue as a fixed-rate payer, the swaption would still be exercised if it is in-the-money but not if it is out-of-the-money.

Question 3

Synthetically Adding a Call to Noncallable Debt

Answer 3

Of course, there are some tricky elements to making this strategy work. We have ignored taxes and transaction costs, which can affect exercise and call decisions. Also, when the swaption is held by another party, there is no guarantee that exercise will occur at the optimal time.

A payer swaption is equivalent to a put option. Payer swaptions would be useful in situations involving put features. Putable bonds do exist but are not particularly common. A putable bond allows the bondholder to sell the bond back, usually at par, to the issuer. Therefore, the option, which is a put, is held by the bondholder and sold by the bond issuer.

Question 4

A Note on Forward Swaps

Answer 4

Called forward swaps, these instruments are commitments to enter into swaps. They do not require a cash payment at the start but force the parties to enter into a swap at a later date at terms, including the fixed rate, set at the start.

Question 5

Synthetically Removing the Call from Callable Debt

Answer 5

Note that the credit spread is not part of the exercise rate. The swaption can be used to manage only the risk of interest rate changes driven by the term structure and not credit.

Question 6

Strategies and Applications for Managing Interest Rate Risk

Answer 6

The interest rate swap, however, is unquestionably the most widely used instrument to manage interest rate risk.

Swaps are not normally used to manage the risk of an anticipated loan; rather, they are designed to manage the risk on a series of cash flows on loans already taken out or in the process of being taken out.

Structured note is a variation of a floating-rate note that has some type of unusual characteristic such as a leverage factor or in which the rate moves opposite to interest rates.

Question 7

Swaption

Answer 7

Swaption is an option to enter into a swap.

There are two kinds of swaptions: those to make a fixed payment, called payer swaptions, and those to receive a fixed payment, called receiver swaptions.

Like options, swaptions require the payment of a premium at the start and grant the right, but not the obligation, to enter into a swap.

Question 8

Four types of swaps

Answer 8

Four types of swaps are interest rate, currency, equity, and commodity swaps.

• Interest rate swaps typically involve one side paying at a floating interest rate and the other paying at a fixed interest rate. In some cases both sides pay at a floating rate, but the floating rates are different.
• Currency swaps are essentially interest rate swaps in which one set of payments is in one currency and the other is in another currency. The payments are in the form of interest payments; either set of payments can be fixed or floating, or both can be fixed or floating. With currency swaps, a source of uncertainty is the exchange rate so the payments can be fixed and still have uncertain value.
• In equity swaps, at least one set of payments is determined by the course of a stock price or stock index.
• In commodity swaps at least one set of payments is determined by the course of a commodity price, such as the price of oil or gold.

Question 9

Duration of a four-year pay-floating, receive-fixed swap with quarterly payments

Answer 9

Duration of a four-year pay-floating, receive-fixed swap with quarterly payments = (0.75)(4) – 0.125 = 2.875

Question 10

Using Swaps to Create and Manage the Risk of Inverse Floaters

Answer 10

Inverse floater is a floating-rate note or bond in which the coupon is adjusted to move opposite to a benchmark interest rate.

Consider a company called Vega Analytics that engages in a variety of arbitrage trades using structured notes. Vega wants to issue an inverse floater paying a rate of b minus Libor, b – L, on notional principal FP. Vega sets the value of b in negotiation with the buyer of the note, taking into account a number of factors. The rate on the note moves inversely with Libor, but if Libor is at the level b, the rate on the note goes to zero. If Libor rises above b, the rate on the note is negative!

The pattern will be the same as the pattern used for the leveraged floater: Finance the structured note by a fixed-rate note and then swap the fixed rate for a floating rate to match the structured note. Exhibit below shows how Vega issues the note to a company called Metrics Finance and uses the proceeds to purchase a fixed-rate note issued by a company called Telltale Systems, Inc., which pays a rate of (ci)(FP). Vega then enters into an interest rate swap with notional principal FP with a counterparty called Denman Dealer Holdings. In this swap, Vega receives a fixed rate of FS and pays L. Observe that the net effect is that Vega’s overall cash flow is FP[– (b – L) + ci + FS – L] = FP(FS + ci – b).

Clearly if b is set below FS + ci, then the overall cash flow is positive. Vega can potentially do this because of the credit risk it assumes. Vega sets b but cannot set FS, and ci is based on both the level of market interest rates and the credit risk of Telltale. The lower Vega sets b, the larger its cash flow from the overall transactions. But one major consideration forces Vega to limit how low it sets b: The lower it sets b, the less attractive the note will be to potential investors.

