7.1Examples of Derivatives
This section introduces a number of derivatives: forwards and futures, swaps, options,
corporate bonds, mortgage-backed securities, and structured notes. The section also
introduces derivatives that are implicit in real assets.
Forwards and Futures
Aforward contractrepresents the obligation to buy (sell) a security or commodity at
a prespecified price, known as the forward price,at some future date. Forward con-
tracts are inherent in many business contracts and have been in existence for hundreds
of years. Exhibit 7.1 illustrates the exchange that takes place at the maturity date, or
settlement date, of the forward contract. At maturity, the person or firm with the long
position pays the forward price to the person with the short position, who in turn deliv-
ers the asset underlying the forward contract. Futures contractsare a special type of
forward contract that trade on organized exchanges known as futures markets.
Exhibits 7.2 and 7.3 introduce foreign exchange forwards and futures. The “Cur-
rency Trading” listing in TheWall Street Journal(see Exhibit 7.2) shows 1-, 3-, and
6-month forward currency rates for exchanging dollars for British pounds, Canadian
dollars, French francs, German marks, Japanese yen, and Swiss francs. The rates are
2An investment bank will often serve as an over-the-counter market maker in the derivative it creates,
standing ready to buy the derivative at a bid price and sell it at an ask price.
3The valuation of options, one of the most popular derivatives, is covered in depth in Chapter 8,
which also touches briefly on forward prices for some complex assets such as bonds, commodities, and
foreign exchange.
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EXHIBIT7.1 |
The Exchange of an Asset forCash in a Forward Contract at Maturity |
|
-
Cash (forward price)
Long position in
Short position in
forward contract
forward contract
Underlying asset
EXHIBIT7.2Currency Trading
Source: Reprinted by permission of TheWall Street Journal,©2000 by Dow Jones & Company. All Rights Reserved.
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EXHIBIT7.3Futures Prices forCurrency
Source: Reprinted by permission of The Wall Street Journal, ©2000 by Dow Jones & Company. All Rights Reserved
Worldwide.
similar to those provided in the futures market (see Exhibit 7.3). For example, the
Japanese yen had a foreign exchange rate on Tuesday, October 24, 2000, at 4 P.M. New
York time, of 107.91 yen to the U.S. dollar. However, the 6-month forward rate was
104.64 yen to the dollar. This means that one could have agreed at 4 P.M.that day to
have exchanged a single U.S. dollar for 104.64 yen 6 month hence. Exhibit 7.3 contains
data on comparable exchange rate futures. The futures exchange rate with the closest
maturity, the March 2001 contract traded on the Chicago Mercantile Exchange, speci-
fies 100 yen is exchangeable for .9493 U.S. dollars, which translates into one U.S. dol-
lar being exchanged for 105.34 yen. The discrepancy between the two, 104.64 vs.
105.34, can be mostly attributed to differences in both the quote times and the matu-
rities of the forward contract and the futures contract.
Markets forForwards and Futures.The first organized futures trading market,
the Chicago Board of Trade, dates back to the U.S. Civil War. Although the Board’s
early trading records were lost in the Great Chicago Fire of 1871, the earliest futures
contracts were probably limited to agricultural commodities that were grown in the
Midwest.
Today, futures and forward markets are also well known for the trading of con-
tracts on financial securities, such as Treasury bonds, stock indexes, short-term inter-
est rate instruments, and currencies. Because of their sheer size and the relevance of
their prices to the actions of investors, the three most important financial futures mar-
kets are those that trade:
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EXHIBIT7.4Futures Prices forOil
Source: Reprinted by permission of The Wall Street Journal,©2000 by Dow Jones & Company. All Rights Reserved.
-
•
U.S. Treasury bond futures, which allows delivery of almost any treasury bondwith 15 years maturity or more remaining.
•
Eurodollar futures, which is a cash settled bet on the future value of three-month LIBOR.
•
S&P500 futures, a cash-settled bet on the future level of the S&P500 stock
index.
The most important financial forward market is the interbank forward market for cur-
rencies, particularly dollars for yen and dollars for Euros.
