An interest rate swap is a contract between two parties to exchange a series of cash flows

interest rate

similar to those that would result if the parties instead were to exchange equal dollar values of

swaps

different types of bonds. Swaps arose originally as a means of managing interest rate risk. The

Contracts between

volume of swaps has increased from virtually zero in 1980 to about $60 trillion today. (Inter-

two parties to trade

est rate swaps do not have anything to do with the Homer“Leibowitz bond swap taxonomy set

the cash flows

corresponding to out earlier.)

different securities To illustrate how swaps work, consider the manager of a large portfolio that currently in-

without actually

cludes $100 million par value of long-term bonds paying an average coupon rate of 7%. The

exchanging the

manager believes that interest rates are about to rise. As a result, he would like to sell the

securities directly.

bonds and replace them with either short-term or floating-rate issues. However, it would be

exceedingly expensive in terms of transaction costs to replace the portfolio every time the

forecast for interest rates is updated. A cheaper and more flexible way to modify the portfolio

is for the manager to “swap” the $7 million a year in interest income the portfolio currently

generates for an amount of money that is tied to the short-term interest rate. That way, if rates

do rise, so will the portfolio™s interest income.

A swap dealer might advertise its willingness to exchange or “swap” a cash flow based on

the six-month LIBOR rate for one based on a fixed rate of 7%. (The LIBOR, or London In-

terBank Offer Rate, is the interest rate at which banks borrow from each other in the Eurodol-

lar market. It is the most commonly used short-term interest rate in the swap market.) The

portfolio manager would then enter into a swap agreement with the dealer to pay 7% on

notional principal of $100 million and receive payment of the LIBOR rate on that amount of

notional principal

notional principal.4 In other words, the manager swaps a payment of 0.07 $100 million for

Principal amount used

a payment of LIBOR $100 million. The manager™s net cash flow from the swap agreement

to calculate swap

is therefore (LIBOR 0.07) $100 million.

payments.

4

The participants to the swap do not loan each other money. They agree only to exchange a fixed cash flow for a vari-

able cash flow that depends on the short-term interest rate. This is why the principal is described as notional. The no-

tional principal is simply a way to describe the size of the swap agreement. In this example, the parties to the swap

exchange a 7% fixed rate for the LIBOR rate; the difference between LIBOR and 7% is multiplied by notional prin-

cipal to determine the cash flow exchanged by the parties.

Bodie’Kane’Marcus: III. Debt Securities 10. Managing Bond © The McGraw’Hill

Essentials of Investments, Portfolios Companies, 2003

Fifth Edition

367

10 Managing Bond Portfolios

Now consider the net cash flow to the manager™s portfolio in three interest rate scenarios:

LIBOR Rate

6.5% 7.0% 7.5%

Interest income from bond portfolio ( 7% of

$100 million bond portfolio) $7,000,000 $7,000,000 $7,000,000

Cash flow from swap [ (LIBOR 7%)

notional principal of $100 million] (500,000) 0 500,000

Total ( LIBOR $100 million) $6,500,000 $7,000,000 $7,500,000

Notice that the total income on the overall position”bonds plus swap agreement”is now

equal to the LIBOR rate in each scenario times $100 million. The manager has in effect con-

verted a fixed-rate bond portfolio into a synthetic floating-rate portfolio.

You can see now that swaps can be immensely useful for firms in a variety of applica-

tions. For example, a corporation that has issued fixed-rate debt can convert it into synthetic

floating-rate debt by entering a swap to receive a fixed interest rate (offsetting its fixed-rate

coupon obligation) and pay a floating rate. Or, a bank that pays current market interest rates to

its depositors might enter a swap to receive a floating rate and pay a fixed rate on some

amount of notional principal. This swap position, added to its floating-rate deposit liability,

would result in a net liability of a fixed stream of cash. The bank might then be able to invest

in long-term fixed-rate loans without encountering interest rate risk.

What about the swap dealer? Why is the dealer, which is typically a financial intermediary

such as a bank, willing to take on the opposite side of the swaps desired by these participants?

