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Swaps

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Title: Swaps


1
Swaps
2
Introduction
  • An agreement between two parties to exchange cash
    flows in the future.
  • The agreement specifies the dates that the cash
    flows are to be paid and the way that they are to
    be calculated.
  • A forward contract is an example of a simple
    swap. With a forward contract, the result is an
    exchange of cash flows at a single given date in
    the future.
  • In the case of a swap the cash flows occur at
    several dates in the future. In other words, you
    can think of a swap as a portfolio of forward
    contracts.

3
Mechanics of Swaps
  • The most commonly used swap agreement is an
    exchange of cash flows based upon a fixed and
    floating rate.
  • Often referred to a plain vanilla swap, the
    agreement consists of one party paying a fixed
    interest rate on a notional principal amount in
    exchange for the other party paying a floating
    rate on the same notional principal amount for a
    set period of time.
  • In this case the currency of the agreement is the
    same for both parties.

4
Notional Principal
  • The term notional principal implies that the
    principal itself is not exchanged. If it was
    exchanged at the end of the swap, the exact same
    cash flows would result.

5
An Example
  • Company B agrees to pay A 5 per annum on a
    notional principal of 100 million
  • Company A Agrees to pay B the 6 month LIBOR rate
    prevailing 6 months prior to each payment date,
    on 100 million. (generally the floating rate is
    set at the beginning of the period for which it
    is to be paid)

6
The Fixed Side
  • We assume that the exchange of cash flows should
    occur each six months (using a fixed rate of 5
    compounded semi annually).
  • Company B will pay
  • (100M)(.025) 2.5 Million
  • to Firm A each 6 months.

7
Summary of Cash Flows for Firm B
  • Cash Flow Cash Flow Net
  • Date LIBOR Received Paid Cash
    Flow
  • 3-1-98 4.2
  • 9-1-98 4.8 2.10 2.5 -0.4
  • 3-1-99 5.3 2.40 2.5 -0.1
  • 9-1-99 5.5 2.65 2.5 0.15
  • 3-1-00 5.6 2.75 2.5 0.25
  • 9-1-00 5.9 2.80 2.5 0.30
  • 3-1-01 6.4 2.95 2.5 0.45

8
Swap Diagram
  • LIBOR
  • Company A Company B
  • 5

9
Offsetting Spot Position
Assume that A has a commitment to borrow at a
fixed rate of 5.2 and that B has a commitment
to borrow at a rate of LIBOR .8
  • Company A
  • Borrows (pays) 5.2
  • Pays LIBOR
  • Receives 5
  • Net LIBOR.2
  • Company B
  • Borrows (pays) LIBOR.8
  • Receives LIBOR
  • Pays 5
  • Net 5.8

10
Swap Diagram
  • Company A Company B
  • The swap in effect transforms a fixed rate
    liability or asset to a floating rate liability
    or asset (and vice versa) for the firms
    respectively.

LIBOR
LIBOR.8
5.2
5
5.8
LIBOR .2
11
Role of Intermediary
  • Usually a financial intermediary works to
    establish the swap by bring the two parties
    together.
  • The intermediary then earns .03 to .04 per annum
    in exchange for arranging the swap.
  • The financial institution is actually entering
    into two offsetting swap transactions, one with
    each company.

12
Swap Diagram
  • Co A FI Co B
  • A pays LIBOR.215
  • B pays 5.815
  • The FI makes .03

LIBOR
LIBOR
5.2
LIBOR.8
5.015
4.985
13
Day Count Conventions
  • The above example ignored the day count
    conventions on the short term rates.
  • For example the first floating payment was listed
    as 2.10. However since it is a money market rate
    the six month LIBOR should be quoted on an actual
    /360 basis.
  • Assuming 184 days between payments the actual
    payment should be
  • 100(0.042)(184/360) 2.1467

14
Day Count Conventions II
  • The fixed side must also be adjusted and as a
    result the payment may not actually be equal on
    each payment date.
  • The fixed rate is often based off of a longer
    maturity instrument and may therefore uses a
    different day count convention than the LIBOR.
    If the fixed rate is based off of a treasury note
    for example, the note is based on a different day
    convention.

