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03-9&-10 Another Financial Engineering Metaphor: Creating Stockholder Value and Managing Enterprise Risk by Synthetic Balance-Sheet Surgery. Edward J. Kane Boston College. Fully Integrated Process of FSF Risk Management. Risk Analysis. Risk Adjustment. IRR & Credit Risk Appraisal.

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03-9&-10Another Financial Engineering Metaphor: Creating Stockholder Value and Managing Enterprise Risk by Synthetic Balance-Sheet Surgery

Edward J. Kane

Boston College

Edward J. Kane, BC, 03-9&10

fully integrated process of fsf risk management
Fully Integrated Process of FSF Risk Management

Risk Analysis

Risk Adjustment

IRR & Credit Risk Appraisal

Originating & structuring deals



Edward J. Kane, BC, 03-9&10

Financial Engineering Can Simplify the Calculation of Duration-Based Measures of the IRR in any Instrument or Position.
  • Begin by stripping coupon bond into two parts whose prices sum to the price of the bond:
    • A single-payment or zero-coupon principal repayment of F to be made at maturity n. Its PDV is =PDVF.
    • Coupons can be analyzed as an n-year annuity. Value is the product of the annual coupon C and the PDV of an n-period unit annuity:

Edward J. Kane, BC, 03-9&10

The duration of a n-period bond DB can be found as the PDV-weighted sum of the durations of the bond’s two components:

Query: What makes this a “financial engineering approach” to calculating DB? ANS. It relies on the concept of synthetic replication and the Law of One Price.

Edward J. Kane, BC, 03-9&10

DF is trivially equal to n.
  • Dn is the same as the PV-weighted duration of the n-year “unit annuity” because C can be factored out of each payment.

Dn =


Edward J. Kane, BC, 03-9&10


It is much easier to use the financial-engineering method to solve our first duration exercise (C=$60, F=$1,000, R=.10, n=10) than to work the problem by the formula that defines duration conceptually:

PVF = 385.54

PVn = 368.67 = = 600[1-.3855]

PVB = $754.21

Edward J. Kane, BC, 03-9&10

financial engineering formulas that might be used to calculate duration on exams
Financial-Engineering Formulas That Might Be Used to Calculate Duration on Exams

Edward J. Kane, BC, 03-9&10



In practice, asset-liability managers no longer need to make tedious calculations. Portfolio valuations and duration/convexity calculations are routinely produced by computer software.

  • The link between decision-support technology and information management and contracting at FSFs is becoming stronger day by day.
  • Regulations requiring lazy managers to adopt a benchmark IRR information system help to protect FSF stockholders from managerial incentive (i.e., ethical) conflict.

Edward J. Kane, BC, 03-9&10

Because the durations of instruments and portfolios vary as interest rates change, “static” control strategies are inadequate.
  • It is a disastrous mistake to suppose that the duration of an institution’s net worth is a constant that managers may set once a quarter or so and then forget about.

[• Reminder: IRR management may be likened to a householder’s trimming the hedges on the boundaries of its yard. The managerial implications of this metaphor turn on the need to expect “rain” (=adversity or good luck) and to plan to respond to the amount of rain that falls. This trimming must be planned to occur from time to time, and to occur more frequently the more it rains.]

Edward J. Kane, BC, 03-9&10


Regular readjustment of hedges resembles "trimming." Continual realignment of the durations of the two sides of an FSF’s balance sheet is called “dynamic hedging.”

  • Dynamic hedging seeks to offset changes in durations of A and L as R changes and options are exercised. Contrast with mindless once-and-for-all or passive “static” strategies for coping with interest-rate change.
  • Difference lies between totally controlling and partially and temporarily managing interest-rate risk exposure.
  • Dynamic Hedging is indispensable because an institution cannot afford not to “sell” hedges to its customers.

Edward J. Kane, BC, 03-9&10

both voluntary vs involuntary portfolio mismatching occur
Both Voluntary vs. Involuntary Portfolio Mismatching Occur
  • Customers routinely hold valuable imbedded options that let them retime loan and deposit contracts: e.g., for early loan repayment, for refinancing, for early deposit withdrawal, and for activating credit lines; for taking down annuities or policy loans in life insurance contracts. The values and durations of these options change with interest rates.
  • Customers pay handsomely for optionality. Compensation paid for optionality is a profitable part of almost every deal a bank writes.
  • Customers often fail to appreciate the cost of these options.
  • FSFs often make options troublesome to exercise.

Edward J. Kane, BC, 03-9&10


The better proprietary FSF models of IRR “internally” adjust “interest spreads” to price the optionality that imbedded puts and calls conveys to its customers.

  • Maturity of a passbook is not really zero. Maturity is entirely at the customer’s option. The speed of customer deposit runoff caused by rising market interest is not fixed. It depends on how quickly an FSF resets its yields when and as market interest rates rise.
  • Correspondingly, on the other side of an FSF balance sheet, deposit flow is also an endogenous variable in the system. The SPEED of loan runoffs rises when interest rates fall.

Edward J. Kane, BC, 03-9&10



  • FSF managers and regulators know that DA and DL change with interest rates, not just because the PDV of given positions change, but because interest-sensitive customers can alter these positions by prepayments, deposit flows, and loan requests that activate implicit or explicit credit lines.
  • Long-run survival in a repeat business forces FSFs to accept customer-initiated variation in the timing of funds flows.