Consider a dealer who takes on one side of a swap, let™s say paying LIBOR and receiving

a fixed rate. The dealer will search for another trader in the swap market who wishes to re-

ceive a fixed rate and pay LIBOR. For example, company A may have issued a 7% coupon

fixed-rate bond that it wishes to convert into synthetic floating-rate debt, while company B

may have issued a floating-rate bond tied to LIBOR that it wishes to convert into synthetic

fixed-rate debt. The dealer will enter a swap with company A in which it pays a fixed rate and

receives LIBOR, and it will enter another swap with company B in which it pays LIBOR and

receives a fixed rate. When the two swaps are combined, the dealer™s position is effectively

neutral on interest rates, paying LIBOR on one swap, and receiving it on another. Similarly,

the dealer pays a fixed rate on one swap and receives it on another. The dealer is an interme-

diary, funneling payments from one party to the other.5 The dealer finds this activity profitable

because it will charge a bid“ask spread on the transaction.

This arrangement is illustrated in Figure 10.9. Company A has issued 7% fixed-rate debt

(the leftmost arrow in the figure) but enters a swap to pay the dealer LIBOR and receive a

6.95% fixed rate. Therefore, the company™s net payment is 7% (LIBOR 6.95%)

LIBOR 0.05%. It has thus transformed its fixed-rate debt into synthetic floating-rate debt.

Conversely, company B has issued floating-rate debt paying LIBOR (the rightmost arrow), but

enters a swap to pay a 7.05% fixed rate in return for LIBOR. Therefore, its net payment is

LIBOR (7.05% LIBOR) 7.05%. It has thus transformed its floating-rate debt into syn-

thetic fixed-rate debt. The bid“ask spread in the example illustrated in Figure 10.9 is 0.1% of

notional principal each year.

5

Actually, things are a bit more complicated. The dealer is more than just an intermediary because it bears the credit

risk that one or the other of the parties to the swap might default on the obligation. Referring to Figure 10.9, if com-

pany A defaults on its obligation, for example, the swap dealer still must maintain its commitment to company B. In

this sense, the dealer does more than simply pass through cash flows to the other swap participants.

Bodie’Kane’Marcus: III. Debt Securities 10. Managing Bond © The McGraw’Hill

Essentials of Investments, Portfolios Companies, 2003

Fifth Edition

368 Part THREE Debt Securities

6.95% 7.05%

7% coupon

Company A Swap dealer Company B

LIBOR

LIBOR LIBOR

Company B pays a fixed rate of 7.05% to the swap dealer in return for LIBOR.

Company A receives 6.95% from the dealer in return for LIBOR. The swap dealer

realizes a cash flow each period equal to .1% of notional principal.

F I G U R E 10.9

Interest rate swap

>

9. A pension fund holds a portfolio of money market securities that the manager

Concept

believes are paying excellent yields compared to other comparable-risk short-term

CHECK securities. However, the manager believes that interest rates are about to fall.

What type of swap will allow the fund to continue to hold its portfolio of short-term

securities while at the same time benefiting from a decline in rates?

SUMMARY • Even default-free bonds such as Treasury issues are subject to interest rate risk. Longer

term bonds generally are more sensitive to interest rate shifts than short-term bonds.

A measure of the average life of a bond is Macaulay™s duration, defined as the weighted

average of the times until each payment made by the security, with weights proportional to

the present value of the payment.

• Duration is a direct measure of the sensitivity of a bond™s price to a change in its yield.

The proportional change in a bond™s price approximately equals the negative of duration

times the proportional change in 1 y.

• Immunization strategies are characteristic of passive bond portfolio management. Such

strategies attempt to render the individual or firm immune from movements in interest

rates. This may take the form of immunizing net worth or, instead, immunizing the future

accumulated value of a bond portfolio.

www.mhhe.com/bkm

• Convexity refers to the curvature of a bond™s price-yield relationship. Accounting for

convexity can substantially improve on the accuracy of the duration approximation for

bond-price sensitivity to changes in yields.

• Immunization of a fully funded plan is accomplished by matching the durations of assets

and liabilities. To maintain an immunized position as time passes and interest rates

change, the portfolio must be periodically rebalanced.