In Exhibit 7.4, the rows under “Crude Oil” provide the New York Mercantile
Exchange’s futures prices (in dollars per barrel) for contracts to buy 1,000 barrels of
light sweet crude oil. The column on the far right is the open interest, which is the
number of contracts outstanding. On October 24, 2000, there were 10,743 May ’01
contracts and 27,347 June ’01 contracts. Open interest can be thought of as the num-
ber of bets between investors about oil prices. The column labeled “Settle” describes
the closing price for October 23, 2000. This price is used, along with the previous day’s
settlement price, to determine how much cash is exchanged between parties to the con-
tract that day. The contracts maturing in mid-May 2001 and mid-June 2001 specify set-
tlement prices of $30.47 and $30.02 per barrel, respectively.
Distinguishing Forwards from Futures.The essential distinction between a forward
and a futures contract lies in the timing of cash flows. With a forward contract, cash
is paid for the underlying asset only at the maturity date, T,of the contract. It is useful
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to think of this cash amount, the forward price, F, which is set prior to maturity, at
0
date 0, as the sum of
1.What one would pay for immediate delivery of the underlying asset at the
maturity date, T, without the forward contract—this is known as the spot
priceat maturity, essentially, the prevailing market price of the underlying
asset. Call this S.
T
2.The profit (or loss) incurred as a result of having to pay the forward price in
lieu of this spot price. This is F S.
0T
With a futures contract, the price paid at maturity is the spot price, which is iden-
tical to the final day’s futures price, F.The profit (or loss) is received (paid) on a daily
T
basis instead of in one large amount at the maturity date. The amount the buyer receives
from (pays to) the seller of the futures contract is the one-day appreciation (deprecia-
tion) of the futures price. For example, if the futures price of oil rises from $30 a bar-
rel to $32 a barrel from Monday to Tuesday, the buyer of a futures contract on 1,000
barrels receives $2,000 from the seller on Tuesday. This procedure, known as mark-
ing to market, reduces the risk of default because the amounts that each side has to
pay on a daily basis are relatively small. Moreover, it facilitates early detection in the
event that one party to the contract lacks sufficient cash to pay for his or her losses.
The marking to market takes place automatically, by transferring funds between the
margin accounts of the two investors agreeing to the contract. These margin accounts
are simply deposits placed with brokers as security against default.
Example 7.1 illustrates how marking to market works.
Example 7.1:Marking to Market with S&P500 Futures
Trevor has a long position in the March futures contract to buy 1 unit of the S&P 500.Gor-
don has a short position in the same contract.If the futures price for the March S&P 500
contract is 1454 on January 12, but it rises to 1457 on January 13, and then falls to 1456.2
on January 14, and falls to 1455.5 on January 15, describe the cash payments and margin
accounts of Trevor’s long and Gordon’s short position.Assume that each of the margin
accounts of Trevor and Gordon initially contains $40.
Answer:The marking-to-market feature implies that the margin accounts of the long and
short positions are described by the table below:
-
Trevor’s
Gordon’s
Long
Change from
Short
Change from
Date
Margin
Day Before
Margin
Day Before
-
Jan.12
$40.0
—
$40.0
—
Jan.13
$43.0
$3.0
37.0
–$3.0
Jan.14
$42.2
–.8
37.8
.8
Jan.15
$41.5
–.7
38.5
.7
With a few exceptions, notably long-term interest rate contracts, the distinction in
the timing of cash flows from profits or losses has a negligible effect on the fair mar-
ket price agreed to in forward and futures contracts.4Hence, this text treats forward
and futures prices as if they are identical.
4See Grinblatt and Jegadeesh (1996).
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EXHIBIT7.5 |
The Cash Flows of a Five-YearSemiannual Fixed-for-Floating Interest Rate Swap:$100 Notional |
Year
0 .5 1 1.5 . . 4 4.5 5
. .
Fixed Rate 8% 8% 8% 8% 8%
Counterparty A$4$4$4. . .$4$104
Floating rate 5% 8% 6% 7% 8.6% 10% – . . . . .