Edward J. Kane, BC, 03-9&10

Optionality is increasingly recognized as creating by itself a negative “asset convexity” and positive “liability convexity.”
    • Increases in R lower values of “borrower-callable” assets but leave values of “depositor-puttable” liabilities (as approximate “par floaters”) more or less unchanged.
    • Decreases in R do what to same values?

Edward J. Kane, BC, 03-9&10


More on Convexity

Setting an appropriately weighted gap = 0 serves to “immunize” NW, but only for infinitesimally tiny changes in r. “Infinitesimal” means “negligible in size.” The criterion that defines an infinitesimally “immunized” state is that the first derivative = zero .

  • If the second derivative, , is positive or negative, a “convexity” in interest sensitivity is said to exist. The larger the absolute value of convexity, the more the (N,rA) curve departs from a straight line.
  • Even higher derivatives may be dealt with by software.]


Edward J. Kane, BC, 03-9&10

why is convexity helpful
Why is Convexity Helpful?

1. Strategically: Using it helps to immunize Net worth against large movements in r.

  • Substantively: In two positions, the algebraically more convex position becomes shorter faster for a given rise in r and becomes longer faster for a given fall in r.

Query: For what movement in interest rates are liability positions more convex than asset positions and vice versa?

Edward J. Kane, BC, 03-9&10

importance of convexity grows with d of position comparing two money market funds
Importance of Convexity Grows with D of Position: Comparing Two Money-Market Funds

Please calculate how much a 2% fall in yield will raise the value of a “dollarsworth” of each fund: dP-D*dr+(.5)(convexity)(dr)2

Edward J. Kane, BC, 03-9&10

self study a last complication in calculating d
Self-StudyA Last Complication in Calculating D

For a real-world bank, RA and RL would actually be weighted-average rates of return. The response of rates of return on individual assets and liabilities to movements in a reference “market” rate R need not be uniform either in sign or in magnitude. Assuming a uniform response keeps calculations simple.

Edward J. Kane, BC, 03-9&10

swap a particular kind of forward contract between two counterparties
Swap: A particular kind of forward contract between two counterparties

Interest-Rate Swap: An agreement to exchange the coupon interest flows from two different hypothetical or “notional” instruments over a series of future settlement dates.

Each coupon-swap agreement creates synthetically a financial instrument that could not otherwise be traded in financial markets. Aim is:

  • to reduce borrowing costs
  • to hedge interest-rate risk, or
  • to speculate (i.e., “gamble”) on the future course of interest rates.

Edward J. Kane, BC, 03-9&10

the maturity of a swap is called its tenor
The maturity of a swap iscalled its “tenor.”
  • The usage traces to tenor’s Latin meaning as a “course of continuous or uninterrupted process.”
  • Two nonfinancial meanings of tenor: Besides its additional meaning as a “voice quality,” tenor can also mean the “subject of a metaphor.”

Edward J. Kane, BC, 03-9&10

more swaps terminology
More Swaps Terminology:
  • Notional Value = assumed face amount P used by contract in translating contract interest rates into cash flows;
  • Selling on market or at-the-market =both halves have equal value: no premium or discount;
  • Selling off-market = instances where obligations imposed by swap are not equally valuable at current interest rates. E.g., the PF and RF values might be substantial, when PV and RV are not.

[• Rates on Reference Securities.]

Edward J. Kane, BC, 03-9&10


Typically, the notional instruments on which swaps are based have an exact or rough cash-market counterpart. The different notional instruments have the same maturity and differ as to whether the contract interest rate on the instrument is fixed (Rt) or floating ( ).

  • The party that is long the fixed-rate obligation is usually of higher credit standing than the short. This side Pays Fixed, Receives Variable = PFRV or RVPF.
  • RxPz Notation mimics the order of a balance sheet.
  • Cash Settlement: only the net cash-flow difference is paid on any settlement date. Why is this efficient?

Edward J. Kane, BC, 03-9&10

Let P be the “notional principal” that is used to calculate the interim cash flows. P need not be precisely the same as the principal on the underlying cash instruments. Rather in an OTC market it is a negotiated variable that can be used to equalize the initial market value of the two sides of the swap.
  • At each settlement date (typically every six months), the floating rate is ordinarily reset, although the settlement and reset dates are in principle contracting variables. The reset makes the payment due at the next reset date knowable in advance = “nonstochastic.”
  • The check written for the difference at each settlement date is called the difference check. The payline equals the absolute value of ( - R) P.
  • At some dates, the payoffs go from the fixed side to the floating side; at other dates, funds flow the other way.

Edward J. Kane, BC, 03-9&10


Financial-Engineering Insight: Swaps are synthetic substitutes for financial intermediation which is an ancient financial-engineering substitute for direct finance.

  • Opportunity Costs of contracting for a swap parallel the three benchmarks we identified in comparing the costs of direct and indirect finance.

1) Expenses of shopping for best deal

2) Expenses of Due Diligence

3) Contracting and Enforcement Expense

Edward J. Kane, BC, 03-9&10

intuitive perspective
Intuitive Perspective
  • FSF managers may use synthetic transactions to hedge or transfer unwanted business or financial risks. The trick is to strip and sell off cash-flow outcomes managers do not want to retain: as entailed by the surgery metaphor.
  • Accommodating customers’ interest in shedding or acquiring particular risks is the central idea in making a market in derivatives and in writing insurance policies.