15
Role of the Intermediary
  • It is unlikely that a financial intermediary will
    be contacted by parties on both side of a swap at
    the same time.
  • The intermediary must enter into the swap without
    the counter party. The intermediary then hedges
    the interest rate risk using interest rate
    instruments while waiting for a counter party to
    emerge.
  • This practice is referred to as warehousing swaps.

16
Why enter into a swap?
  • The Comparative Advantage Argument
  • Fixed Floating
  • A 10 6 mo LIBOR.3
  • B 11.2 6 mo LIBOR 1.0
  • Difference between fixed rates 1.2
  • Difference between floating rates 0.7
  • B Has an advantage in the floating rate.

17
Swap Diagram
  • Co A FI Co B
  • A pays LIBOR.065 instead of LIBOR.3
  • B pays 10.965 instead of 11.2
  • The FI makes .03

LIBOR
LIBOR
10
LIBOR1
9.965
9.935
18
Spread Differentials
  • Why do spread differentials exist?
  • Differences in business lines, credit history,
    asset and liabilities, etc

19
Valuation of Interest Rate Swaps
  • After the swap is entered into it can be valued
    as either
  • A long position in one bond combined with a short
    position in another bond or
  • A portfolio of forward rate agreements.

20
Relationship of Swaps to Bonds
  • In the examples above the same relationship could
    have been written as
  • Company B lent company A 100 million at the six
    month LIBOR rate
  • Company A lent company B 100 million at a fixed
    5 per annum

21
Bond Valuation
  • Given the same floating rates as before the cash
    flow would be the same as in the swap example.
  • The value of the swap would then be the
    difference between the value of the fixed rate
    bond and the floating rate bond.

22
Fixed portion
  • The value of either bond can be found by
    discounting the cash flows from the bond (as
    always). The fixed rate value is straight
    forward it is given as
  • where Q is the notional principal and k is the
    fixed interest payment

23
Floating rate valuation
  • The floating rate is based on the fact that it is
    a series of short term six months loans.
  • Immediately after a payment date Bfl is equal to
    the notional principal Q. Allowing the time
    until the next payment to equal t1
  • where k is the known next payment

24
Swap Value
  • If the financial institution is paying fixed and
    receiving floating the value of the swap is
  • Vswap Bfl-Bfix
  • The other party will have a value of
  • Vswap Bfix-Bfl

25
Example
  • Pay 6 mo LIBOR receive 8
  • 3 mo 10
  • 9 mo 10.5
  • 15 mo 11
  • Bfix 4e .-1(.25)4e -.105(.75)104e
    -.11(1.25)98.24M
  • Bfloat 100e -.1(.25) 5.1e -.1(.25) -102.5M
  • -4.27 M

26
A better valuation
  • Relationship of Swap value to Forward Rte
    Agreements
  • Since the swap could be valued as a forward rate
    agreement (FRA) it is also possible to value the
    swap under the assumption that the forward rates
    are realized.

27
To do this you would need to
  • Calculate the forward rates for each of the LIBOR
    rates that will determine swap cash flows
  • Calculate swap cash flows using the forward rates
    for the floating portion on the assumption that
    the LIBOR rates will equal the forward rates
  • Set the swap value equal to the present value of
    these cash flows.

28
Swap Rate
  • This works after you know the fixed rate.
  • When entering into the swap the value of the swap
    should be 0.
  • This implies that the PV of each of the two
    series of cash flows is equal. Each party is
    then willing to exchange the cash flows since
    they have the same value.
  • The rate that makes the PV equal when used for
    the fixed payments is the swap rate.

29
Example
  • Assume that you are considering a swap where the
    party with the floating rate will pay the three
    month LIBOR on the 50 Million in principal.
  • The parties will swap quarterly payments each
    quarter for the next year.
  • Both the fixed and floating rates are to be paid
    on an actual/360 day basis.