Counterparty B$2.50$4$3$4.30$105
If day 0 forwards and futures prices for contracts maturing on day Tare identical,
it is easy to see that the total profit (excluding interest on cash balances) is iden-
tical with both the forward and the futures contract. With the forward contract, the
profitis
S F,all earned in cash on date T
T0
With the futures contract, at the same futures price of Fset at date 0, the profit is the
0
same
S F
T0
but this total profit is earned piecemeal, with
F Fthe difference between the day 1 and day 0 futures prices earned (lost)
10
on date 1
F Fearned (lost) on date 2
21
F Fearned (lost) on date 3
32
and so forth until the final days before maturity when
F Fis earned on date T 1 and
T 1T 2
S Fis earned on date T
TT 1
The day-to-day futures profits still sum to the same amount, S F,but the timing
T0
of the cash differs from the forward contract.
Swaps
Aswapis an agreement between two investors, or counterpartiesas they are some-
times called, to periodically exchange the cash flows of one security for the cash flows
of another. The last date of exchange determines the swap maturity. For example, a
fixed-for-floating interest rate swap(see Exhibit 7.5) exchanges the cash flows of a
fixed-rate bond for the cash flows of a floating-rate bond. The notional amountof the
swap represents the size of the principal on which interest is calculated.
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Netting in an Interest Rate Swap.The cash flows in an interest rate swap are net-
ted so that periodically, typically every six months, only one of two swap counterparties
pays cash and the other receives cash. In the typical swap, the floating rate is LIBOR.5
Example 7.2 illustrates how netting affects swap payments.
Example 7.2:Netting Payments in an Interest Rate Swap
If the fixed interest rate in a swap with semiannual payments is 8 percent per year (4 per-
cent for 6 months) and the floating interest rate is 8.6 percent per year, how much does the
party who pays the floating rate and receives the fixed rate receive or pay? What would hap-
pen to that party if, six months later, the floating interest rate had increased to 10 percent
per annum?
Answer:As seen in Exhibit 7.5, at year 4.5, counterparty Aswaps its fixed payments of
8%floating rate%
$4 $100with counterparty B’s floating payments $100.
22
8.6% 8%
Counterparty Bwould thus pay$.30 $100per $100 of notional amount
2
to counterparty A.If interest rates at year 4.5 increase to 10 percent, counterparty Bpays
10% 8%
$1.00 $100per $100 of notional amount to counterparty Aat year 5.
2
Growth of the Interest Rate Swap Market.Interest rate swaps are one of the great
derivatives success stories. At the end of 1987, the aggregate notional amount of inter-
est rate swaps outstanding was less than $800 billion. By the end of the decade, that
amount had more than doubled. Three years later, at the end of 1993, the aggregate
notional amount had grown to almost $10 trillion. By the middle of 2000, the estimated
notional amount of interest rate swaps exceeded $58 trillion, more than half the entire
derivatives market—many times the value of all U.S. stocks!6
Currency Swaps.Acurrency swap(see Chapter 2) exchanges cash flow streams in
two different currencies. Typically, it involves the periodic exchange of the cash flows
of a par bond denominated in one currency for those of a par bond denominated in
another currency. In contrast with a fixed-for-floating interest rate swap, which nets out
the identical principal of the two bonds at maturity and thus exchanges only interest
payments, the typical currency swap exchanges principal, which is denominated in two
different currencies, at the maturity date of the swap.
Example 7.3:Payments in a Currency Swap
Describe the exchange of payments in a fixed-for-fixed dollar-yen currency swap with annual
payments and a $100 notional amount as shown in Exhibit 7.6.The dollar bond has an inter-
est rate of 7 percent, the yen bond has an interest rate of 5 percent, and the current
exchange rate is ¥80/$.
Answer:Here, the interest rates of both bonds are fixed, but each is denominated in a
different currency.Thus, counterparty Awill exchange its $7 [(7%)$100] fixed payments
with counterparty B’s fixed payments of ¥400 [(5%)$100(80¥/$)], as illustrated in Exhibit
7.6.
5Swaps are often used in conjunction with interest rate caps and floors, which are also popular
derivatives. Caps pay when prevailing interest rates exceed a prespecified rate and floors pay if the
prespecified rate exceeds the prevailing rate. See Chapter 2 for further discussion.
6Swaps Monitor,website: www.swapsmonitor.com.