Edward J. Kane, BC, 03-9&10


As an incremental balance sheet, every interest-rate swap has two parts: a “pay half” and a “receive half.” Each side accepts an obligation and receives a claim to something valuable:

-- PFRV: Pay Fixed Rate, Receive Variable Rate

-- PVRF: Pay Variable Rate, Receive Fixed Rate

[Concept of a “half-swap”:

“Pay half”  an on-balance-sheet liability;

“Receive half “ an on-balance-sheet asset]

Edward J. Kane, BC, 03-9&10

What is the PDV of owning both sides of an interest-rate swap? ANS. Net flows constitute a string of zero payments.
  • Why not describe the swap as paying and receiving “fixed” and “floating?” ANS. The acronyms for both sides would be identical: RFPF and RFPF.
  • If value of RFPV side is zero, why must the value of the RFPV side also be zero?ANS. Abstracting from dealer market-making “vigorish,” the value of each side equals minus the value of the other.

Edward J. Kane, BC, 03-9&10

standard rfpv swaps example
Standard RFPV Swaps: Example

July 1, 1998

initiate fixed-for-floating interest rate swap with notional principal of $1,000,000 and tenor of 2 years

January 1, 1999

RECEIVE 5% per annum fixed rate

PAY OUT July 1, 1998 six-month LIBOR rate (4.5%)

July 1, 1999

RECEIVE 5% per annum fixed rate

PAY OUT six-month LIBOR rate set January 1, 1999

January 1, 2000

RECEIVE 5% per annum fixed rate

PAY OUT six-month LIBOR rate set July 1, 1999

July 1, 2000

RECEIVE 5% per annum fixed rate

PAY OUT six-month LIBOR rate set January 1, 2000

Edward J. Kane, BC, 03-9&10

Hypothetical Cash Flows from Plain-Vanilla RFPV Interest Rate Swap for Firm ANotional Principal = $1,000,000, Tenor = 2 years

Why the lag in the pay floating rate? Reduce uncertainty of PV

How does the “1/2” figure in? (semiannual settlement)

Edward J. Kane, BC, 03-9&10

standard swaps with market maker
Standard Swaps with Market Maker*

Pays LIBOR +

Pays LIBOR +

Firm A


Firm B

  • Bank acts as a market-maker, providing “immediacy” by simultaneously borrowing and lending at LIBOR, and borrowing at a fixed rate but lending at this fixed rate plus about 3 basis points.
  • In exchange for the spread, the bank performs services. It absorbs default risk of the counterparties and may temporarily warehouse either side of the swap.

Receives 4.985%

Receives 5.015%

* Arrows point to receiver and away from payer

Edward J. Kane, BC, 03-9&10

indicative pricing schedule banks charge rfpv and rvpf counterparties
Indicative Pricing Schedule Banks Charge RFPV and RVPF Counterparties

Note: TN stands for “Treasury Note”

Edward J. Kane, BC, 03-9&10

performance risk in swaps role of swap brokers and dealers
Performance Risk in Swaps: Role of swapbrokers and dealers:
  • Most swaps are arranged by a third party called a dealer that accepts the nonperformance risk by taking other sides of each counterparty’s position and undertakes the search for a matching counterparty.
  • Dealerstake a spread which they load into the fixed-rate side of each swap (about 3 b.p.).
  • Vs.Brokers, who perform their search function only for a commission & take no risk.

Edward J. Kane, BC, 03-9&10


Issuer Perspectives on the Pay Halves: The issuer of an FR bond is obligated to pay a fixed stream of coupons; the VR issuer accepts a PV obligation.

  • How does a fixed-rate (FR) bond of maturity n differ from a VR bond of the same maturity?

ANS: By the “difference” being swapped.

  • A swap transaction exchanges the value of the physical coupons issuers owe on a FR and a VR Bond. The FR coupon sizes the PF obligation

FR coupon obligation + RFPV=VR obligation

VR coupon obligation + RVPF=FR obligation

Edward J. Kane, BC, 03-9&10

bondowner perspectives on the receive halves
Bondowner Perspectives on the Receive Halves:

Bond owners could equally well swap coupons:

FR claim + PFRV=RV claim

VR claim + PVRF=RF claim

[FR coupon is a Pay-Fixed obligation of the Issuer. What is a RV coupon?]

Edward J. Kane, BC, 03-9&10

-- This exercise shows that Interest Swaps may be interpreted as a synthetic “missing link” between FR and VR instruments: completes these two markets.

--Any VR bond can be decomposed logically into the sum of a FR bond and an appropriate swap.

-- The parallel decomposition of an FR bond is the sum of a VR bond and an appropriate swap.

Edward J. Kane, BC, 03-9&10

new topic
New Topic:

Using swaps to manage IRR begins with knowing how to calculate the Duration of a Swap.