• A more direct form of immunization is dedication or cash flow matching. If a portfolio is

perfectly matched in cash flow with projected liabilities, rebalancing will be unnecessary.

• Active bond management can be decomposed into interest rate forecasting techniques and

intermarket spread analysis. One popular taxonomy classifies active strategies as

Bodie’Kane’Marcus: III. Debt Securities 10. Managing Bond © The McGraw’Hill

Essentials of Investments, Portfolios Companies, 2003

Fifth Edition

369

10 Managing Bond Portfolios

substitution swaps, intermarket spread swaps, rate anticipation swaps, or pure yield pickup

swaps.

• Interest rate swaps are important instruments in the fixed-income market. In these

arrangements, parties trade the cash flows of different securities without actually

exchanging any securities directly. This can be a useful tool to manage the duration of a

portfolio.

KEY

cash flow matching, 358 interest rate swaps, 366 pure yield pickup

TERMS

contingent immuni- intermarket spread swap, 362

zation, 364 swap, 362 rate anticipation swap, 362

convexity, 359 Macaulay™s duration, 342 rebalancing, 355

dedication strategy, 358 modified duration, 345 substitution swap, 362

horizon analysis, 363 notional principal, 366 tax swap, 363

immunization, 350

PROBLEM

1. A nine-year bond has a yield of 10% and a duration of 7.194 years. If the bond™s yield

SETS

changes by 50 basis points, what is the percentage change in the bond™s price?

2. Find the duration of a 6% coupon bond making annual coupon payments if it has three

years until maturity and a yield to maturity of 6%. What is the duration if the yield to

maturity is 10%?

3. A pension plan is obligated to make disbursements of $1 million, $2 million, and

$1 million at the end of each of the next three years, respectively. Find the duration of

the plan™s obligations if the interest rate is 10% annually.

4. If the plan in problem 3 wants to fully fund and immunize its position, how much of its

portfolio should it allocate to one-year zero-coupon bonds and perpetuities, respectively,

if these are the only two assets funding the plan?

5. You own a fixed-income asset with a duration of five years. If the level of interest rates,

which is currently 8%, goes down by 10 basis points, how much do you expect the price

of the asset to go up (in percentage terms)?

6. Rank the interest-rate sensitivity of the following pairs of bonds.

a. Bond A is an 8% coupon bond, with 20-year time to maturity selling at par value.

Bond B is an 8% coupon, 20-year maturity bond selling below par value.

b. Bond A is a 20-year, noncallable coupon bond with a coupon rate of 8%, selling at par.

Bond B is a 20-year, callable bond with a coupon rate of 9%, also selling at par.

7. Rank the following bonds in order of descending duration.

Bond Coupon Time to Maturity Yield to Maturity

A 15% 20 years 10%

www.mhhe.com/bkm

B 15 15 10

C 0 20 10

D 8 20 10

E 15 15 15

8. Philip Morris has issued bonds that pay annually with the following characteristics:

Coupon Yield to Maturity Maturity Macaulay Duration

8% 8% 15 years 10 years

Bodie’Kane’Marcus: III. Debt Securities 10. Managing Bond © The McGraw’Hill

Essentials of Investments, Portfolios Companies, 2003

Fifth Edition

370 Part THREE Debt Securities

a. Calculate modified duration using the information above.

b. Explain why modified duration is a better measure than maturity when calculating

the bond™s sensitivity to changes in interest rates.

c. Identify the direction of change in modified duration if:

i. The coupon of the bond were 4%, not 8%.

ii. The maturity of the bond were 7 years, not 15 years.

9. You will be paying $10,000 a year in tuition expenses at the end of the next two years.

Bonds currently yield 8%.

a. What is the present value and duration of your obligation?

b. What maturity zero-coupon bond would immunize your obligation?

c. Suppose you buy a zero-coupon bond with value and duration equal to your

obligation. Now suppose that rates immediately increase to 9%. What happens to

your net position, that is, to the difference between the value of the bond and that of

your tuition obligation? What if rates fall to 7%?