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EXHIBIT7.6 |
The Cash Flows of a Five-YearAnnual Yen-DollarFixed-Rate Currency Swap: $100 Notional |
Year
1 2 3 4 5
Dollar Rate ($100) 7% 7% 7% 7% 7%
Counterparty A$7$7$7$7$107
¥400¥400¥400¥400¥8,400
Counterparty B
Yen Rate (¥ 8,000) 5% 5% 5% 5% 5%
The typical forward contracts, futures contracts, and swap contracts are self-
financing, or zero-cost instruments7—
that is, the terms of these contracts are set so
that one party does not have to pay the other party to enter into the contract. In many
instances, margin or collateral is put up by both parties, which protects against default
in the event of extreme market movements, but this is not the same as paying some-
one to enter into the contract because the terms of the contract are more favorable to
one side than the other. There are exceptions to this zero-cost feature, however. Finan-
cial contracts can be modified in almost every way imaginable.
Options
Options exist on countless underlying securities. For example, there are swap options,
bond options, stock options, and options that are implicit in many securities, such as
callable bonds, convertible preferred stock, and caps and floors, which are options on
interest rates.8
Options give their buyers the right, but not the obligation, to buy (call option) or
sell (put option) an underlying security at a prespecified price, known as the strike
price. The value of the underlying security determines whether the right to buy or sell
will be exercised and how much the option is worth when exercised.
Most options have a limited life and expire at some future expiration date, denoted
as T. Some options, which are called American options (see Chapter 8), permit exer-
cise at any date up to T;others, which are called European options (see Chapter 8),
permit exercise only on date T.
Values of Calls and Puts at Expiration.Exhibit 7.7 outlines the values of a call and
put at their expiration date, T,as a function of S,the value of the underlying asset (for
T
example, here, a share of stock) at that date. Exhibit 7.7 illustrates that if an option is
7
See Chapter 5 for the first use of the term self-financing.
8See Chapter 2.
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EXHIBIT7.7 |
The Value of a Call Option and a Put Option at Expiration |
-
Call
Panel A: Call Option
value
-
No
Exercise region
exercise region
45
S T
Strike price
-
Put
Panel B: Put Option
value
-
No
Exercise region
exercise region
45
S T
Strike price
exercised at T,its value is the difference between the stock price and the strike price
(call) or between the strike price and the stock price (put). For example, if the stock is
selling at $105 at the expiration date, a call option with a strike price of $100 is worth
$5 because holding it is like having a coupon that allows the holder to buy stock at $5
off the going rate. If the stock is selling for $117, the call option is like a coupon for
a $17 mark-off. If the stock is selling for $94, the option is worthless since it is better
to buy the stock at the market price than to exercise the option and pay the price spec-
ified by the option. Exercise of a put allows the option holder to sell the stock at an
unfairly high price. For example, the right to sell a share of stock worth $48 at a price
of $50 is worth $2.
Panel Ain Exhibit 7.7 (a call) illustrates this point more generally. The horizontal
axis represents S,the price of the stock at expiration dateT, while the vertical axis
T
represents the value of the call at date T.If the price of the stock is below the strike
price of the call, the call option will not be exercised. Thus, the call has zero value. If
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the stock price is greater than the strike price, the value of the call rises one dollar for
each dollar increase in the stock price. The value of the call at date Tequals the max-
imum of either (1) zero or (2) Sless the strike price.
T
Panel B of Exhibit 7.7 (a put) illustrates that the opposite relation holds between
the value of the put and the value of the stock. Recall that the holder of a put possesses
the right to sellthe stock at the strike price. Thus, the value of the put at date Tequals
the maximum of either (1) zero or (2) the strike price less S.
T
In contrast to forwards, futures, and swaps, options benefit only one side of the
contract—the side that receives the option. Hence, the investor who receives an option
pays for it up front, regardless of the terms of the option.
Exchange-Traded Options.Options are an important segment of the securities markets
in the United States; four major options exchanges trade equity options. The Chicago
Board Options Exchange (CBOE) is the first and largest such exchange. The other
notable exchanges are the American Exchange, which is a division of the American
Stock Exchange; the Pacific Exchange, a division of the Pacific Stock Exchange; and
the Philadelphia Exchange. Exchange-traded options comprise the bulk of traded options,
although options on futures contracts, swaps, and bonds also are extremely popular.
The first three columns of The Wall Street Journal’s options quotations page (see
the bottom portion of Exhibit 7.8) reflect the call and put features described above.
