Finance Chapter Twenty | Course Paper

Chapter Twenty Six

Swaps

Chapter Outline

Introduction

Interest Rate Swaps

Realized Cash Flows on an Interest Rate Swap

Macrohedging with Swaps

Currency Swaps

Fixed-Fixed Currency Swaps

Fixed-Floating Currency Swaps

Credit Swaps

Total Return Swaps

Pure Credit Swaps

Swaps and Credit Risk Concerns

Summary

Appendix 26A: Pricing an Interest Rate Swap

Pricing a Swap: An Example

65

Solutions for End-of-Chapter Questions and Problems: Chapter Twenty Six

1. Explain the similarity between a swap and a forward contract.

A forward contract requires delivery or taking delivery of some commodity or security at some

specified time in the future at some price specified at the time of origination. In a swap, each

party promises to deliver and/or receive a pre-specified series of payments at specific intervals

over some specified time horizon. In this way, a swap can be considered to be the same as a

series of forward contracts.

2. Forward, futures, and option contracts had been used by FIs to hedge risk for many years

before swaps were invented. If FIs already had these hedging instruments, why do they

need swaps?

Although similar in many ways, the following distinguishing characteristics cause the

instruments to be differentiated:

(a) The swap can be viewed as a portfolio of forward contracts with different maturity dates.

Since cash flows on forward contracts are symmetric, the same can be said of swaps. This

is in contrast to options, whose cash flows are asymmetric (truncated either on the positive

or negative side depending upon the position).

(b) Options are marked to market continuously, swaps are marked to market at coupon

payment dates, and forward contracts are settled only upon delivery (at maturity).

Therefore, the credit risk exposure is greatest under a forward contract, where no third

party guarantor exists as in options (the options clearing corporation for exchange-traded

options) and swaps (the swap intermediary).

(c) The transactions cost is highest for the option (the nonrefundable option premium), next for

the swap (the swap intermediary’s fee), and finally for the forward (which has no up-front

payment).

(d) Swaps also have a longer maturity than any other instrument and provide an additional

opportunity for FIs to hedge longer term positions at lower cost. Moreover, since the

package of forward contracts mirrors debt instruments, the swap provided FIs with a hedge

instrument that is attractive and less costly than separate forward contracts.

(e) Finally, the introduction of a swap intermediary reduces the credit risk exposure and the

information and monitoring costs that are associated with a portfolio of individual forward

contracts.

3. Distinguish between a swap buyer and a swap seller? In which markets does each have the

comparative advantage?

The swap buyer makes the fixed-rate payments in an interest rate swap, and the swap seller

makes the variable-rate payments. This distinction occurs by convention. The notation in this

66

text refers to the comparative advantage party as that which makes the specific swap payment.

Thus, the buyer is said to have the comparative advantage in fixed-rate payments. Students will

note that some other authors refer to the comparative advantage in the markets in which the cash

financing occurs, which may not be the same market that would reduce the interest rate risk on

the balance sheet, and therefore the reason for the swap. Thus, in the example on page 623 in the

text, the money center bank raises money in the fixed-rate market, even though the loans are

variable-rate.

4. An insurance company owns $50 million of floating-rate bonds yielding LIBOR plus 1

percent. These loans are financed by $50 million of fixed-rate guaranteed investment

contracts (GICs) costing 10 percent. A finance company has $50 million of auto loans with

a fixed rate of 14 percent. The loans are financed by $50 million of CDs at a variable rate

of LIBOR plus 4 percent.

a. What is the risk exposure of the insurance company?

The insurance company (IC) is exposed to falling interest rates on the asset side of the

balance sheet.

b. What is the risk exposure of the finance company?

The finance company (FC) is exposed to rising interest rates on the liability side of the

balance sheet.

c. What would be the cash flow goals of each company if they were to enter into a swap

arrangement?

The IC wishes to convert the fixed-rate liabilities into variable-rate liabilities by swapping

the fixed-rate payments for variable-rate payments. The FC wishes to convert variable-rate

liabilities into fixed-rate liabilities by swapping the variable-rate payments for fixed-rate

payments.

d. Which company would be the buyer and which company would be the seller in the

swap?

The FC will make fixed-rate payments and therefore is the buyer in the swap. The IC will

make variable-rate payments and therefore is the seller in the swap.

e. Diagram the direction of the relevant cash flows for the swap arrangement.

Please see the diagram at the top of the next page. Note that the fixed-rate swap payments

from the finance company to the insurance company will offset the payments on the

fixed-rate liabilities that the insurance company has incurred. The reverse situation occurs

regarding the variable-rate swap payments from the insurance company to the finance

company. Depending on the rates negotiated and the maturities of the assets and liabilities,

67

both companies now have durations much closer to zero on this portion of their respective

balance sheets.

