2 March 2011

Demystifying Financial Derivatives: Interest Rate Swaps and Municipal Derivatives1

Summary This paper reviews the economics of interest rate swaps and other interest rate derivatives. We

begin by illustrating how interest rate swaps work and how they can be used to expand the set

of financing options available to a company, to manage exposure to interest rate risks, and to

speculate on interest rate expectations. Using recent municipal swaps as an example, we then

illustrate potential issues of contention between swap counterparties and review the economic

principles behind them.

While interest rate swaps offer a borrower potential cost savings justifiable on economic

grounds, they may also expose him to risks not present in other financing alternatives. For

example, a borrower that issues revolving debt and enters into a swap to hedge against interest

rate changes is not in the same position of a borrower that borrows long-term at the same

rate. The former is subject to changes in his credit risk whereas the latter is not. The Jefferson

County, Alabama case reviewed in this paper is an example of a realization of this risk.

When interest rate swaps are used to hedge a company’s exposure to interest rate risk, their

ex-post performance in terms of financing costs may be inferior to an alternative that leaves

a borrower exposed to interest rate risk. We argue that the economic soundness of a swap

should be evaluated on an ex-ante basis, taking into account its risk-return trade-off relative to

alternative financing options.

We also review some common swap pricing practices important in determining the value of

a swap and understanding swap-dealer fees. While a standard principle in swap pricing is

the mid-market pricing, or zero net present value, in practice the net present value of a swap

at inception is positive for a dealer. We review the main adjustments dealers make to arrive

at a fair market value, including credit risk, profit margins, and liquidity adjustments. The

adjustments should rely on sound economic models, and the models should make appropriate

risk adjustments to expected losses and expected defaults.

By Dr. Massimiliano De Santis

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I. IntroductionWhile the role of financial markets in facilitating lending and providing investment capital to

business often steals the limelight, the role of the financial system in facilitating the separation

and trade of economic risks is no less essential to economic growth. The idea is that trading

risks lowers the cost of financing risky projects by separating one risk from another and placing

each with the party that is able to bear it at the lowest cost. Financial derivatives are contracts

that facilitate the separation and trade of economic risks.2

This paper reviews the economic benefits of one type of contract designed to trade in risk,

interest rate swaps, and related interest rate derivatives. By allowing two parties to swap cash

flows, interest rate derivatives expand the set of financing options available to borrowers. This

allows them to lower financing costs, manage mismatches between assets and liabilities, and

manage their exposure to interest rate risk. Some of the earliest interest rate swaps were done

by Sallie Mae in the early 1980s with the goal of reducing the duration of its liabilities. Since

then, the market for interest rate derivatives has increased exponentially. According to the

Bank for International Settlements (BIS), the global notional amount of interest rate derivatives

(including interest rate swaps and other derivatives described below) was about $347 trillion

as of June 2010.3 The amount was $51 trillion as of June 2000 according to the same source,

and only $182 billion in 1987, according to data from the International Swap and Derivatives

Association (ISDA).4

This paper is motivated in part by recent activity in the market for municipal interest-rate

derivatives. Just like companies in the private sector, states and local governments have sought

to benefit from interest rate swaps, and the market for municipal interest rate derivatives

has experienced similar growth. For example, today, 70% of issuers of variable-rate demand

obligations (VRDOs), a certain type of long-term floating rate bond, have entered into interest

rate swaps.5 With the increased usage, the economic soundness of some municipal swap

transactions has been questioned recently, and some local governments are bringing lawsuits

against the financial institutions that wrote the swaps. A wave of allegedly suspect municipal

swap transactions has surfaced both in the US and Europe, and Italy in particular. We review

some of the economic aspects of current and potential litigation in Section III.

Like most financial assets, interest rate swaps have inherent risks. Some of these risks can be

off-set by other risks on the balance sheet of a business or a government entity, in which case

the swap can be used as a hedging instrument. Other risks are swap-specific though, and

may or may not be easily mitigated. All these risks need to be considered in deciding among

alternative financing options. Further, when using swaps as hedging instruments, a user gives

up potential gains in some states of the world in exchange for protection from potential losses

in other states of the world. This implies that there may be a difference between ex-ante

optimality and ex-post performance of a given swap. Questions related to risks, optimality, and

performance of swaps are elements of contention in recent swap litigation.

The next section describes the basic functioning of a (plain vanilla) interest rate swap. Section

III describes the use of interest rate swaps by municipalities, and gives a high-level overview of

recent litigation involving municipal interest rate swaps in the US. We also give an overview of

similar litigation, some with potentially high stakes, brought by local governments in Italy. In

Section IV we analyze the economic benefits of swaps and discuss economic aspects of interest

rate swaps that are of relevance in current and potential swap litigation.

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II. Interest Rate SwapsAn interest rate swap is a periodic exchange of fixed coupon payments by one counterparty

(called the fixed-rate payer) in return for variable-rate payments by another counterparty

(called the floating-rate payer), until a stated maturity.6

By combining interest rate swaps with alternative financing options, interest rate swaps increase

the number of ways in which a firm can borrow. This can lead to lower borrowing costs and

better interest rate risk management. The following example explains how a swap between two

counterparties works.

A relatively risky borrower, BBB Corp., needs a fixed rate to finance new long-term investment.

