Chapter 6
Market Making by Financial
Engineering
1
A.
Market Making by Financial Innovation

Conversion arbitrage：The investment bank takes
one (or more) financial instruments and, through a
process of composition or decomposition, creates one
(or more) very different financial instruments.




Mortgage Pass-through
Zero coupon bonds
Interest rate swaps
Financial Innovations
2
B.
a.
Zero Coupon Securities
Definition
A zero coupon bond is a debt instrument that is sold
at a deep discount from face value.



b)
No periodic coupons
Accrual interest
Redeem for full face value at maturity
TIGRs (Treasury Investment Growth Receipts)





Merrill Lynch, 1982
Separated cash flows
A created irrevocable trust with a custodial bank
Trust units
Fully collateralized by Treasury obligations
3
Risk of fixed income securities
c.
Interest rate risk
1.
1)
Definition
The value of a securities will change after its purchased
in response to changes in interest rates and its yield.
2)
Measurement
Duration vs. interest rate risk
3)
Managing the interest rate risk
i.
Maturity/Horizon Matching method：
To match the maturity of the instrument to the investor’s
investment horizon
ii.
Short-term Rollovers method：
To invest shorter maturity instrument and roll over, with
the final rollover having a maturity date identical to the
investor’s horizon.
iii.
Hedging method：
To invest a maturity greater than the investor’s horizon, but then
to hedge the interest rate risk in futures, forwards, or other derivatives.
4
Default risk
2.
1)
Definition
Default risk is the risk that the issuer of the security will default on its
financial obligations so that the holder of the instrument does not
receive full payment of interest and/or principal in a timely fashion.
2)
Measurement
Debt rating
3)
Managing the default risk
i.
ii.
iii.
Low risk method
Diversification method
Default swap
Reinvestment risk
3.
1)
Definition
The periodic coupons received will be reinvested at rates which differ
from the yield prevailing on the bond at the time of its purchase.
2)
Measurement
Fluctuations of the reinvestment rate
3)
Managing the reinvestment risk
No periodic coupons
5
Call risk
4.
1)
Definition
The risk that the investor is prepaid the loan principal
prior to the security’s maturity date.
2)
Measurement
Fluctuations of the reinvestment rate
1)
Managing the call risk
Call protection
Purchase power risk
5.
1)
Definition
The risk of unexpected purchasing power due to the
unexpected inflation rate
2)
Measurement
unexpected inflation rate
3)
Managing the purchasing power
Inflation-indexed bonds
6
Zeros and Conversion Arbitrage
d)
Conversion arbitrage model
1.
Input
Securities
Output
Securities
Security 1
Security 2
•
•
•
Security 1
Combine or Decompose
Input Cash Flows
Security n
Security 2
•
•
•
Security m
Zeros generation from conventional bonds
2.
Output
Securities
Input
Security
½ year zero
Decompose (Separate)
N-year
Conventional
bond
Cash Flows
1 year zero
•
•
•
n year zero
7
Yield curves
3.




Conventional yield curve
Spot yield curve (Zero coupon yield curve)
Implied zero coupon yield curve
Bootstrapping
Zeros in Financial Engineering
4.


Replicate the cash flow pattern of a great many
conventional and nonconventional forms of debt
Taking position of the mispricing between
conventional debts and synthetic forms
8
C.
a.
Mortgage-Backed Securities
Definition
The securities issued by mortgage pools of loans
which are
secured by real property, such as buildings or land.



Ginnie mae, Government National Mortgage Associate
(GNMA), FNMA, Federal National Mortgage associate,
FHLMC, Federal Home Loan Mortgage Corporation
Pass-through certificates
Embedded call option：The right of the mortgagor to
prepay the mortgage principal
•
•


Option-adjusted spread
Option-adjusted duration
Conventional mortgage amortization schedule
Cash flow patterns of mortgage debt
9
b.
Pass-through certificates
StepⅠ： GNMA specifies mortgage standards
Ⅱ： Pool the mortgage and purchase a performance guarantee
from GNMA
Ⅲ： Issue pass-through certificates in the pools
Ⅳ： Distribute by an investment bank syndicate
Example p.214
Figure 8.4 The Structure of the Passthrough Market
GNMA
Mortgage
Originator
10.75﹪
Mortgagors
(homeowners)
Owns
Servicing rights
44 basis points
6basis
points
guarantee
Pool
10.25﹪
Investors
(pass-through holders)
10
Collateralized Mortgage Obligation (CMO)
c.
The First Boston Corporation and Salomon Brothers, 1983
Purchase mortgage pass-through (or whole mortgage) and
then issue special bonds that are collateralized by the
mortgages.
Multiclass mortgage back securities
Reduce reinvestment risk
Primary market making, SEC