  • Think of a swap as establishing an incremental balance sheet
  • Duration of a Swap is the duration of the net value of long and short positions

Edward J. Kane, BC, 03-9&10


Our goal is to explain how to Use Swaps to Lessen IRR of market cap. This means you must learn to Calculate Duration at least for Default-Free Interest-Rate Swaps

  • Recall that --when weighted by proportionate present value-- durations of the two halves of anycontract add: Dswap w1DPF + w2DRV .
  • One weight will be negative. Why? It is an obligation, in an incremental balance sheet.
  • If swap is “on market,” w1=-w2, but net worth of position is zero, so we can’t divide by it to calculate relative weights. Traders arbitrarily set w’s equal to 1 in this case.

Edward J. Kane, BC, 03-9&10


The duration DF of the Pay- or Receive-Fixed (RF) half of a just-agreed-upon interest-rate swap may be calculated as the duration of a stream of fixed-rate payments due on an n-period unit annuity (=Dn,1)

  • One can’t strictly “calculate” the duration of the pay-variable-rate (PV) half of this swap position because one cannot know how the “reference yield” will move.
  • By convention, traders assign an “implied duration” equal to the amount of time that is remaining until the next interest-rate “reset date.” The Receive-Variable half of a RVPF is a modified “par floater.” Value resets to par at each reset date.

Edward J. Kane, BC, 03-9&10


Query: As we approach each quarterly or semiannual reset date, what is the algebraic sign of the duration of the RFPV side of an interest rate swap?


Duration (RF) = DF > 0

Duration (PV)  0

Duration of Net Position = DF - 0 > 0.

Edward J. Kane, BC, 03-9&10

What must be the duration of the reverse RVPF side of an on-market interest-rate swap at the same date? Duration must be 0 - DF < 0.
  • This negative duration is the “building block” used in constructing a swaps position to offset the IRR imbedded in a short-funded FSF’s market cap (S) by its book of customer-initiated core business.

Edward J. Kane, BC, 03-9&10



Suppose tenor of a RVPF swap is 5 years, notional amount B is $100 million, the FR bond yield index I is 10%, and settlement occurs once a year.

a. At contracting date:

DV = 1 year (= overly long reset date)

DF= Dn,1=

= 11 – 8.190 = 2.81 years

b. Convention for on-market swaps sets weights at unity.

Dswap = DV –DF

= [1-2.81] = -1.81 years.

Edward J. Kane, BC, 03-9&10

If reset date were quarterly, DF would shorten to 2.42 and DV to .25. Dswap would be -2.17 years.
  • Effect of increasing n (i.e., increasing swap “tenor”) affects the DURATION of the fixed half only:
  • What would be DF in a 20-year swap with the same 10% yield?

11 - 7.5 years

Edward J. Kane, BC, 03-9&10

To explore how to use the Duration of Swaps in risk management, it is easier to employ “Modified Duration,” D*.

D* =

Reminder: The percentage price of any income stream responds to a tiny change in yield as follows:

Edward J. Kane, BC, 03-9&10

D* formulation expresses the approximate price sensitivity of a positionworth P to a specified basis-point change in the yield.
  • Setting R=.01%=.0001, the formula -PD*R gives the marginal “price value of a basis point:” pvbp.
  • Netting this value across both halves generates the marginal net interest-rate sensitivity of the swap itself.

Edward J. Kane, BC, 03-9&10

In an on-market swap, each side has the same value.
  • For R=.0001, we may write the pvbp of an on-market RVPF swap to a parallel change in market yields as pvbp of the two halves:
  • Dimensionality of pvbp lies in the currency in which the swap obligations are expressed: $, ¥, etc.

Edward J. Kane, BC, 03-9&10

As an example, suppose F is equal to $1 at contracting date and DPF=7.7 and R = .10.

 .06¢ per b.p.

Edward J. Kane, BC, 03-9&10

how to use the pvbp of a swap to manage interest rate risk sample problem
How to Use the pvbp of a Swap to Manage Interest-Rate Risk: Sample Problem

Suppose a bank’s market capitalization S is $220 million and the modified duration of S is:

a. If R=10%, what is the pvbp of S?


x one b.p. = ($220 mil.)(.0001)

= (-4) (200 mil.) (.0001)

= -$8 mil. (.01) = -$80,000 per b.p. at the

margin (interpret)

Edward J. Kane, BC, 03-9&10

b. If the pvbp of an on-market RVPF swap with a notional value of $1 is .00060909, how large would the notional value of the swap F have to be to neutralize the interest-rate sensitivity of S?

ANS. $80,000=F(.00060909) = F x per-dollar pvbp

F = $131.34 mil.

Doublecheck (looks at “hedge ratio” ):

Relative variability of a “dollarsworth” of S and a dollarsworth of the swap is minus the ratio of modified durations of the two positions:

F  .60 ($220 mil.) = $132 mil.


Edward J. Kane, BC, 03-9&10

irr control cont using swaps in deposit institution hedging programs
IRR Control (cont.): Using Swaps in Deposit-Institution Hedging Programs
  • Swaps can transform long-term assets (or short-term deposits) collected in an FSF’s core “natural geographic market area” into shorter-term global assets (or longer-term global liabilities).
    • Typical early (I.e., brokered) swap transactions involved a U.S. thrift with FR mortgage assets and floating-rate brokered deposits, and (say) a European bank with VR assets (usually tied to LIBOR) and fixed-rate liabilities.
    • FR assets + PFRV swap = VR income stream which covers the interest due on the thrift’s VR liabilities. If rates go up, the swap generates the earnings needed to pay depositors.