The company can finance the investment either by borrowing from a bank or in the direct

market by issuing bonds. The company is able to borrow from the bank at a variable rate of

LIBOR + 2%.7 Because it is a company with a relatively large default risk, it can only issue bonds

at a rate of 10%. Next, consider a good credit risk, AAA Corp., which would like to borrow at

a variable rate. Because it has high credit ratings and a low probability of default, the company

pays LIBOR + 1% on its bank loans and can issue bonds at a rate of 7%.

Assuming LIBOR is 5%, the following table shows the interest rates faced by the two companies

in the two different markets:

Table 1. Hypothetical Interest Rates on AAA Corp. and BBB Corp.’s Obligations

Bank Loan Bonds

(Short Term) (Long Term)

BBB Corp. 7.00% 11.00%

AAA Corp. 6.00% 7.00%

Quality Spread (difference) 1.00% 4.00%

BBB Corp. pays more to borrow in both markets. However, the bond market requires a quality

spread 3% larger than the bank loan market (4% - 1%). BBB Corp. is said to have a comparative

advantage in the bank loans market, while AAA Corp. is said to have a comparative advantage

in the bond market.

Without swaps, BBB Corp. can meet its financing needs by borrowing long term at 11%,

and AAA Corp. by taking a renewable bank loan at LIBOR + 1% (6%). Alternatively, they can

each borrow from the market in which they have a comparative advantage, and then swap

the payments.

Assume both companies need $10 million in fresh capital. BBB Corp. takes a renewable loan

at LIBOR + 2% (starting at 7%) from its bank; AAA Corp. issues a 10-year bond at a 7% rate.

Under the terms of the 10-year swap for a $10 million notional principal, BBB Corp. pays a fixed

rate of 9% to AAA Corp., and AAA Corp. pays 2% over LIBOR to BBB Corp.

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Notice the fixed rate paid by BBB Corp. is two percentage points below the rate it would pay if

it issued 10-year bonds. AAA Corp. pays LIBOR + 2% in the swap, but receives a spread of 2%

over its fixed interest payment in the bond market from BBB Corp., so it ends up paying LIBOR

after the swap, a gain of one percentage point. The total potential gain from trade is three

percentage points. We analyze this potential gain from swaps in more detail in Section IV.B.

A. Pricing vs. Value of a SwapIn the example above, we have taken the fixed rate on the swap as given. This rate depends

on several factors, some of which are explained below. Determining the fixed rate at inception

is referred to as pricing of the swap. The swap is priced so that there is no upfront cash

exchange between the parties involved.

In practice, the fixed and floating payments are offset (or netted) against each other as

of each payment date, and the party paying the higher rate of interest remits a payment

to the counterparty equal to the notional amount multiplied by the difference between

the interest rates. So that if the swap rate (9% in our example) is greater than LIBOR, the

fixed-rate payer pays

(swap rate – LIBOR) × notional principal.

If LIBOR is greater than the swap rate, the floating-rate payer pays

(LIBOR – swap rate) × notional principal.8

Figure 1. An Interest Rate Swap Between BBB Corp. and AAA Corp.

BBB Corp.

Net Cost: LIBOR

LIBOR + 2%

LIBOR + 2% 7%

BondHolders

Bank

Net Cost: 9%

9%

AAA Corp.

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The swap rate determined at the inception of the swap reflects, among other things, market

expectations about future LIBOR rates and about the future ability of both payers to make the

payments. The rate at inception makes the swap a fair wager so that neither party is favored

at the expense of the other. Supply and demand in the market for swaps will establish a rate

that the market considers to be fair. At this rate, given market expectations about the future

payments, the net present value of the swap contract is zero.

The swap rate is determined by market conditions and expectations at inception. When these

conditions change, the rate for a new swap—the rate at which its net present value is zero—

also changes. This implies that the value of an old swap, whose rate is contractually fixed,

changes over time, and could become either positive or negative depending on the new

swap rate.

Consider the above example between BBB Corp. and AAA Corp. again. Suppose that at some

point after the swap contract is signed, interest rates are lower so that both companies could

borrow at a lower rate in both markets. Also assume that rates are such that the rate for a new

swap is 8%. Because the rate on the old swap is contractually fixed at 9%, BBB Corp., the fixed-

rate payer, would be willing to pay to cancel the old swap and enter into a new one at 8%. The

net present value of the old swap with a 9% rate is negative to the fixed-rate payer.

Conversely, if the rate for a new swap (the new prevailing swap rate) is 10%, the fixed-rate

payer gains from the old swap, and now AAA Corp. would be willing to pay to cancel the

swap. The net present value of the old swap is positive to the fixed-rate payer and the swap is

said to be in the money. To summarize:

The value of an outstanding swap to a fixed-rate payer is positively correlated with changes in

market interest rates. When interest rates increase, the value of the swap increases, and when

interest rates decrease, the value of the swap decreases.

B. Hedging and Speculating Using SwapsThe correlation between swap values and interest rates can be used to both hedge interest rate

risk and speculate on interest rate fluctuations.

Consider again the net cash flows of the two swap counterparties. At each payment date,

which party makes a payment depends on the LIBOR rate at the time. So, contingent on the

LIBOR rates over the life of a swap, the swap will result in a loss or a gain, ex-post. For a

variable rate borrower like BBB Corp.—someone that has an underlying position—this loss

or gain is completely off-set by the variable payments that also depend on LIBOR; in net, the

borrower pays the fixed rate at each date, so he is completely hedged.9

Swaps can also be used to transform the nature of a company’s balance sheet assets, allowing

a company to obtain the desired exposure to interest rates. For example, a company that owns

long-term assets yielding a fixed rate is subject to interest rate risk as the value of those assets is

negatively correlated to interest rates. So to hedge against a capital loss when interest rates fall,

the company can swap the fixed interest payments for floating interest payments.10

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For various reasons—including risk management, regulatory requirements, and debt

restructuring—companies and local governments routinely use interest rate swaps to hedge

their interest rate exposure. This practice has increased in the last decade.