•
•
Due diligence
Shelf registration
Secondary market making, bid ask spread

•
•
•
•
•
•
Variation of CMO
PACs, Planned amortization classes
TACs, Targeted amortization classes
IOs, Interest only
POs, Principal-only
FRCMOs, Floating rate CMOs
11
The structure of the CMO
1.
Tranche 1
Interest
Principal
Master
servicer
Tranche 2
(fastest-pay)
Tranche 3
Tranche 4
CMO with accrual bond tranches
1.


Accrual bond, accretion bond, Z-bond
A deferred interest obligation resembling a zero coupon bond.
The accrual bond does not receive any interest or principal
until the preceding tranches are fully retired.
12
Swap
d.
a)
Definition
A Contractual agreement in which two parties, call counterparties,
agree to exchange a series of payments over a period of time.

Currency swap, London, 1979

Interest rate swap, London, 1981

Commodity swap, Chase Manhattan Bank, 1986

Equity swap, Bankers trust, 1989
b)
The structure of a generic swap
1.
A typical swap
Counterparty
A
notionals
notionals
Swap
Dealer
notionals
notionals
Counterparty
B
Figure 9.2 Swap：Periodic Service Payments (required)
Counterparty
A
fixed price
Floating price
Swap
Dealer
fixed price
Floating price
Counterparty
B
Figure 9.3 Swap：Reexchange of Notionals
Counterparty
A
notionals
notionals
Swap
Dealer
notionals
notionals
Counterparty
B
13
1.
A swap with cash market transactions
Cash Market
A
actuals
and/or
payments
Cash Market
B
Counterparty
A
actuals
and/or
payments
Counterparty
B
Currency swap
c)
1.
Case：one counterparty has comparatively cheaper access to one
currency than it does to another