Edward J. Kane, BC, 03-9&10

Financial Engineering treats a thrift’s book of core “customer-initiated business” as equivalent to a RFPV swap offered to the firm by its customers.
  • A hedging thrift or GSE could rebalance its core position by using a swap to turn an “appropriate” amount of its projected fixed-rate receipts into fixed-rate liabilities.
  • Profitability of this turns on likelihood that the larger consolidated transactions size of an institution-to-institution swap allows it to extract a lower price (i.e., a better interest rate) than the thrift could get in the VR loans it could negotiate within its limited customer base.

Edward J. Kane, BC, 03-9&10

cash flow streams on swaps may tie to anything
Cash-flow streams on swaps may tie to anything:
  • Interest rates - an interest rate swap
  • Foreign exchange rates - a foreign currency rate swap
  • A combination of changes in interest rates and foreign currency rates - a foreign currency interest rate swap
  • A bond credit rating - a credit derivative
  • A combination of bond credit and interest rates - a total return swap.
  • Indexes of option volatility.

Edward J. Kane, BC, 03-9&10


Summary Intuition-Builder: A swap may be analyzed as a “string” of privately negotiated forward contracts. These contracts may be written with or without a third-party guarantee of performance. Three unwinding possibilities exist:

1) To buy out one’s preciseposition from the dealer or counterparty at a prenegotiated fee schedule.

2) To trade the precise position to another party in the secondary market.

3) To develop an offsetting position. But this doubles counterparty risk unless the new position is written with the same dealer = option 1).

Edward J. Kane, BC, 03-9&10


Some Potential Exam Questions Covered in Week 9/10

1. Please draw up and label deal-making boxes and arrows appropriate for illustrating each of the following:

a. The Receive Variable Pay Fixed (RVPF) side of an Interest-Rate Swap

b. How a RVPF swap can turn a fixed-rate bondholding into a floating-rate one

c. How a total return credit-default swap can turn a low-rate bond into a “riskless” security.

2. Please indicate how one can calculate the Duration of pvbp of a specified RVPF interest-rate swap.

3. At the margin, how large a notional position in a specified RVPF swap would neutralize the interest-rate risk of a bank’s market capitalization S when the pvbp of S= = $z?

4. Explain how residuals from index swaps have resulted in high loss rates in failed banks.

Edward J. Kane, BC, 03-9&10


Banc One Case

The Principal issue is: Why did “something bad” happen in 1993, despite management’s financial-engineering efforts?

Edward J. Kane, BC, 03-9&10

some vocabulary street lingo
Some Vocabulary: Street Lingo:
  • Concept of a balanced or "even position" means no net exposure to interest-rate risk.
  • Metaphor that likens new and old yields to baked goods such as bread. Speak of whether and how divergences in "fresh" and "stale" yields influence the FSF’s target account.
  • So called “stress tests” focus on “scenarios” in which yields move up or down by (say) 100 or 200 basis points in one year. [Usually focus only on earnings and tangible NW.]

Edward J. Kane, BC, 03-9&10


Intuition-Builder: Liability rolloverrisk may be thought of as located in future: specifically in the time interval when the repricing of both sides of the balance sheet is going to unfold unevenly = DA-DL. Metaphor: One can think of customers that hold FSF liabilities and assets as standing in different ticket lines. The first up to the window, gets served first.

Edward J. Kane, BC, 03-9&10

Short-Funding (Banc One officials describe this --from an income perspective-- as being “liability sensitive.”): DA>wDL
  • Long-Funding: DA<wDL.

Edward J. Kane, BC, 03-9&10


What was the “something bad” that the bank experienced?

  • What were management’s goals?
  • What was management’s theory of their IRR?
  • What remedy was chosen and did it help?
  • Why did management efforts backfire?
  • 1) Management and Wall Street Analyst Theory
  • 2) Economists’ theory

Edward J. Kane, BC, 03-9&10


IRR Management: Whatever is explicitly targeted, programs to manage the interest sensitivity must control or offset mismatching of durations across the asset and liability side of the balance sheet.

  • Four principal targets whose duration could be managed on an unweighted vs. weighted basis.
  • 1) BVA net worth
  • 2) MVA net worth ( market capitalization S)
  • 3) accounting income
  • 4) net economic income
        • Each of four targets has a “gap” to be controlled
        • Sometimes “immunization targets” are stated on a percentage basis: NW/A; Income/A.

Edward J. Kane, BC, 03-9&10


Review: Text contrasts Duration Management with a less high-tech “maturity buckets” approach. This strategy partitions the time line of future business. It treats “contract timing segments”in which net cash flows from repayments of (A-L) are scheduled as metaphorical “buckets” in which inflows of liquidity may accumulate. Idea is for managers to calculate the algebraic sign and amount of scheduled net profit flows across a parallel grid of maturity classes for fixed-rate instruments and a parallel grid of time-to-repricing segments for adjustable-rate instruments.

Edward J. Kane, BC, 03-9&10


What was Banc One’s program to measure IRR? What kind of gaps were tracked and controlled? Maturity vs. Duration

  • Did this program truly mirror “best practice” in the banking industry at the time?
  • --Esty et al. Opinion
  • --Opinion of other academics in symposium

Edward J. Kane, BC, 03-9&10


Did IRR risk management program focusing on accounting earnings work as economists would predict, give the nature of the Bank’s core customer-relationship business?