As with any other financial instrument, swaps can also be used to speculate. An investor

is taking a speculative position if he does not have a corresponding underlying position (an

asset or a liability to hedge). His swap position is motivated solely by the prospect of a change

in value in the swap as a result of changing interest rates. A speculator may take a fixed-rate

payer position if he expects interest rates to rise or a floating-rate payer position if he expects

rates to decline.

III. Use of Interest Rate Swaps by Municipalities and Interest Rate Swaps Litigation Municipalities have several different options in issuing debt to generate needed cash flows.

Typically, municipalities issue short-term notes in anticipation of upcoming revenue, a practice

that allows them to cover temporary deficits. Long-term bonds, on the other hand, are issued

to finance ongoing budget deficits arising from investments in construction or other capital

projects. Whether issuing long- or short-term debt, municipalities must also decide on whether

to use a fixed or a floating rate. Furthermore, within each of these categories, there exist

several different types of securities. This can lead to complicated balance sheets with numerous

revenue obligations, all with different cash flow characteristics.

Other SwapsThere are many variations that can be applied to the plain vanilla fixed-for-floating interest rate swap contract. The

following are just a few, more common examples. In an amortizing swap, the principal notional is reduced over time

in a pre-determined way, often timed to match the amortization schedule of existing loans. The principal notional can

also increase over time, as in a step-up swap.

Swaps can be designed to exchange two floating payments that reference two different rates, as in basis (or floating-

to-floating) swaps. These serve to reduce basis risk, the risk that arises from an imperfect match between a

derivative contract (which may depend on LIBOR) and the underlying position, e.g., an asset returning a variable rate

based on commercial paper rates, or a liability with interest rates linked to short-term US Treasuries.

Notional amounts can be based on different currencies, as in a currency swap. These can be designed in any

combination of fixed and floating payments (fixed-for-fixed, fixed-for-floating, floating-for-floating).

Options on swaps and forward swaps are also traded. With a swaption, a party can acquire the right, at a future

time, to enter into a swap at a predetermined rate. In a forward swap, the two parties agree to exchange payments

starting at a future date.

Swaps are sometimes combined with other interest rate options. For example, a floating rate payer can limit his/her

interest rate payments with a ceiling, or can sell part of his/her gains from low interest rate payments with a floor.

Or s/he can collar his/her payments with both a floor and a ceiling.

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A municipality may find it useful to change the structure of some of its bonds in order to better

match its changing asset positions.11 Interest rate swaps can be useful to change floating-rate

debt into fixed-rate, or vice versa.

A study conducted by the Securities and Exchange Commission (SEC) in 2004 shows that 94%

of all municipal securities had a fixed coupon (77% by principal amount).12 However, relative to

fixed-rate securities, variable-rate securities were more likely to be long term.13 To hedge against

the risk of a rising interest rate, municipalities can enter into floating-to-fixed swap agreements,

wherein they receive a variable interest rate and pay a fixed rate. In some cases, this can also

provide the municipality with a lower cost of borrowing than simply issuing fixed-rate debt.14

For example, today, 70% of issuers of VRDOs, a certain type of long-term floating rate bond,

have entered into floating-to-fixed swaps.15 On the other hand, municipalities can also utilize

fixed-to-floating swaps on their fixed-rate debt depending on their overall hedging needs. For

municipalities, like private companies, swaps are a useful tool for liability management and they

can use them to restructure the existing debt mix any time they feel it is unbalanced.

A. US Municipal Interest Rate Derivatives LitigationRecent changes in reference interest rates have caused losses in swap positions taken by

hundreds of US municipalities.

With the fall in interest rates brought by the recent global financial crisis, the municipalities

are losing money on floating-to-fixed swap agreements they made during the bull market to

protect themselves against rising interest rates.16 In some cases, even with falling interest rates,

municipalities have found that the floating payments they make on their debt have increased,

due to downgrades to the credit companies insuring the debt.17 To compound the problem,

unwinding or terminating the swaps may be costly. For instance, the city of Oakland, California,

under an interest rate swap with Goldman Sachs, stands to pay a reported $5 million in 2010;

however, terminating the swap would cost an estimated $19 million.18

Many of the cases in which municipalities have suffered losses due to swap agreements have

led to litigation against banks, resulting in settlements or the restructuring of swap agreements

to provide more favorable terms to the municipalities. In a 2009 case, the Alabama Public

School and College Authority (APSCA) sued to void a swaption it had sold to JPMorgan and

refused to make payments on this swaption until a court decision had been made.19 The APSCA

agreed to pay $19 million in a settlement with JPMorgan on 28 December 2010.20 Many other

municipalities have pursued similar litigation, alleging that banks have understated the riskiness

of interest rate swaps.