These columns are labeled “OPTION/STRIKE,” “EXP.,” “VOL.,”and “LAST.” Under
632525.
AMD, for example, one finds 20, 25, Dec, 515, 1, 10, and 6What does all this
mean? It notes that AMD stock is the underlying risky asset, the strike price is $25 a
share, and the expiration date is a particular date in December 2000. At the close of
trading on October 24, 2000, AMD stock traded at $20.63 per share, the call option on
AMD traded at $1.25, and the put option traded at $6.25. The volume of trading—515
calls, each on 100 shares, and 10 puts, each on 100 shares—is reflected in the volume
column. The options with the largest volume, the exchange they trade on, and whether
they are calls or puts are listed in the top portion of the exhibit.
The day of expiration is not printed. Most brokers provide option expiration
calendars that contain this information free of charge. Also, it is understood that Ameri-
can options are the type of option traded on exchanges listed in The Wall Street Journal.
It is also important to understand other option terminology. The underlying asset
of a call (or put) option that is in the moneyhas a current price that is greater (less)
than the strike price. The underlying asset of a call (or put) option that is out of the
moneyhas a current price that is less (greater) than the strike price. An option at the
moneyis one for which the strike price and underlying asset’s price are the same.9As
you can see from Exhibit 7.8, the AMD call option is out of the money, but the put
option is in the money.
Investors seem to be most interested in options that are slightly out of the money.
Hence, most exchange-traded options are initially designed to be slightly out of the
money. As the underlying asset’s price changes, however, they can evolve into at-the-
money or in-the-money options.
You may notice from Exhibit 7.8 that most of the equity option volume is concen-
trated in the options expiring within the next six months. Afew stocks have substantial
9As implied by the terms, an in the moneyoption means that exercising the option is profitable
(excluding the cost of the option). Similarly, at-the-moneyand out-of-the-moneyimply that exercising the
option produces zero cash flow and negative cash flow, respectively, and thus, exercise should not be
undertaken.
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EXHIBIT7.8Listed Options Quotations
S
ource:
Reprinted by permission of The
Wall Street Journal,©2000
by Dow Jones & Company. All Rights Reserved Worldwide.
volume in longer dated options, known as LEAPS,but maturities of more than three
years for these are rare.
Corporations are not involved in exchange-based trading of options on their stock.
These options, like most derivatives, are merely complicated bets between two counter-
parties. As such, the number of long positions in an option is exactly the same as the
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number of short positions. This feature also applies to options traded in loosely organized
“over-the-counter markets” between institutions like banks, pension funds, and corporations.
Dealing with a single counterparty can be burdensome when liquidating or exercis-
ing an option position. If the call or put seller does not perform according to the option
contract (that is, does not deliver the cash or underlying asset required in exercising the
option), there is a high probability that a costly lawsuit will ensue. The institutional over-
the-counter options markets mitigate this possibility by investigating the creditworthi-
ness of each counterparty before entering into the contract. As a result, different option
prices exist for different option sellers, depending on their degree of creditworthiness.
The organized exchanges solve the problem of counterparty default risk differently.
Instead of performing the investigation function, each exchange uses a clearinghouse,
which is a corporation set up by the exchange and its member brokers to act as a coun-
terparty to all option contracts. All options are legal contracts between the investor and
the clearinghouse. When an investor exercises an option, the clearinghouse’s computer
randomly selects one of the outstanding short positions in the option and requires the
holder of this short position either to buy or to sell the underlying security at the exer-
cise price under the terms of the investor’s contract with the clearinghouse. The clear-
inghouse mitigates the need for lawsuits by requiring those who short options to put
up margin and have their creditworthiness verified by their brokers. In the rare instance
of a lawsuit, the clearinghouse is responsible for suing the counterparty.
The eagerness of investors to place bets with optionlike payoffs determines the num-
berof outstanding exchange-listed options. This number increases by one when an
investor places an order to sell an option that he or she does not have and the order is
executed. In option markets, the procedure for shorting an option is commonly referred
to as writing an option. When an order to write an option is executed, the clearing-
house acts as the legal intermediary between the two parties, announcing that there is
an increase in the number of contracts outstanding. Hence, the mechanism for shorting
most options differs from the mechanism for shorting stocks and bonds, which requires
some form of borrowing of securities to execute a short sale because the number of out-
standing shares is fixed by the original issuer. Conversely, when an investor cancels a
long position in an option by selling it and someone else—not necessarily the investor
from whom the option was purchased—with a short position simultaneously agrees that
this is a fair price at which to close out his or her short position, the clearinghouse closes
out its contracts with both parties. This leaves one less option contract outstanding.