30
First floating payment
  • Assume that the current 3 month LIBOR rate is
    3.80 and that there are 93 days in the first
    period.
  • The first floating payment would then be

31
Second floating payment
  • Assume that the three month futures price on the
    Eurodollar futures is 96.05 implying a forward
    rate of 100-96.05 3.95
  • Given that there are 91 days in the period.
  • The second floating payment would then be

32
Example Floating side
Period Day Count Futures Price Fwd Rate Floating Cash flow
91 3.80
1 93 96.05 3.95 490,833.3333
2 91 95.55 4.45 499,236.1111
3 90 95.28 4.72 556,250.0000
4 91 596,555.5555
33
PV of Floating cash flows
  • The PV of the floating cash flows is then
    calculated using the same forward rates.
  • The first cash flow will have a PV of

34
PV of Floating cash flows
  • The PV of the floating cash flows is then
    calculated using the same forward rates.
  • The second cash flow will have a PV of

35
Example Floating side
Period Day Count Fwd Rate Floating Cash flow PV of Floating CF
91 3.80
1 93 3.95 490,833.3333 486,061.8263
2 91 4.45 499,236.1111 489,495.4412
3 90 4.72 556,250.0000 539,396.1423
4 91 596,555.5555 525,668.5915
36
PV of floating
  • The total PV of the floating cash flows is then
    the sum of the four PVs
  • 2,040,622.0013

37
Swap rate
  • The fixed rate is then the rate that using the
    same procedure will cause the PV of the fixed
    cash flows to have a PV equal to the same amount.
  • The fixed cash flows are discounted by the same
    rates as the floating rates.
  • Note the fixed cash flows are not the same each
    time due to the changes in the number of days in
    each period.
  • The resulting rate is 4.1294686

38
Example Swap Cash Flows
Period Day Count Fwd Rate Floating Cash flow Fixed CF
91 3.80
1 93 3.95 490,833.3333 533,389.7003
2 91 4.45 499,236.1111 521,918.9541
3 90 4.72 556,250.0000 516,183.5810
4 91 596,555.5555 521,918.9541
39
Swap Spread
  • The swap spread would then be the difference
    between the swap rate and the on the run treasury
    of the same maturity.

40
Swap valuation revisited
  • The value of the swap will change over time.
  • After the first payments are made, the futures
    prices and corresponding interest rates have
    likely changed.
  • The actual second payment will be based upon the
    3 month LIBOR at the end of the first period.
  • Therefore the value of the swap is recalculated.

41
Currency Swaps
  • The primary purpose of a currency swap is to
    transform a loan denominated in one currency into
    a loan denominated in another currency.
  • In a currency swap, a principal must be specified
    in each currency and the principal amounts are
    exchanged at the beginning and end of the life of
    the swap.
  • The principal amounts are approximately equal
    given the exchange rate at the beginning of the
    swap.

42
A simple example
  • Assume that company A pays a fixed rate of 11 in
    sterling and receives a fixed interest rate of 8
    in dollars.
  • Let interest payments be made once a year and the
    principal amounts be 15 million and L10 Million
  • Company A
  • Dollar Cash Sterling Cash
  • Flow (millions) Flow (millions)
  • 2/1/1999 -15.00 10.00
  • 2/1/2000 1.20 -1.10
  • 2/1/2001 1.20 -1.10
  • 2/1/2002 1.20 -1.10
  • 2/1/2003 1.20 -1.10
  • 2/1/2004 16.20 -11.10

43
Intuition
  • Suppose A could issue bonds in the US for 8
    interest, the swap allows it to use the 15
    million to actually borrow 10million sterling at
    11 (A can invest L 10M _at_ 11 but is afraid that
    will strength it wants US denominated
    investment)

44
Comparative Advantage Again
  • The argument for this is very similar to the
    comparative advantage argument presented earlier
    for interest rate swaps.
  • It is likely that the domestic firm has an
    advantage in borrowing in its home country.

45
Example using comparative advantage
  • Dollars AUD (Australian )
  • Company A 5 12.6
  • Company B 7 13.0
  • 2 difference in US .4 difference in AUD

46
The strategy
  • Company A borrows dollars at 5 per annum
  • Company B borrows AUD at 13 per annum
  • They enter into a swap
  • Result
  • Since the spread between the two companies is
    different for each firm there is the ability of
    each firm to benefit from the swap. We would
    expect the gain to both parties to be 2 - 0.4
    1.6 (the differences in the spreads).