In 2008, there were 136 defaults on municipal securities.21 The largest among these was

the default on $3.8 billion worth of sewer bonds by Jefferson County, Alabama.22 Like many

other municipalities, the county lost money on floating-to-fixed interest rate swaps following

the credit crisis.23 This has led to several lawsuits filed by the citizens of Jefferson County—

not only against Wall Street banks, but also against officials of the municipality. Chief among

the complaints alleged were that “unscrupulous investment bankers” took advantage of

the county’s lack of financial knowledge and that county commissioners neglected their

fiduciary duties.24

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Common among the above cited cases is the allegation that financial institutions have misled

or misrepresented municipalities about the risks involved with interest rate swaps and related

derivatives. In other litigation, the fees and profits that the banks made are called into question.

For example, in a lawsuit filed in August 2008, the Erie City School District in Philadelphia,

Pennsylvania alleged that JPMorgan and a Pennsylvania financial adviser colluded to charge

undisclosed fees on swaptions the municipality sold to the bank.25

B. Italian Interest Rate Derivatives LitigationSwaps between local governments and financial institutions are being investigated throughout

Italy by the “Guardia di Finanza,” the Italian police force under the authority of the Ministry

of Economy and Finance. As of 1 September 2010, swaps between 53 local governments and

several major banks had been investigated. The local governments include large cities, like

Milan, Rome, Florence, and Naples, and small ones, like Polino, a town of 290 people,26 as well

as the regional governments of Piedmont, Tuscany, and Lazio. In some cases charges have been

pressed, and at least the Milan case went to trial in May 2010 (no decision has been reached

yet). The banks involved in the Milan deal were Deutsche Bank, JP Morgan, DEPFA, and UBS.

As of 30 June 2010, almost 700 local governments had outstanding swap contracts for a total

notional principal of about €35 billion.27 Banca d’Italia statistics show that local governments’

derivative transactions with negative market value (including interest and credit derivatives)

add up to about €1.2 billion, as of June 2010. As of the same date, derivative transactions with

positive market value add up to about €143 million.28

Derivative transactions under investigation include fixed-to-floating and floating-to-fixed swaps,

step-up swaps, amortizing swaps, interest rate floors, ceilings, and interest rate collars.

The City of Milan issued a €1.68 billion, 30-year, fixed-rate bond in 2005 to retire a number

of existing loans. In connection with the bond issuance, it swapped the fixed bond payments

for “collared” variable payments (a fixed-to-floating with collar swap). Under the collared swap

agreement, the city pays a variable rate that is allowed to vary in reference to Euribor within the

boundaries of the collar. Milan prosecutors started investigating the transactions in June 2008

and the case culminated in the first criminal case against banks in Europe.29

There are two main allegations in the case. The first has to do with representations made by the

banks about the riskiness of the swap and its effect on the overall cost of debt. The city alleges

that the banks represented that refinancing with the swap would lower the city’s overall cost

of debt. The second main allegation is that the pricing of the swap was unfavorable to the city,

given that the banks booked an allegedly large profit when the swap was issued.30

The Milan case is seen as a litmus test for other Italian municipalities that have large negative

market value on their swaps, and the ruling could serve as a catalyst for many future lawsuits.

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Investigations and allegations in other current cases are similar. For example, in the Polino case,

the debt restructuring and the collared swaps of the town are effectively the same as the ones

in Milan, although with slightly higher interest rates. The investigation in progress in Rome

involves several derivative transactions connected to the issuance of a fixed-rate €1.4 million

bond. The derivatives include an amortizing swap, a fixed-to-fixed step-up swap, and a fixed-

to-variable swap. The swaps are reported to have a negative value as of September 2009.31

The investigation, carried on by the Rome Prosecutor office, is examining whether the

transactions constituted appropriate hedges, and whether the banks booked excessive profits

from the transactions.32

Litigation involving municipal interest rate swaps is not new. Between 1987 and 1989, the

London Borough of Hammersmith and Fulham undertook a total of 592 swap transactions with

a notional value of over £6 billion, at some point about 20 times its total debt.33 The London

High Court ruled in 1989 that the swap agreements were not legal because the trades were

deemed speculative, and not just hedges.34 The case went all the way to the House of Lords,

which decided that the swap agreements were unlawful and the transactions were void.

IV. Economic AnalysisWe have seen above that in current and potential litigation, two main aspects of swaps are

in contention. The first is whether the swaps were sound economic choices, once the risk-

return trade-off offered by the swaps is taken into account. The second element of contention

has to do with the pricing of the swap. In this section, we examine the main economic and

financial considerations of optimal swap decisions, highlighting potential trade-offs between

risk and reward. We then expand on the main aspects of swap pricing to understand the main

determinants of bank fees.

A. Comparing Financing AlternativesWhether a borrower should pay a fixed rate or a variable rate depends on his cash flow needs

subject to risk management considerations like balance sheet gaps between assets and liabilities

and cash flow hedging needs. Once a borrower has decided what type of financing fits his

needs best, swaps can be used to expand the set of available financing options. For example, if

the borrower desires a long-term fixed-rate loan, he can borrow directly in the bond market, or

borrow at a variable rate from a bank, and swap the floating rate for a fixed rate.35

In choosing between alternative financing and swap options, economic decision rules should be

based on the maximization of incremental firm value or, for a government agency, minimizing

financing costs, making appropriate risk-return considerations. For example, a floating-rate plus

swap option may result in a lower fixed rate than simple bond financing, but may leave the

borrower exposed to basis or other risks that we discuss below.