Warrants.Warrants are options, usually calls, that companies issue on their own stock
(see Chapter 3). In contrast to exchange-traded options, which are mere bets between
investors on the value of a company’s underlying stock—in which the corporation
never gets involved—warrants are contracts between a corporation and an investor.
Warrants are sources of capital for newer growth firms. They are more common in
some countries, like Japan, where the warrants are often linked to a bond issue. In the
United States, warrants are most frequently seen in the form of employee stock options,
in which case the “investor” is the employee (typically, an executive).
Most of the warrants used to finance companies are traded on stock exchanges.
These warrants can be sold short by borrowing them from a warrant holder in the same
way that the stock is sold short (see Chapter 4).10Thus, the number of warrants is fixed
for a given issue. Warrants issued as employee compensation are generally not traded.
10This
is in notable contrast to exchange-traded options where a short position is created along with
every long position because both positions merely represent the sides of a “bet” between parties.
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The major distinction between a warrant and other types of call options is that the
company issues additional stock when an investor exercises a warrant. Upon exercise,
the stock is sold to the warrant holder at the strike price. Since exercise occurs only
when the strike price is less than the current price of the stock, the exercise of the war-
rant involves the issuance of new shares of stock at bargain prices. The new shares
dilute the value of existing shares. Because of this dilution, option pricing models used
to value warrants differ from option pricing models used to value exchange-traded
options. For example, if IBM is trading at $117 a share, warrants with a strike price of
$120 that expire in one year might be worth $10; they are worth slightly more than
$10 if one values them with models that do not account for the dilution. Generally, the
percent of a corporation’s equity represented by warrants is so small that one can ignore
the effect of dilution and value them like any other option. Hence, for the example of
IBM, the difference between $10 (the value with dilution) and $10.01 (the value assum-
ing no dilution) might be a realistic portrayal of the warrant dilution effect.11
Embedded Options.In addition to warrants, a number of corporate securities have
optionlike components. For example, when a corporation issues a convertible bond, it
gives the bondholder the option to exchange the bond for a prespecified number of
shares of stock in the corporation. Similarly, many long-term corporate bonds are
callable or refundable bonds, which means that the corporation has the option to buy
back the bonds at a prespecified price after a certain date.
Options are also implicit in simple equity and simple debt even when they lack a
call or conversion feature. One can look at the common equity of a firm with debt on
its balance sheet as a call option that allows the equity holders the right, but not the
obligation, to purchase the firm’s assets from the debt holders by repaying the debt.
Such common equity can be valued in relation to the assetsas a derivative.12Simi-
larly, one can look at simple corporate debt as risk-free debt and a short position in a
put option that effectively (through the default option) allows the put option holder to
sell the firm’s assets to the debt holders for a price equal to outstanding debt obliga-
tion; thus, corporate debt can be valued in relation to the assets (or the equity) with the
techniques developed in this chapter.
Real Assets
Investors can view many real assets as derivatives. For example, a copper mine can be
valued in relation to the price of copper.13Sometimes other derivatives, such as options,
are implicit in these real assets. For example, the option to shut down a copper mine
often needs to be accounted for when valuing a mine. These implicit options also can
be valued with the techniques developed here.
Mortgage-Backed Securities
U.S. residential mortgages are generally packaged together into a pool and resold to a
bank with a guarantee against default. Pooled mortgages are known as mortgage
passthroughsbecause they pass on the interest and principal payments of the mortgage
11It is important to note that exchange-traded options and otherwise identical warrants necessarily
have the same value. Hence, if both warrants and identical exchange-traded options exist at the same
time, the dilution effect of the warrants must be taken into account in valuing boththe warrant and the
exchange-traded options. However, this is rarely done in practice.
12
See Chapter 8.
13See
Chapter 12.