47
Swap Diagram
  • Co A FI Co B
  • A pays 11.9 AUD instead of 12.6 AUD
  • B pays 6.3 US instead of 7 US
  • The FI makes .2

AUD 11.9
AUD 13
5
AUD 13
6.3
5
48
Valuation of Currency Swaps
  • Using Bond Techniques
  • Assuming there is no default risk the currency
    swap can be decomposed into a position in two
    bonds, just like an interest rate swap.
  • In the example above the company is long a
    sterling bond and short a dollar bond. The value
    of the swap would then be the value of the two
    bonds adjusted for the spot exchange rate.

49
Swap valuation
  • Let S the spot exchange rate at the beginning
    of the swap, BF is the present value of the
    foreign denominated bond and BD is the present
    value of the domestic bond. Then the value is
    given as
  • Vswap SBF BD
  • The correct discount rate would then depend upon
    the term structure of interest rates in each
    country

50
Other swaps
  • Swaps can be constructed from a large number of
    underlying assets.
  • Instead of the above examples swaps for floating
    rates on both sides of the transaction.
  • The principal can vary through out the life of
    the swap.
  • They can also include options such as the ability
    to extend the swap or put (cancel the swap).
  • The cash flows could even extend from another
    asset such as exchanging the dividends and
    capital gains realized on an equity index for a
    fixed or floating rate.

51
Beyond Plain Vanilla Swaps
  • Amortizing Swap -- The notional principal is
    reduced over time. This decreases the fixed
    payment. Useful for managing mortgage portfolios
    and mortgage backed securities.
  • Accreting Swap The notional principal increases
    over the life of the swap. Useful in
    construction finances. For example is the
    builder draws down an amount of financing each
    period for a number of periods.

52
Beyond Plain Vanilla
  • You can combine amortizing and accreting swaps to
    allow the notional principal to both increase and
    decrease.
  • Seasonal Swap -- Increase and decrease of
    notional principal based of f of designated plan
  • Roller Coaster Swap -- notional principal first
    increases the amortizes to zero.

53
Off Market Swap
  • The interest rate is set at a rate above market
    value.
  • For example the fixed rate may pay 9 when the
    yield curve implies it should pay 8.
  • The PV of the extra payments is transferred as a
    one time fee at the beginning of the swap (thus
    keeping the initial value equal to zero)

54
Forward and Extension Swaps
  • Forward swap the payments are agreed to begin
    at some point in time in the future
  • If the rates are based on the current forward
    rate there should not be any exchange of
    principal when the payments begin. Other wise it
    is an off market swap and some form of
    compensation is needed
  • Extension Swap an agreement to extend the
    current swap (a form of forward swap)

55
Basis Swaps
  • Both parties pay floating rates based upon
    different indexes.
  • For example one party may pay the three month
    LIBOR while the other pays the three month T-
    Bill.
  • The impact is that while the rates generally move
    together the spread actually widens and narrows,
    Therefore the return on the swap is based upon
    the spread.

56
Yield Curve Swaps
  • Both parties pay floating but based off of
    different maturities. Is similar to a basis swap
    since the effective result is based on the spread
    between the two rates. A steepening curve thus
    benefits the payer of the shorter maturity rate.
  • This is utilized by firms with a mismatch of
    maturities in assets and liabilities (banks for
    example). It can hedge against changes in the
    yield curve via the swap.

57
Rate differential (diff) swap
  • Payments tied to rate indexes in different
    currencies, but payments are made in only one
    currency.

58
Corridor Swap
  • Payments obligation only occur in a given range
    of rates. For example if the LIBOR rate is
    between 5 and 7.
  • The swap is basically a tool based on the
    uncertainty of rates.

59
Flavored Currency Swaps
  • The basic currency swap can be modified similar
    to many of the modifications just discussed.
  • Swaps may also be combined to produce desired
    outcomes.
  • CIRCUS Swap (Combined interest rate and currency
    swap). Combines two basic swaps

60
Circus Swap Diagram
  • LIBOR
  • Company A Company B
  • 5 US
  • 6 German Marks
  • Company A Company C
  • LIBOR

61
Circus Swap Diagram
  • Company B
  • Company A 5 US
  • 6 German Marks
  • Company C

62
Swapation
  • An option on a swap that specifies the tenor,
    notional principal fixed rate and floating rate
  • Price is usually set a a of notional principal
  • Receiver Swapation
  • The holder has the right to enter into a swap as
    the fixed rate receiver
  • Payer Swapation
  • The holder has the right to enter into a
    particular swap as the fixed rate payer.