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B. Borrowing CostsIn the swap example of Section II, BBB Corp. and AAA Corp. exploited an apparently riskless

profit opportunity given by the difference in quality spreads between short-term and long-term

financing (a 3% quality difference). With the swap, BBB Corp. borrows long term at 9% instead

of the 11% without the swap, and AAA Corp. can borrow short-term at LIBOR instead of LIBOR

+ 1%. Why is it possible to lower the cost of financing using swaps? At least part of the answer

is that use of the swap leads to an efficient allocation of risks. Recall that our premise is that

BBB Corp. needs a 10-year fixed-rate loan. There are two risks associated with this loan: interest

rate risk and credit risk, and the two markets differ in their ability to bear these risks.

Relationship lenders like banks have an advantage in handling credit risk for small companies

with relatively higher risks of defaults like BBB Corp.: they may know more about the company,

they are better at monitoring, and are more flexible in dealing with repayment problems.

Because the bond market does not deal with the risks of small companies as well, bond

investors require a higher risk premium, reflected in a higher interest rate.

In contrast, typical bond investors—such as pension funds and life insurance companies—have

long-term liabilities, so long-term bonds match their liabilities and minimize interest rate risks.

As a result, the bond market is better suited to bear the interest rate risk inherent in a long-term

loan. On the other hand, banks typically have short-term liabilities on which they pay a variable

interest rate, and so are susceptible to interest rate risks when they lend long term.36

The swap allows credit risk to be separated from interest rate risk, and allows each risk to be

allocated to different markets according to their ability to handle the risks. The result is lower

financing costs for both parties.37

The example of BBB Corp. is relatively common. Typically, companies with good credit ratings

are able to borrow more cheaply than other borrowers, and their relative advantage is greatest

when borrowing at fixed rates for maturities of five years or longer.38

With highly developed financial markets, an important question is why there should be such an

apparent risk-free profit opportunity. The answer to this question is that BBB Corp. will borrow

at 9% only if it can continue to borrow short term at LIBOR + 2%. If BBB Corp.’s rating declines

over the life of the swap, its rate will be greater than 9%. So one reason why the quality spread

is higher for long-term bonds is that the financial markets expect BBB’s short-term spread over

LIBOR to rise over the life of the swap. In other words, the market expects the borrowing rate

to be higher than 9%, on average.

Similarly, AAA Corp. will borrow short term at LIBOR (instead of LIBOR + 1%) only if BBB Corp.

does not default. In case of default, AAA Corp. would either have to find another counterparty,

or borrow at LIBOR + 1%. Part of the difference in quality spreads between long-term and

short-term financing is the probability of a default by BBB.

To summarize, the lower fixed rate of a swap relative to long-term financing represents, in part,

compensation for risks that would not be faced by a borrower with long-term financing.

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C. Basis RiskTypically, swap payments depend on a common reference rate like LIBOR.39 If the variable

interest rate payments of a borrower reference the same rate, the swap provides a perfect

hedge. But if the variable interest rate is not the same as LIBOR, the borrower faces what is

called basis risk. The borrower receives LIBOR, but his variable payments could be higher or

lower than LIBOR. In this case the hedge is not perfect and the borrower will not be able to

achieve exact fixed-rate payments. Basis risk and the choice of the reference rate should be

considered when making a financing decision.

As a solution to basis risk, the issuer can enter into what is called a cost-of-funds swap, where

the financial institution in the swap agrees to match the variable interest rate on the actual

obligation, at a cost. This eliminates basis risk but makes a swap less tradable and less liquid.

There may be other, external factors that can cause a mismatch between variable-rate

payments and swap payments. For example, as we have seen in the Jefferson County case, the

downgrade of a bond insurer could lead to a large increase in the variable interest rate without

a corresponding increase in the reference rate. To the bond issuer, this is ultimately a form

of basis risk, a risk that should be considered when entering into a swap agreement.

D. Ex-Ante vs. Ex-Post Considerations Financing costs of different swaps and financing strategies will differ, ex-post, depending on

the behavior of interest rates. And a financing strategy that is optimal ex-ante can result in

higher financing costs ex-post. Consider a fixed-rate payer that has chosen, optimally, to issue

a variable rate obligation and swapped to fixed payments with a counterparty. If the variable

rate declines over the life of the swap, the borrower will find himself paying more with the

swap than he would have without the swap.

This does not necessarily mean that the swap was not an economically sound decision. In this

example, the purpose of the swap is to transform a variable-rate loan into a fixed-rate loan to

eliminate the risk of changing interest rates. With the swap, a borrower gives up the potential

gains from lower interest rates to avoid the potential losses from higher interest rates. The

potential gains/losses depend on future market conditions and the fixed rate determined at

inception. Competition in the swap market will ensure that the fixed rate at inception is such

that the swap is a fair wager, as explained in Section II.A.

E. Swap Value and Interest RatesWe have seen in Section II.A that as expectations and economic conditions change, the rate on

a new swap will differ from the rate on an old swap. In a competitive market, the change in the

swap rate will also affect the value of the old swap. Consider a plain vanilla swap that had value

of zero at inception, and suppose the rate on a new swap with the same maturity is lower than

the rate at inception. The market value of the swap from the fixed-rate-payer’s side must now

be negative. Otherwise, the fixed-rate payer could terminate the old swap, pocket its value, and

enter into a new swap at a lower rate. Similarly, if the swap rate goes up, the value of the old

swap will be positive.