Counterparty A can borrow
DM for 7 years at a fixed rate of 9﹪
US＄ for 7year at a floating rate of 1 year
LIBOR (floating rate dollar financing)
Counterparty B can borrow
DM for 7years at a fixed rate of 10.1﹪
US＄ for 7year at a floating rate of 1 year
LIBOR (fixed rate DM financing)
14
2.
Process：Investment bank’s financial engineering for DM-US＄
currency swap
Dealer pays a fixed rate of 9.45﹪on DM against dollar LIBOR
Dealer pays dollar LIBOR against a fixed rate of 9.55﹪on DM.
Figure 9.8 Currency Swap with Cash Market Transactions
(initial borrowings and exchanges of notional principal)
CASH MARKET TRANSACTIONS
Debt Market
Deutschemarks
deutschemark
principal
Debt Market
Dollars
deutschermark
principal
Counterparty
A
dollar
principal
dollar
principal
deutschemark
principal
Swap
Dealer
dollar
principal
Counterparty
B
SWAP
15
Figure 9.9 Currency Swap with Cash Market Transactions
(debt service with swap payments)
CASH MARKET TRANSACTIONS
Debt Market
Deutschemarks
Debt Market
Dollars
9﹪ DEM
9.45﹪ DEM
Counterparty
A
USD LIBOR
Swap
Dealer
USD LIBOR
9.55﹪ DEM
SWAP
Counterparty
B
USD LIBOR
Figure 9.10 Currency Swap with Cash Market Transactions
(repayment of actuals and reexchanges of notional principal)
CASH MARKET TRANSACTIONS
Debt Market
Deutschemarks
deutschemark
Debt Market
Dollars
principal
deutschermark
principal
Counterparty
A
dollar
principal
Swap
Dealer
SWAP
dollar
principal
deutschemark
principal
Counterparty
B
dollar
principal
16
3.
Results
Counterparty A：
Borrows DM, swap to dollars, floating rate, net cost of LIBOR
-45 basis points, net saving of 45 basis point.
Counterparty B：
Borrows dollar, swap to DM, net cost of 9.55﹪, net saving of
55 basis points.
Interest rate swap
d)
1.
Case：one party has access to comparatively cheap fixed- rate funding
but desires floating rate funding. Another party has access to
comparatively cheap floating rate funding but desires fixed rate funding.
Counterparty A：
Borrows a floating rate of 6M LIBOR＋50 bps, or at a semiannual fixed
rate of 11.25﹪, desires a fixed rate obligation.
Counterparty B：
Borrows a floating rate of 6M LIBOR, or at a semiannual fixed rate of
10.25﹪, desires a floating rate obligation.
17
2.
Process：The swap dealer enter a swap as either
fixed-rate payer or floating rate payer.
i.
ii.
Fixed rate payer --- 10.40﹪ s.a.
Fixed rate receiver --- 10.50﹪s.a.
Figure 9.5 interest Rate Swap with Cash Market Transactions
(initial borrowing of principals)
CASH MARKET TRANSACTIONS
Debt Market
(floating rate)
principal
Debt Market
(fixed rate)
principal
Counterparty
A
Swap
Dealer
Counterparty
B
SWAP
18
Figure 9.6 Interest Rate Swap with Cash Market Transactions
(debt service payments with swap service payments)
CASH MARKET TRANSACTIONS
Debt Market
(floating rate)
6－M LIBOR＋50 bps
Debt Market
(fixed rate)
10.50﹪ (sa)
Counterparty
A
Swap
Dealer
6－M LIBOR
10.25﹪ (sa)
10.40﹪ (sa)
Counterparty
B
6－M LIBOR
Figure 9.7 Interest Rate Swap with Cash Market Transactions
(repayment of principals)
CASH MARKET TRANSACTIONS
Debt Market
(floating rate)
principal
Debt Market
(fixed rate)
principal
Counterparty
A
Swap
Dealer
Counterparty
B
19
1.
Results
Counterparty A：
Pays LIBOR＋50bps, receives LIBOR, net payment 10.50﹪ s.a.,
adjusted net cost 11.01﹪, net benefit 24 basis points.
Counterparty B：
Pays fixed 10.25﹪, receives 10.40﹪, net ahead 15 basis points,
net benefit 15 basis points.
Swap dealer：
Pays 10.40﹪, receive 10.50﹪, net benefit 10 basis points, bid-ask spread.
Commodity Swaps
e)
1.
Case：
One counterparty make periodic payments to the other at a fixed
price for a given quantity of notional commodity, while the second
counterparty pays the first counterparty a floating price for the
same quantity of notional commodity.
Counterpaty A --- A crude oil producer want to fix the price of
8,000 barrels oil received for 5 years.
Counterpaty B --- An oil refiner
Want to fix the price of 12,000 barrels oil paid for 5 years.
20
2.
Process：
The swap dealer sets the fixed price on ＄18.25 a barrel.
Pays ＄18.20 per barrel to counterparty A；
Receives ＄18.30 a barrel from counterparty B.
Figure 9.11 Commodity Swap with Cash Market Transactions
CASH MARKET TRANSACTIONS
actuals
Spot price
Spot
Oil
Market
＄18.20
(per barrel)
Spot price
(average)
actuals
＄18.30
(per barrel)
Counterparty
B
Swap
Dealer
Counterparty
A
(Oil producer)
Spot price
Spot price
(average)
(refiner)
21
3.
Results：
Counterparty A set a fixed price of oil received.