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Chapter 7
Pricing Derivatives
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borrowers (home owners) less servicing and guarantee fees (usually, about 50 to 75
basis points). These guarantees are given by three agencies: the Government National
Mortgage Association (GNMAor “Ginnie Mae”), the Federal National Mortgage Asso-
ciation (FNMAor “Fannie Mae”), and the Federal Home Loan Mortgage Corporation
(FHLMC or “Freddie Mac”). The latter two buy mortgages from the original lenders
and package them.
Once these mortgages are packaged and sold, markets are made chiefly by the same
set of dealers who make markets in U.S. Treasury securities. Many mortgage
passthroughs are carved up into a series of derivatives, known as collateralized mort-
gage obligations (CMOs). The most popular carve-up of this type consists of differ-
ent tranches, which are individual bonds with different rights to the principal payments
of the mortgage passthrough. Tranches can be used to design mortgage securities with
different amounts of prepayment risk, which is the risk that borrowers will prepay their
mortgages, particularly when market interest rates for new mortgages fall below the
interest rates on their mortgages.
Ahypothetical series of such mortgage-backed securities might consist of a mort-
gage passthrough that is carved up into two tranches and an additional bond that serves
the purpose of equity. The first tranche has the shortest expected life. It is entitled to
all principal payments from the mortgage passthrough until the first tranche’s principal
is paid off. Its value is least affected by prepayments on the mortgage. As mortgages
prepay—in response to home sales or to mortgage refinancings at lower interest rates—
and all of the first-tranche bonds are paid off, the second tranche, which has always
received a share of interest payments, will begin to receive principal payments. The
second tranche behaves more like a Treasury note or bond because for a while it
receives only interest and later receives the principal. Unlike Treasury notes and bonds,
however, the interest payments decline over time as prepayments occur and the prin-
cipal payments are a series of declining payments rather than a single payment at matu-
rity. After this second tranche is paid off, all remaining cash flows are paid to the
remaining bond. Hence, the last “equity piece” is more like a zero-coupon bond than
a Treasury bond. Depending on the prepayment rate, this cash may flow relatively early
or relatively late. Hence, the value of the equity piece is more sensitive to prepayment
risk than the values of the other two bonds.
The carve-ups also can be based on the principal and interest components of a
mortgage pool. For example, principal-only securities (POs)receive only the princi-
pal from a pool of mortgages. In Michael Lewis’s book, Liar’s Poker,the losses of
Howie Rubin of Merrill Lynch were tied to his positions in POs, and “no bond plum-
mets faster when interest rates go up than a PO.”14
Similarly, interest-only securities
(IOs)receive only the interest from pools of mortgages. These tend to increase in value
when interest rates rise. Not only can these carve-ups of the cash flows be valued as
derivatives, but—to the extent that variability in the rate of mortgage prepayments
depends largely on interest rates—even the mortgage passthrough—the basis for the
carve-up—can be valued as a derivative on other riskless bonds.
Structured Notes
Alarge percentage of the new issues of traded debt securities issued by U.S. corpo-
rations are in the form of structured notes(see Chapter 2), which are bonds of any
maturity sold in small amounts by means of a previously shelf-registered offering (see
14
Michael Lewis, Liar’s Poker:Rising through the Wreckage on Wall Street(New York; W. W.
Norton, 1989), p. 145.
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476 Titman: FinancialII. Valuing Financial Assets
7. Pricing Derivatives
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230Part IIValuing Financial Assets
Chapter 1). They are customized for investors in that they often pass on the cash flows
of derivative transactions entered into by the issuer.
Examples of structured notes include inverse floaters,15which have coupons that
decline as interest rates increase; bonds with floating-rate coupons part of the time and
fixed-rate coupons at other times; and bonds with coupons that depend on the return
of the S&P500, an exchange rate, a constant times a squared benchmark interest rate,
such as LIBOR, or a commodity price. Basically, anything goes.
Why are structured notes so popular? From an economic perspective, structured
notes are derivatives. From a legal and public relations standpoint, however, they are
bonds, “blessed” by the regulatory authorities, investment banks, and ratings agencies.
Some investors, such as state pension funds, may be prohibited from investing in deriv-
atives directly. One hypothesis about the popularity of structured notes is that they per-
mit an investor to enter into a derivatives transaction while appearing to the public like
an investor in the conservative bonds of an AAA-rated corporation.