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More generally, swap values depend directly on prevailing swap rates, which are affected by all

the interest rates with maturities up to the maturity of the swap, i.e., the yield curve of interest

rates.40 In contrast, swap values are not very sensitive to changes in the reference rate (like

LIBOR), all else equal. In this respect, interest rate swaps are similar to long-term bonds. For

example, the value of a floating-to-fixed swap will increase if the yield curve becomes steeper.41

In general, a hedger should not be concerned with this type of fluctuation in the value of the

swap. The fact that the value of the swap is negative at some point in time due to changes in

interest rates does not necessarily mean that the swap was a bad decision for a fixed-rate payer.

If it was determined at inception that a fixed-rate payment was optimal, the borrower’s interest

rate costs are exactly as expected.

However, certain value considerations should be made at the time of financing. Because the

hedging and financing needs of a company or government agency can change over time, it

is possible that the company or agency will need to unwind or restructure existing swaps at

a later date. In this case, it is important to understand the sensitivity of the swap to interest

rates, which can constitute a risk to the company or government agency. Because the value of a

swap responds to interest rate changes as a long-term bond with the same maturity, short-term

swaps may be preferable to long-term swaps in situations where hedging needs may change.

F. How the Swap Market WorksSo far, we have abstracted from the question of how the two parties in a swap transaction

meet. The swap market is not an auction market organized through an exchange; rather, it is

a dealer or over-the-counter (OTC) market where swaps are traded under standard contractual

terms organized through the ISDA. In this market, any counterparty, like BBB Corp., negotiates

the contractual terms of the swap with a dealer. In the case of plain vanilla interest rate swaps,

only the fixed rate and the maturity need to be negotiated. While we have so far focused on

the floating-to-fixed (plain vanilla) swap, the OTC market trades a high number of interest rate

derivatives tailored to the particular needs of different counterparties.

On economic principles, the competitiveness of a market—and the prices formed in it—does

not depend on whether trading is through bilateral negotiation (as in the OTC market) or in an

organized exchange. How competitive a market is depends on the number of buyers and sellers

in the market, the information available to them, and the type of instrument being traded. For

plain vanilla interest rate swaps, bid and ask rates are widely reported, dealers are numerous,

and they compete for business. Bid-ask spreads in these markets tend to be low, on the order

of 3-4 basis points (100 basis points equal 1%), indicating relatively high liquidity and low profit

margins, both signs of a competitive market.42 Market prices are therefore good indicators of

fair value for most plain vanilla swaps between counterparties with good credit (AA or higher,

more on this below).

Dealers in the OTC market, mainly banks and securities firms, provide liquidity to the market

by standing ready to enter either side of a swap transaction at their quoted rates, without

waiting to find a counterparty. They also provide liquidity by allowing counterparties to cancel a

contract in exchange for an appropriate payment.

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To balance their positions and manage their exposure to interest rate risk, dealers will frequently

offset the positions by swapping their exposure with other dealers in the interdealer market.

Alternatively, market makers can hedge their positions on exchange-traded markets, like in the

T-bond futures market.

One particularly appealing feature of the OTC market is the willingness of the dealers to tailor

contracts to the needs of a counterparty. This allows a counterparty to hedge more precisely,

without incurring the risk involved with an imperfect hedge. Even if a tailored contract may be

less liquid relative to plain vanilla swaps or other options and futures traded on exchanges, for a

counterparty whose hedging needs are unlikely to change suddenly, the relative lack of liquidity

may be of secondary importance.

G. Mid-Market Pricing and ValuationDealers stand ready to write swap contracts with counterparties. This provides liquidity to the

market but leaves the dealers with certain risks and costs. To be profitable, dealers need to

pass these costs, along with a mark-up, to the counterparties in the swap. In practice, dealers

publish bid and ask swap rates at which they are willing to bid or offer a swap with another

dealer of good credit in the swap market (a AA credit or better). The bid rate is the fixed rate

paid by the dealer to a floating rate payer; the ask is the rate paid to the dealer by a fixed-rate

payer. The average between the bid and the ask is called mid-market swap rate. Mid-market

swap rates for different maturities make what is called the swap curve or “par” curve. The

mid-market swap rates have the property that the net present value of a swap between good

credit counterparties at inception is zero (hence the “par” rate). That is, the net present value of

the cash flows to the floating-rate payer is equal to the net present value of the cash flows to

the fixed-rate payer.

1. Adjustments to Pricing

To arrive at a swap rate for a non-dealer client, a dealer typically adds certain costs to the mid-

market rate. This model of pricing a swap is called mid-market pricing with adjustments.

Adjustments can vary depending on the counterparty and the type of transaction, and may

include adjustments for credit risk, hedging costs, administrative and other costs, liquidity, and

a profit margin.43 Typically, at the inception of the swap, no money changes hands between the

dealer and the counterparty. Dealers incorporate these cost adjustments into the fixed swap

rate, which will be higher (lower) than the mid-market rate for a fixed-rate payer (receiver). As a

result, the net present value of the swap at inception will not be zero. It will be positive for the

dealer, and negative for the swap counterparty.

To quantify the value added of the transaction, a dealer will subtract some of the costs

described above, like credit and hedging costs, from the positive value, and will arrive at a

measure known as initial net present value (INPV), which will typically be positive.44 This value is

a measure of the dealer’s compensation for the costs and risks involved in the swap transaction.

2. Credit Risk Adjustments

Consider a dealer that has entered into offsetting contracts with two counterparties. If neither

party defaults, the dealer is fully hedged. If one of the two parties defaults, the dealer still has

to honor the contract with the other party. Suppose a fixed-rate payer defaults. The dealer will

have to pay the floating-rate payer

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(swap rate – LIBOR) × notional principal

any time the swap rate is above LIBOR, and will receive

(LIBOR – swap rate) × notional principal

any time the swap rate is below LIBOR.