Regardless of where Vega sets b, the possibility remains that L will exceed b. Metrics may have Vega guarantee that the interest rate on the floater will go no lower than 0 percent. To manage the risk associated with this guarantee, Vega will buy an interest rate cap.

Suppose the swap fixed rate, FS, is 6 percent, and ci, the rate on Telltale’s note, is 7 percent. Vega sets b at 12 percent and guarantees to Metrics that the interest rate will go no lower than zero. Then the inverse floater pays 12 percent – L. As long as Libor is below 12 percent, Vega’s cash flow is 6 + 7 – 12 = 1 percent. Suppose L is 14 percent. Then Vega’s cash flows are

+7 percent from the Telltale note

0 percent to Metrics

+6 percent from Denman

14 percent to Denman

Net: outflow of 1 percent

Vega’s net cash flow is negative. To avoid this problem, Vega would buy an interest rate cap in which the underlying is Libor and the exercise rate is b. The cap would have a notional principal of FP and consist of individual caplets expiring on the dates on which the inverse floater rates are set. Thus, on a payment date, when L exceeds b, the inverse floater does not pay interest, but the caplet expires in-the-money and pays L – b.

The premium on the cap would be an additional cost that Vega would pass on in the form of a lower rate paid to Metrics on the inverse floater.

Question 11

Changing an Asset Allocation between Stocks and Bonds

Answer 11

Fixed-income swaps, like equity swaps, require the payment of the total return on a bond or bond index against some other index, such as Libor. They are very similar to equity swaps in many respects: The total return is not known until the end of the settlement period, and because the capital gain can be negative, it is possible for the overall payment to be negative. In contrast to equity swaps, however, fixed-income swaps are more dominated by the fixed payment of interest. For equities, the dividends are small, not fixed, and do not tend to dominate capital gains. Other than the amounts paid, however, fixed-income swaps are conceptually the same as equity swaps.

The performance of the various sectors of its equity and fixed-income portfolios are not likely to match perfectly the indices on which the swap payments are based.

Question 12

Diversifying a Concentrated Portfolio

Answer 12

Equity swaps can be used to achieve diversification without selling the stock.

Both parties, however, must keep in mind a number of considerations. One is that a cash flow problem could arise.

Cash flow management can be a major difficulty in equity swaps.

Question 13

Using Interest Rate Swaps to Convert a Floating-Rate Loan to a Fixed-Rate Loan (and Vice Versa)

Answer 13

Using a swap to convert a floating-rate loan to a fixed-rate loan is a common transaction, one ostensibly structured as a hedge. Such a transaction, despite stabilizing a company’s cash outflows, however, increases the risk of the company’s market value. Whether this issue is of concern to most companies is not clear.

Question 14

Market value risk and cash flow risk when using swaps

Answer 14

The swap reduces cash flow risk but increases market value risk

Question 15

Using Currency Swaps to Create and Manage the Risk of a Dual-Currency Bond

Answer 15

A financial innovation in recent years is the dual-currency bond, on which the interest is paid in one currency and the principal is paid in another. Such a bond can be useful to a multinational company that might generate sufficient cash in a foreign currency to pay interest but not enough to pay the principal, which it thus might want to pay in its home currency. Dual-currency bonds can be shown to be equivalent to issuing an ordinary bond in one currency and combining it with a currency swap that has no principal payments.

Question 16

Reducing Insider Exposure

Answer 16

Reducing Insider Exposure has important issues in addition to the cash flow problem

• One is that under US law, this transaction is considered an insider sale and must be reported to the regulatory authorities. Thus, there is some additional paperwork.
• This transaction has no tax advantages

The executive’s incentive to perform well would certainly be reduced.

Question 17

Structured notes

Answer 17

Structured notes are short- or intermediate-term floating-rate securities that have some type of unusual feature that distinguishes them from ordinary floating-rate notes. This unusual feature can be in the form of leverage, which results in the interest rate on the note moving at a multiple of market rates, or can be an inverse feature, meaning that the interest rate on the note moves opposite to market rates. Structured notes are designed to be sold to specific investors, who are often motivated by constraints that restrict their ability to hold derivatives or use leverage.

Question 18

Strategies and Applications Using Swaptions

Answer 18

A swaption is an option to enter into a swap.

Swaptions to enter into interest rate swaps, which is by far the largest swaptions market.