  • Stipulation: DA>DL in deals showing substantial optionality and interest rates rose.
  • Nevertheless, the bank’s accounting earnings in first 3 quarters of 1993 were extremely stable
  • What were the chief misunderstandings and who owned them?

Edward J. Kane, BC, 03-9&10


Principal lesson in the 1993-1994 Banc One case :Controlling the unweighted gap [DA-DL] stabilizes the accounting "spread" rA-rL. This does not protect against stock-price declines or even against insolvency, though it would slow interest-induced losses.

• How does Table 2 on p. 65 support these contentions?

Edward J. Kane, BC, 03-9&10

Weighted Gaps are of form DA-wDL. The most-important "w" weights the duration of debt funds by the debt ratio, (1 - NW/A).
  • NW = N(rA, rL) = A(rA) - L(rL)
  • This weighted gap links to DN. Because of the importance of staying solvent and managers’ duty to stockholders, is always instructive to calculate the duration of N itself.
  • For an FSF, DN is often a largemultiple of the unweighted gap. This is because high leverage is a typical feature of the FSF business. Suppose deposit-to-asset ratio is 99%?

Edward J. Kane, BC, 03-9&10

how does an fsf that swaps away all of its irr earn profits
How does an FSF that swaps away all of its IRR earn profits?
  • Presumably, the FSF is swapping out of an activity –interest-rate speculation—in which it enjoys no comparative information advantage. It still stands to earn profits for its credit analysis and to earn implicit interest for the particular services it provides its customers.
  • The FSF may be interpreted as trading out of selected portions of its local core business risk via the global “wholesale” swap market.
  • Accepts incremental counterparty and liquidity risk as new costs.

Edward J. Kane, BC, 03-9&10

next unit futures vs forwards
Next Unit: Futures vs. Forwards

Edward J. Kane, BC, 03-9&10

Financial Engineers Strip and Recombine Three Types of Financial Contracts: Spot, Forward, and Futures Contracts.
  • A spot contract entails the exchange of a security for “cash” or its equivalent. It is executed either instantaneously or at a nearby “settlement date.”
  • A forward contract has a deferred execution date. Off-exchange forward contracts are bilaterally negotiated with a “dealer” in an OTC setting.
  • A futures contract is a forward contract whose delivery terms have been standardized and that is traded with performance guarantees and margin accounts on an organized futures exchange.

Edward J. Kane, BC, 03-9&10

timing patterns in dealmaking
Timing Patterns in Dealmaking

Edward J. Kane, BC, 03-9&10

A forward contract is an advance agreement to exchange a designated asset A at a specified future date for a predetermined “delivery” price (PD)
  • Spot price of the designated asset is PA.
  • The “virtual” delivery price that would reset value of a forward contract to zero tracks payoff to the long forward position (PF). PF difference between spot & delivery price PA-PD, and rises and falls with PA.

Edward J. Kane, BC, 03-9&10

in a logical sense forward contracts are to spot contracts as checks are to currency
In a logical sense, forward contracts are to spot contracts as checks are to currency.
  • A check gives its owner a delayed right to receive the “deliverable” of currency or deposit balances. A long forward position gives its owner the right to receive a specified spot contract. The forward contract and the check both are derivative instruments that expose the counterparty to nonperformance risk.
  • Extending the checking-account metaphor, how is the relation between a futures contract and a customized (or OTC) forward contract the same as that between a certified (or “positive pay”) check and an ordinary check?

Edward J. Kane, BC, 03-9&10


An exchange combines the idea of a specific “place for trading” with exchange operated “systems” for clearing, settling, and guaranteeing trades.

  • Value of each side of a futures contract is marked to market daily and margin accounts are maintained.
  • The standardization and guarantees permit anonymous trading and a more competitive and liquid market than forward traders enjoy.

Edward J. Kane, BC, 03-9&10


Daily gains and losses in the value of futures positions are posted to margin accounts each day. Margin calls resemble a thermostat’s calling for heat from a furnace: calls issued when an account falls below its “maintenance margin.” Usually, the maintenance margin lies below the initial margin.

  • Posting aims to keep value of both positions in contract at zero.
  • Because explicit forward positions are not marked to market, forward positions develop plus and minus values, sometimes very large values.
  • For large moves, some exchanges slow margin calls by daily price limits. Limits force gainers to provide losers a temporary line of credit at zero interest to cover unrecorded price movement. Size of price limits typically expands when limit days occur back to back.

Edward J. Kane, BC, 03-9&10

forward and futures contracts are not completely different
Forward and futures contracts are not completely different.
  • Two delivery dates in each contract: The document-delivery “making date” and the “performance date.”
  • In both cases, counterparties to the contract may be called shorts and longs. At the performance or execution date, shorts make delivery and Longs take delivery on prespecified terms.

Edward J. Kane, BC, 03-9&10

futures contracts may be regarded as enhanced forward contracts futures differ in
Futures contracts may be regarded as “enhanced” forward contracts.Futures differ in:
  • formality: exchanges standardize contract terms and oversee margin accounts;
  • convey performance guarantees from exchange clearinghouse;
  • offer delivery options;
  • and [possibly impose daily price limits].