Recall that at inception, the swap rate is set so that the present value of the two streams of

contingent payments are equivalent. So, even with counterparties with higher risk, the risk of

default to a dealer is relatively small, although not zero, right after inception. As we move away

from inception though, with changes in interest rates, the net present value of the contingent

payments could be substantially different from zero, either positive or negative.

Consider the case of a fixed-rate payer that defaults. If the net present value to a fixed-rate

payer is negative, s/he will be expected to pay more than s/he expects to receive. These

payments will now fall on the financial institution that wrote the swap. If it wants to offset this

position, the financial institution will be asked to pay roughly the net present value amount

to induce a third party to accept the position. This amount represents the dealer’s expected

exposure. If the net present value is positive, it’s unlikely that the dealer would be able to

realize the gain, as the fixed-rate payer could sell the position and realize the gain before

default. This implies that the expected exposure conditional on a default follows the hockey-

stick pattern below as a function of the value of the swap to the fixed-rate payer.

Figure 2. Dealer Exposure Given Default as a Function of Swap Value

Swap Value to FixedRate Payer

DealerExposure

0

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Numerical simulation methods can be used, along with the payoff structure of the above

chart, to estimate a dealer’s expected exposure at any given time (when a default has not yet

occurred). The expected exposure can be used to adjust the pricing of the swap to account for

credit risk. There are two main sources of changes in the expected exposure, and therefore the

pricing adjustment: (i) interest rate changes and (ii) a change in the credit risk of the borrower.

The exposure can be large if, some time after inception, interest rates change or the credit

quality of the counterparty deteriorates.

The same considerations apply to a floating-rate payer, with the sign of contingent payments

(and the present value) reversed.

In addition to credit adjustments, financial institutions can manage their exposure to

counterparty risk by requiring that the counterparty posts collateral against the exposure.

Collateralization is very common in OTC derivatives and has been increasing over the years.45

3. Other AdjustmentsWhen a market-maker writes a swap with a counterparty, he does it without waiting to match

fixed-rate and floating-rate payers. This exposes the market maker to interest rate risk. And

balancing this risk through the inter-dealer market or exchange-traded contracts is costly.

A dealer will pass these hedging costs to its counterparties through the quoted rates. The

same situation arises when the market-maker agrees to cancel an existing swap. An example

of hedging costs is the fraction of the interdealer bid-ask spread a dealer would have to pay

to offset a transaction in the interdealer market.

Because swap transactions use dealers’ capital, dealers include a profit margin adjustment

to the mid-market valuation to reflect compensation for the use of funding (cost of capital).

Other adjustments include administrative and other costs, and liquidity adjustments. For some

exotic or infrequently traded derivatives, mid-market pricing overstates the value of these

assets. A dealer will adjust the pricing to compensate for the lack of liquidity of the assets.

V. ConclusionsThis paper presents an overview of the economics of swaps and the market they trade in.

Taking recent municipal swap litigation as a starting point, we have also analyzed some of the

risk-return trade-offs that users of swaps face.

In choosing between alternative financing and swap options, economic decision rules should

be based on the minimization of the present value of interest costs subject to risk management

considerations like balance sheet gaps between assets and liabilities and cash flow hedging

needs. As with other risky assets, the benefits from using swaps are, at least in part,

compensation for bearing certain risks, like the risk of a rating downgrade, a default, and

basis risk.

Determining the appropriate value of a swap at any point in time is clearly crucial in making the

right decisions. We have reviewed and motivated the main pricing approach, the mid-market

model, and the main adjustments to this model, particularly credit risk. The adjustments should

rely on sound economic models, and the models should make appropriate risk adjustments to

expected losses and expected defaults.

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1 Special thanks to Lucy Allen, Jonah Bernstein, Renzo Comolli, James Overdahl, and Vivienne Zhao for many helpful comments. Vivienne Zhao also provided outstanding research assistance.

2 Financial derivatives originated in their basic form in the Middle Ages, with the need to mitigate some of the risks involved with maritime merchants. One of the first contracts was the sea loan, an attempt to trade casualty risk. See Meir Kohn, Risk Instruments in the Medieval and Early Modern Economy, mimeo, Dartmouth College, 1999.

3 As explained below, the notional principal is used to calculate periodic swap payments, but does not actually changes hands. BIS statistics available at http://www.bis.org/statistics/derstats.htm.

4 Statistics available at http://www.isda.org/.

5 “Speech by SEC Chairman: Remarks at Investment Company Institute 2010 General Membership Meeting,” Dow Jones Newswire, 7 May 2010.

6 The fixed-rate payer is said to have a long position in the (floating-to-fixed) swap, while the floating-rate payer is said to have a short position in the swap.

7 LIBOR is short for London Interbank Offered Rate, the rate published by the British Bankers’ Association. It represents an average rate at which a financial institution is prepared to make a deposit with other AA-rated banks.

8 We use LIBOR throughout to simplify exposition. But swaps may use other reference rates, like Treasury rates, commercial paper rates, etc. These payoffs assume that the parties will perform on their payments. Credit risk adjustments are discussed in Section IV.G. Because the principal in a swap is not exchanged at maturity, it is termed notional and is only used to calculate the periodic payments.

9 We are abstracting from basis risk here. As we’ll see below, basis risk and other risks can interfere with this mechanism, and so even with falling rates, a variable rate issuer can find themselves with increased variable liabilities.