Finance Company Insurance Company

Fixed-rate Fixed-rate swap payments Variable-rate assets

assets

Variable-rate swap payments

Cash

Variable-rate Financing Fixed-rate

liabilities @ L + 4% Markets liabilities @ 10%

Swap Cash Flows

Note to instructors: I find it very helpful to diagram the cash-market financing cash flows

when I present the material on swaps.

f. What are reasonable cash flow amounts, or relative interest rates, for each of the

payment streams?

Determining a set of reasonable interest rates involves an analysis of the benefits to each

firm. That is, does each firm pay lower interest rates than contractually obligated without

the swap? Clearly, the direction of the cash flows will help reduce interest rate risk.

One feasible swap is for the IC to pay the FC LIBOR + 2.5 percent, and for the FC to pay

the IC 12 percent. The net financing cost for each firm is given below.

Finance Insurance

Company Company

Cash market liability rate L + 4% 10.0%

Minus Swap-in rate -(L + 2.5%) -12.0%

Plus Swap-out rate + 12% +(L + 2.5%)

Net financing cost rate 13.5% L + 0.5%

Whether the two firms would negotiate these rates depends on the relative negotiating

power of each firm, and the alternative rates for each firm in the alternate markets. That is,

the fixed-rate liability market for the finance company and the variable-rate liability market

for the insurance company.

5. In a swap arrangement, the variable-rate swap cash flow streams often do not fully hedge

the variable-rate cash flow streams from the balance sheet due to basis risk.

a. What are the possible sources of basis risk in an interest rate swap?

First, the variable-rate index on the liabilities in the cash market may not match perfectly

the variable-rate index negotiated into the swap agreement. This source of basis risk is

similar to the cross-hedge risk in the use of futures contracts. Second, the premium over

68

the index in the cash-market variable-rate liability may change over time as credit (default)

risk conditions change.

b. How could the failure to achieve a perfect hedge be realized by the swap buyer?

Swap pricing normally is based on a fixed notional amount over the life of the swap. If the

fixed-rate asset portfolio of the buyer decreases over time, a fixed-notional amount swap

agreement may not reflect accurately the desired interest-rate risk goals of the buyer over

the life of the swap. This situation could occur as loans are amortized (repaid in the normal

context) or as prepayment rates change on either loans or bonds as macroeconomic

conditions change.

c. How could the failure to achieve a perfect hedge be realized by the swap seller?

The swap seller is subject to basis risk as discussed in part (a) above.

6. A commercial bank has $200 million of floating-rate loans yielding the T-bill rate plus 2

percent. These loans are financed by $200 million of fixed-rate deposits costing 9 percent.

A savings bank has $200 million of mortgages with a fixed rate of 13 percent. They are

financed by $200 million of CDs with a variable rate of the T-bill rate plus 3 percent.

a. Discuss the type of interest rate risk each FI faces.

The commercial bank is exposed to a decrease in rates that would lower interest income,

while the savings bank is exposed to an increase in rates that would increase interest

expense. In either case, profit performance would suffer.

b. Propose a swap that would result in each FI having the same type of asset and liability

cash flows.

One feasible swap would be for the bank to send variable-rate payments of the T-bill rate +

1 percent (T + 1%) to the savings bank and to receive fixed-rate payments of 9 percent

from the savings bank.

c. Show that this swap would be acceptable to both parties.

Savings Bank Com. Bank

Cash market liability rate T + 3% 9.0%

Minus Swap-in rate -(T + 1%) -9.0%

Plus Swap-out rate + 9% +(T + 1%)

Net financing cost rate 11.0% T + 1%

The net interest yield on assets is 2 percent (13% – 11%) for the savings bank and 1 percent

First Bank Second Bank

Fixed-rate Fixed-rate swap payments Variable-rate assets

assets 11.0%

P+0.5%

Variable-rate swap payments

Cash

Variable-rate Financing Fixed-rate

liabilities @ P+1% Markets liabilities @ 11%

Swap Cash Flows

First Bank Second Bank

Fixed-rate Fixed-rate swap payments Variable-rate assets

assets 12.5%

P+1.0%

Variable-rate swap payments

Cash

Variable-rate Financing Fixed-rate

liabilities @ P+1% Markets liabilities @ 11%

Swap Cash Flows

Firm A Firm B

Fixed-rate Fixed-rate swap payments Variable-rate assets

assets 11.0%

L+0.5%

Variable-rate swap payments

Cash

Variable-rate Financing Fixed-rate

liabilities @ L+0.5% Markets liabilities @ 10%

Swap Cash Flows