Edward J. Kane, BC, 03-9&10


Explicit forward transactions (repos or futures) can be contrasted with the “implicit” forward transactions that an investor makes in holding an n-period debt contract. Consider, e.g., the difference between holding an explicitforwardposition in 3-mo. T-bills to be issued in 3 months and the similar implicit or synthetic position, contained in an actual 6-month bill.

  • Explicit forward positions bear counterparty default risk. Each position can be separated and directly transferred to another party
  • Implicit positions give borrowers prior possession of loan proceeds and permit no reneging by the implicit forward lender at the rollover date.

Edward J. Kane, BC, 03-9&10

features of a financial futures contract t bill or t bond futures
Features of a Financial Futures Contract: (T-bill or T-bond Futures)

1. Long promises to take delivery of specified quantity of a particular issue or issues of (say) T-bills or T-bonds at scheduled date t+x for execution price specified in the contract. Short promises to make delivery.

2. Standardization of contract terms(e.g., deliverable issues, times, and places), with execution prices determined by trading on an organized exchange (“open outcry” on a trading floor as depicted in 1984 movie Trading Places).

3. Parties may unwind their positions by buying any opposite contract, not necessarily the specific one they originally signed.

4. Both long and shorts are required to pass reputational and net-worthscreens and to post margin accounts with their futures brokers.

5. Dual Back-up of Counterparty Obligations: Brokers and clearing members of exchange (i.e., the so-called clearinghouse) provide back-up guarantees of performance.

Edward J. Kane, BC, 03-9&10

movements in spot price of underlying asset generates gains and losses on bond futures
Movements in Spot Price of Underlying Asset Generates Gains and Losses on Bond Futures

Long Futures Position






Spot Price of Underlying at Execution




Execution Price

Short Futures Position

Edward J. Kane, BC, 03-9&10

standardized contract specifications
Standardized Contract Specifications:

The T-bond futures contract traded on the Chicago Board of Trade has the following:

  • basic trading unit: $100,000 face value US Treasury Bond
  • deliverable grade: T-bonds maturing at least 15 years from first day of delivery month; cannot be callable during this 15 year period
  • delivery method: Federal Reserve book entry wire transfer system
  • price quotation: in decimals of $1000 “points”
  • daily price limit: 3 points ($3,000/contract, no limit in delivery month)
  • contract months: March, June, September, and December
  • last trading day: business day prior to last 7 days of delivery month
  • delivery period: any time during delivery month
  • speculator margin: $2,025 (initial), $1,500 (maintenance)
  • first listed: August 22, 1977

Source: 1997 Contract Specifications booklet, CBOT.

Edward J. Kane, BC, 03-9&10

features of unenhanced forward contracts
Features of Unenhanced Forward Contracts
  • Customization: Negotiated terms may be tailored to specific cash-flow concerns of either counterparty.
  • Absence of automatic third-party guarantees is counterbalanced by deal-generated contractual risk controls: so-called “internal” credit enhancements that strengthen incentives for repayment. E.g., taking direct or indirect physical possession of the securities; overcollateralization; reputational and net-worth screens; negotiating escrow balancesvs. external guarantors.
  • Risk of nonperformance faces shorts if spot price at performance date t+x falls greatly from the execution price. Weaselly longs may refuse delivery if spot price falls far enough. What risk faces longs? That shorts will renege on making delivery if spot price rises high enough.
  • Limited Liquidity: long or short parties can unwind a forward position only by buying out their specific counterparties

Edward J. Kane, BC, 03-9&10

simple index swaps

Illustration of a Swap Contract whose PF/RF elements are written as a “Total Return Swap” on a Government Bond Index I

  • Notation

B: Initial Notional Amount (N.B. Notional Amounts are Never Paid)

B*: Final Notional Amount Determined by PF Index (1+I)B

R: The PV index (usually LIBOR)

Edward J. Kane, BC, 03-9&10


The final figure is the amount to be exchanged on the next settlement date. The PV faces the net outflow if R>I.

Edward J. Kane, BC, 03-9&10

instructive foil contrast with parallel leveraged position in an actual bond
Instructive Foil: Contrast with Parallel Leveraged Position in an Actual Bond

Edward J. Kane, BC, 03-9&10


The difference between the two cases is whether one holds a tangible bond that pays a given return “h” or one holds a claim on a counterparty that pays the virtual yield h given by the PF index “I”.

  • The swap position adds counterparty risk to the extent the swap is not perfectly enhanced.
  • Residuals from index swaps have resulted in high loss rates in failed banks (Supervisors are watching a night game without lights.)

Edward J. Kane, BC, 03-9&10

Interest-rate changes on lesser-quality credits may be driven by changes in market interest rates or changes in market perceptions of an issuer’s default risk.
  • When an index Bond B carries default risk, a total-return swap transfers two kinds of risk: = default event risk and not just market-wide resale risk.

Edward J. Kane, BC, 03-9&10


Swaps are Refinements on Collateralized Obligations. Succeeding generation of derivatives are called “Index Note Derivatives.” “Synthetic” strips are defined as cash flows tied to a partition established by an observable index return.

  • Assembler can define a “variable-rate floater” by subtracting out an index-governed payment stream security from a pool of fixed-rate mortgages. The claim to the RESIDUAL AMOUNTS is called an “inverse floater”. Sometimes likened to “toxic waste.”
  • Value is not transparent because the behavior of the index triggering obligations is uncertain.