There are two types of swaptions, payer swaptions and receiver swaptions, which are analogous to puts and calls. A payer swaption is an option that allows the holder to enter into a swap as the fixed-rate payer, floating-rate receiver. A receiver swaption is an option that allows the holder to enter into a swap as the fixed-rate receiver, floating-rate payer. In both cases, the fixed rate is specified when the option starts. The buyer of a swaption pays a premium at the start of the contract and receives the right to enter into a swap. The counterparty is the seller of the swaption. The seller receives the premium at the start and grants the right to enter into the swap at the specified fixed rate to the buyer of the swaption. A swaption can be European style or American style, meaning that it can be exercised only at expiration (European) or at any time prior to expiration (American). We shall illustrate applications of both.

A swaption is based on an underlying swap. The underlying swap has a specific set of terms: the notional principal, the underlying interest rate, the time it expires, the specific dates on which the payments will be made, and how the interest is calculated. All of the terms of the underlying swap must be specified. Although an ordinary option on an asset has an exercise price, a swaption is more like an interest rate option in that it has an exercise rate. The exercise rate is the fixed rate at which the holder can enter into the swap as either a fixed-rate payer or fixed-rate receiver. When a swaption expires, the holder decides whether to exercise it based on the relationship of the then-current market rate on the underlying swap to the exercise rate on the swaption. A swaption can be exercised either by actually entering into the swap or by having the seller pay the buyer an equivalent amount of cash.

A swaption can also be viewed as an option on a coupon bond. Specifically, a payer swaption with exercise rate x in which the underlying is a swap with notional principal P and maturity of N years at the swaption expiration is equivalent to an at-the-money put option in which the underlying is an N-year bond at expiration with a coupon of x percent. Likewise, a receiver swaption is analogous to an at-the-money call option on a bond.

Question 19

Using Swaps to Create and Manage the Risk of Leveraged Floating-Rate Notes

Answer 19

A company issues a floating-rate note that pays a rate of twice Libor on notional principal FP. It uses the proceeds to buy a bond paying a rate of ci. It also enters into a swap with a fixed rate of FS to manage the risk of the Libor payment on the leveraged floater.

• Demonstrate how the company can engage in these transactions, leaving it with a net cash flow of 2(FP)(ci – FS).

The company has issued a leveraged floater at a rate of 2L on notional principal FP. Then it should purchase a bond with face value of 2(FP) and coupon ci. It enters into a swap to pay a fixed rate of FS and receive a floating rate of L on notional principal 2(FP). The net cash flows are as follows:

From leveraged floater –2L(FP)
From bond +(ci)2(FP)
Floating side of swap +(L)2(FP)
Fixed side of swap –(FS)2(FP)
Total 2FP(ci – FS)

• Explain under what condition the amount (ci – FS) is positive.

The difference between the bond coupon rate, ci, and the swap fixed rate, FS, will be positive if the bond has greater credit risk than is implied by the fixed rate in the swap, which is based on the Libor term structure and reflects the borrowing rate of London banks. Thus, the gain of 2(ci – FS)(FP) is likely to reflect a credit risk premium.

Question 20

Synthetically Removing (Adding) a Call Feature in Callable (Noncallable) Debt

Answer 20

A swaption can be used to effectively sell the embedded call. This strategy involves synthetically removing the call from callable debt by selling a receiver swaption. A receiver swaption (receive fixed) becomes more valuable as rates decline, thus balancing the short call. In effect, the call feature is sold for cash. Recall that a receiver swaption is like a call option on a bond. Because the issuer of the callable bond holds a call on the bond, it would need to sell a call to offset the call embedded in the debt.

Question 21

Economic risk

Answer 21

Economic risk refers to longer term noncontractual exchange rate risk and the amount to hedge is not readily determined.

Question 22

Converting a Loan in One Currency into a Loan in Another Currency

Answer 22

This type of transaction is an extremely common use of currency swaps. The advantage of borrowing this way rather than directly in another currency lies in the fact that the borrower can issue a bond or loan in the currency in which it is better known as a creditor. Then, by engaging in a swap with a bank with which it is familiar and probably already doing business, it can borrow in the foreign currency indirectly.

A currency swap party’s choice to pay a fixed or floating rate depends on its views about the direction of interest rate movements. Companies typically choose floating rates when they think interest rates are likely to fall. They choose fixed rates when they think interest rates are likely to rise.

One important way in which currency swaps differ from interest rate swaps is that currency swaps involve the payment of notional principal. However, not all currency swaps involve the payment of notional principal.

Question 23

Major use of equity swaps

Answer 23

An asset allocation change is the major use of equity swaps.