10 Technically, using interest rate swaps, a company can change the duration of its assets and liabilities to obtain a desired exposure to interest rates.

11 Chu, Eric H., et al., “Interest Rate Swaps and Their Application to Tax-Exempt Financing,” in Handbook of Municipal Bonds, Fabozzi & Feldstein editors, Wiley, 2008, p. 313.

12 Report on Transactions in Municipal Securities, Office of Economic Analysis, United States Securities and Exchange Commission, 1 July 2004.

13 Ibid.

14 Chu, Eric H., et al., “Interest Rate Swaps and Their Application to Tax-Exempt Financing,” in Handbook of Municipal Bonds, Fabozzi & Feldstein editors, Wiley, 2008, p. 313.

15 “Speech by SEC Chairman: Remarks at Investment Company Institute 2010 General Membership Meeting,” Dow Jones Newswire, 7 May 2010.

16 “Interest-Rate Deals Sting Cities, States,” Wall Street Journal, 22 March 2010.

17 “Alabama Schools to Skip Payment on JPMorgan Swap Deal (Update2),” Bloomberg, 8 April 2009.

18 The swap has a negative value to the city. Interest-Rate Deals Sting Cities, States,” Wall Street Journal, 22 March 2010.

19 “Alabama Schools to Skip Payment on JPMorgan Swap Deal (Update2)”, Bloomberg, 8 April 2009.

20 “Judge OKs Deal in Alabama, JPMorgan Swaption Suit,” Bloomberg, 27 December 2010.

21 “Speech by SEC Chairman: Remarks at Investment Company Institute 2010 General Membership Meeting,” Dow Jones Newswire, 7 May 2010.

22 Ibid.

23 “Alabama County Won’t Pledge $184 Million for Swaps (Update3),” Bloomberg, 6 March 2008.

24 “Alabama group files suit over Jefferson County debt,” Reuters, 5 September 2008; “JPMorgan, 11 Others Sued Over Jefferson County Crisis (Update),” Bloomberg, 17 June 2008.

25 “JP Morgan, Facing Federal Probe, Exits Municipal Swaps (Update 3),” Bloomberg.com, 4 September 2008.

26 “Derivati: Indagini in corso su 53 enti,” ilSole24Ore.com, 1 September 2010; “Impossible to Understand Swap Burns 290-Person Italian Hamlet,” Bloomberg, 19 June 2009.

27 According to the Ministry of Economy and Finance data, see “Ma I radar del Tesoro non segnalano allarmi,” ilSole24Ore.com, 1 September 2010.

28 Banca d’Italia, “Local Government Debt,” Supplements to the Statistical Bulletin, Volume XX, 29 October 2010.

29 “Quattro banche rinviate a giudizio per i derivati al comune di Milano,” Il Sole 24 Ore, 17 March 2010.

30 “Quattro banche rinviate a giudizio per i derivati al comune di Milano,” Ibid.

31 “L’inchiesta sui derivati di Roma,” Sole 24 Ore, 1 September 2010.

32 In Milan, the allegation of excessive profits is that the banks have charged “commissioni occulte,” i.e., hidden fees at inception, similar to the Erie City School District case.

33 “Interest rate swaps—law lags behind financiers,” Law Society Gazette, 8 November 1989.

34 “British Curb On Rate Swaps,” New York Times, 23 February 1990.

35 See Titman, S., “Interest Rate Swaps and Corporate Financing Choices,” The Journal of Finance, Vol XLVII, 1992, for a theoretical justification of swaps.

36 See Meir Kohn, Financial Institutions and Markets, Second Edition, Oxford University Press, 2004.

37 This is simply an application of David Ricardo’s comparative advantage principle to trading in risk. See for example, Bicksler and Chen, “An Economic Analysis of Interest Rate Swaps,” Journal of Finance, Vol. 41, Issue 3, 1986: 645-655; and Meir Kohn, Financial Institutions and Markets, Second Edition, Oxford University Press, 2004.

38 See, for example, Marcia Stigum, Stigum’s Money Market, Fourth Edition, McGraw-Hill, 2004; and Bicksler and Chen, “An Economic Analysis of Interest Rate Swaps,” Journal of Finance, Vol. 41, Issue 3, 1986: 645-655.

39 Other rates are short-term treasury rates, commercial paper rates, the SIFMA rate, etc.

40 The yield curve is a chart of interest rates as a function of the maturity of the underlying bonds.

41 That is, long-term rates increase more than short-term rates. In contrast, the value of the swap will decrease over time if the yield curve remains unchanged (and upward sloping). See, for example, Jorion, Philippe, Financial Risk Manager Handbook, Fifth Edition, Wiley Finance, 2009.

42 See, for example, Hull, J., Options, Futures, and Other Derivatives, 7th Edition, 2008; or Bank One Corporation v. Commissioner of Internal Revenue, 120 T.C. No. 11, 2 May 2003, p. 52.

43 See also ISDA, “The Value of a New Swap,” ISDA Research Notes, Issue 3, 2010, for a description of mid-market pricing and more details about some of the costs.

44 ISDA “The Value of a New Swap,” ISDA Research Notes, Issue 3, 2010.

45 See ISDA, ISDA Margin Survey 2010, International Swaps and Derivatives Association, 2010, for statistics about usage of collateralization. According to the ISDA Margin Survey 2010, 84% of fixed-income derivatives trades are subject to collateral arrangements.

Notes

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For further information and questions, please contact the author:

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