Edward J. Kane, BC, 03-9&10



Majority of major corporates using derivatives - Isda 9 April - An overwhelming majority of the world’s largest 500 companies use derivatives to hedge their risks, according to the first corporate derivatives survey by the International Swaps and Derivatives Association (Isda), published at the association’s 18th annual general meeting in Tokyo today. The survey, which spanned companies in 26 countries, found that 92% use derivatives to manage and hedge their risks more effectively. Of these companies, 92% use derivatives to manage interest rate risk, 85% use them to hedge foreign exchange risk, 25% hedge commodity risk and 12% use derivatives to manage equity price risk. UK-based corporates have the highest usage, with all 35 surveyed companies using derivatives. In the US, 94% of the 196 companies questioned said they use derivatives, the same percentage as German corporates. French and Japanese companies followed closely behind, with 92% and 91% respectively using derivatives. "We weren’t very surprised by the results," said Keith Bailey, managing director of Merrill Lynch and chairman of Isda. "It is a very compelling endorsement of the product by the largest companies in the world, and shows it is very important to use derivatives in a competitive environment." The survey will be released on an annual basis, and may include further information in future, including volumes outstanding and product breakdown.

Edward J. Kane, BC, 03-9&10


Self-StudyTopic # 1

Instead of swapping its RF receipts, a Thrift or GSE could swap the other (i.e., the PV) half of its customer-initiated “value difference.”

  • Swap the interest payments on its VR liabilities for responsibility for the stream of interest payments on fixed-rate obligations supported by a European bank that has FR liabilities.
  • This swap assigns a minus sign to the thrift’s customer-initiated PV position. (-PV) is equivalent to a RV position:
  • Similarly, the European bank would offset its PF customer-initiated obligations with the -PF=RF position established by the swap.

Edward J. Kane, BC, 03-9&10

Ignoring “counterparty risk,” swapping lets a U.S. thrift lockin a fixed rate on its liabilities without increasing its on-balance-sheet footings.
  • Of course, the thrift would still carry default and prepayment risk on its mortgage assets.
  • Opportunities for further deal-making exist today: credit swaps can be used to cross-hedge either or both of the counterparty and customer default risks.

Edward J. Kane, BC, 03-9&10


-- Suppose: Notional amount is $100,000

Fixed-rate instrument pays 9% once a year

Variable-rate formula equals LIBOR plus 3%, paid once a year (Size of risk premium implies low credit quality.)

Tenor is 5 years

-- For expositional simplification, suppose over the next 5 years Both Parties Project LIBOR to equal 3%, 5%, 7%, 9%, 11%.

[-- Perhaps these projections are read as “forward rates” off a yield curve.]

Edward J. Kane, BC, 03-9&10










Edward J. Kane, BC, 03-9&10


In the previous slide, when is the settlement check an inpayment to PV counterparty (i.e., projected “receipt”) and when is it an inpayment to the PF side?

ANS. The first two checks are PV inpayments; the last three are PV outpayments.

Edward J. Kane, BC, 03-9&10


Self-StudyTopic # 2

A bank ought to track exposure of each swap position to changes in value in some way.

Query: Looking at the RFPV contract in isolation, how can one calculate the expected loss to dealer at each date if this contract were to fail irrevocably and be voided at t+1? at t+2? at t+3? at t+4? t+5?

  • Discounting of cash flows addresses evolution of value and exposure if LIBOR moves away from its projected values.

Edward J. Kane, BC, 03-9&10


The equivalent 5-year FR facing the PV side in the tangible bond market would have to exceed 12% to make the deal desirable. To show this, let us discount the last 3 payments to the PFRV side at 12%. What would be their projected value at t+3?

ANS. 1,000 + = $7,664.54.

What is PDV of these RF inpayments at t+1?

= $6,110.12.

  • This is greater than PDV at t+1 of RF outpayments valued at 12%. =$3,000+1,000/1.12=$3,892.86.

Edward J. Kane, BC, 03-9&10

To understand pricing of swaps, one must understand a key point: changes in the PDV of the VR half of most swaps seldom depart far from zero, so that the pricing of a swap is dominated by its fixed half.
  • Only the PV half of a RFPV swap has unpredictable payments. Its value approximates that of a “par floater” because value is reset to par on the reset dates.
  • Changes in value of contract occur as market forces move the RF contract rate “above” or “below” current market yields.

Edward J. Kane, BC, 03-9&10

Might higher credit risk for the RFPV party initially balance the deal to make the contract on-market?
  • Risk Premium would have to be high enough for credit of the RFPV party to be priced at LIBOR plus 3% at all times.
  • In this case, the PDV of both sides would be equal at the notional value F used at t.

Edward J. Kane, BC, 03-9&10

value of rfpv inpayments at t when r f on 5 year bonds is 9
Value of RFPV inpayments at t when RF on 5-year bonds is 9%
  • If this swap is placed on-market, a substantial risk premium is paid to the PFRV party. Tabled sum = expected value of net RF inpayments at initial date, ignoring credit risk.
  • Passage-of-time effects: PFRV side’s exposure to nonperformance risk rises after making payments at t+1 and t+2.

Edward J. Kane, BC, 03-9&10