Counterparty B set a fixed price of oil paid.
Swap dealer enjoys a bid ask spread of ＄.10 per barrel.
Equity Swaps
f)
1.
Case：
One leg is pegged to the return on a stock index. The other leg
can be pegged to a floating rate of interest, can be fixed, or a
different stock index.
2.
Process：
1)
Converting a fixed income return to an equity return
Fixed
Income
portfolio
Fixed income return
Fixed income return
Fixed Income
Portfolio
Owner
S＆P return
Equity
Swap
Dealer
Investment
bank
22
2)
Converting an equity return to a fixed income return
equity
portfolio
S＆P return
Equity
Portfolio
Owner
2)
S＆P return
Fixed income return
Equity
Swap
Dealer
Investment
bank
Converting a foreign equity return to a domestic equity return
Japanese
equity
portfolio
Nikkei return
Japanese
Equity
Portfolio
Owner
Nikkei return
S＆P return
Equity
Swap
Dealer
Investment
bank
23
g)
Swap Variants --- The Circus Swap
1.
2.
Case：
Converting a fixed-rate DM obligation to a fixed rate dollar
obligation.
Process：
Pay floating rate dollar by entering a fixed-for-floating DM/US
＄ currency swap；
Receive floating rate dollar by entering a dollar based interest
rate swap.
Figure 9.15 The Circus Swap
German
lenders
fixed rate DEM
Counterparty
A
Circus swap
Counterparty
A
fixed rate DEM
Currency
Swap
Dealer
USD libor
USD libor
Fixed rate USD
Interest
Rate
Swap
Dealer
24
Interest Rate Caps
h)
1.
Case：
The writer of a cap pays the cap holder each time the contract’s
reference rate of interest is above the contract’s “cap rate” of
interest on a settlement date.
2.
Process：
The cap dealer and the customer enter a cap agreement.
Dealer pays ＝ D*MAX[RR－CR , 0]*NP*LP
D：cap seller, ＋1；cap purchaser, －1,
RR：reference rate of interest,
CR：cap rate,
NP：notional payment,
LP：length of payment,
Profit
MAX[RR – CR, 0] × NP× LP - premium
Cap rate
0
Reference rate
Per-period premium
(amortized)
25
3.
Applications：
Capped floating rate debt
1)
Figure 9.18 Capped Floating Rate Debt
MAX[LIBOR - 10﹪, 0]
Cap
Dealer
5-year rate cap
LIBOR＋ 80 bps
Firm
5-year FRN
3rd party
lender
Note：This cash flow diagram depicts only interest flows. It does not
show the principal flows between the firm and the third party
lenders or the up-front fee for the cap paid to the cap dealer.
2)
A rate-capped swap
Figure 9.19 A Rate-Capped Swap
Swap
Dealer
Fixed rate
Fixed rate
Floating rate
Cap
Dealer
Firm
Fixed rate
lender
Cap on floating rate
Investment bank
26
Interest Rate Floors
i)
1.
Case：
The writer of a floor pays the floor holder each time the contract’s
reference rate of interest is below the contract’s “floor rate” of
interest on a settlement date.
2.
Process：
The floor dealer and the customer enter a floor agreement.
Dealer pays ＝ D*MAX[FR－RR , 0]*NP*LP
D：cap seller, ＋1；cap purchaser, －1,
RR：reference rate of interest,
FR：floor rate,
NP：notional payment,
LP：length of payment,
Figure 9.20 Payoff Profile for a Floor Purchaser
(Per Settlement Period)
MAX[FR – RR, 0] × NP × LP - premium
Profit
Floor rate
Per-period premium
(amortized)
0
Reference rate
27
3.
Return protection by interest rate floor
Treasury
Bills
6-M T-bill rate
Floor
Dealer
MAX[7﹪ - T-bill rate, 0]
Annuity
Holders
7.00 percent
Firm
10-year rate floor
10-year policy
Note：This cash flow diagram only depicts interest flows. It does not
show the principal flows between the firm and the annuity
holders or the up-front fee for the floor paid to the floor dealer.
4.
Achieve a minimum return by floor
Fixed
Rate
asset
Fixed return
Fixed rate
Firm
Swap
Dealer
Floating rate
Max[FR-CR, 0]
floor
Dealer
Investment bank
28
Interest Rate Collars
j)
Definition：
1.
A combination of a cap and a floor. The purchaser of a collar buy
a cap and simultaneously sell a floor.
Payoff file：
2.
Figure 9.23 Payoff Profile for a Collar Purchaser
(Per Settlement Period)
Cap settlement received less
Settlement paid and net premium
Profit
Floor rate
0
Cap rate
.
Reference rate
Difference between premium paid
On the cap and premium received on
The floor (per-period equivalents).
29
3.
An interest rate collar
Assets
10 percent
Cap
Dealer
Max[prime – 9.5﹪, 0]
Prime rate
Firm
floor
Dealer
Lender
Max[7﹪ - prime , 0]
Note：This cash flow diagram ignores the cost of the collar and the
exchanges of principals on both assets and liabilities.
4.
A collar swap
Figure 9.25 A Collar Swap at Work
Swap
Dealer
Cap
Dealer
floor
Dealer
Fixed rate
LIBOR
Fixed rate
Firm
Lender
Max[LIBOR – cap, 0]
Max[floor – LIBOR, 0]
30