63
Swapation as call (or put) Options
  • Receiver swapation similar to a call option on
    a bond. The owner receives a fixed payment (like
    a coupon payment) and pays a floating rate (the
    exercise price)
  • Payer swapation if exercised the owner is
    paying a stream similar to the issue of a bond.

64
In-the-Money Swapations
  • A receiver swapation is in the money if interest
    rates fall. The owner is paying a lower fixed
    rate in exchange for the fixed rate specified in
    the contract.
  • Similarly a payer swapation is generally in the
    money if interest rates increase since the owner
    will receive a higher floating rate.

65
When to Exercise
  • The owner of the receiver swapation should
    exercise if the fixed rate on the swap underlying
    the swapation is greater than the market fixed
    rate on a similar swap. In this case the swap is
    paying a higher rate than that which is available
    in the market.

66
A fixed income swapation example
  • Consider a firm that has issued a corporate bond
    with a call option at a given date in the future.
  • The firm has paid for the call option by being
    forced to pay a higher coupon on the bond than on
    a similar noncallable bond.
  • Assume that the firm has determined that it does
    not want to call the bond at its first call date
    at some point in the future.
  • The call option is worthless to the firm, but it
    should theoretically have value.

67
Capturing the value of the call
  • The firm can sell a receiver swapation with terms
    that match the call feature of the bond.
  • The firm would receive for this a premium that is
    equal to the value of the call option.

68
Example
  • Assume the firm has previously issued a 9 coupon
    bond that makes semiannual payments and matures
    in 7 years with a face value of 150 Million.
  • The bond has a call option for one year from
    today.

69
Example continued
  • The firm can sell a European Receiver Swapation
    with an expiration in one year. The Swapation
    terms are for semiannual payments at a fixed rate
    of 9 in exchange for floating payments at LIBOR.
  • The firm receives a premium for the swapation
    equal to a fixed percentage of the 150 Million
    notional value (equal to the value of the call
    option).
  • The firm can keep the premium but has a potential
    obligation in one year if the counter party
    exercises the swap.

70
Example Continued
  • In one year the fixed rate for this swap is 11
  • The option will expire worthless since the owner
    can earn a fixed 11 on a similar swap.
  • The firm gets to keep the premium.

71
Example Continued
  • If in one year the fixed rate of interest on a
    similar swap is 7 the owner will exercise the
    swap since it calls for a 9 fixed rate.
  • The firm can call the bond since rates have
    decreased. It can finance the call by issuing a
    floating rate note at LIBOR for the term of the
    swap.
  • The floating rate side of the swap pays for the
    note and the firm is still paying the original 9
    fixed, but it has also received the premium on
    the swapation

72
Extendible and Cancelable swaps
  • Similar to extension swaps except extension swaps
    represent a firm commitment to extend the swap.
    An extendible swap has the option to extend the
    agreement.
  • Arranged via a plain vanilla swap an a swapation.

73
Extendible and Cancelable
  • Extendible pay fixed swap
  • plain vanilla pay fixed plus payer swapation
  • Extendible Receive-Fixed Swap
  • plain vanilla receive fixed swap receiver
    swapation
  • Cancelable Pay Fixed Swap
  • plain vanilla pay fixed swap receiver
    swapation
  • Cancelable Receive Fixed Swap
  • plain vanilla receive fixed swap payable
    swapation

74
Creating synthetic securities using swaps
  • The origins of the swap market are based in the
    debt market.
  • Previously there had been restrictions on the
    flow of currency.
  • A parallel loan market developed to get around
    restrictions on the flow of currency from one
    country to another, Especially restrictions
    imposed by the Bank of England.

75
The Parallel Loan Market
  • Consider two firms, one British and one American,
    each with subsidiaries in both countries.
  • Assume that the free-market value of the pound is
    L11.60 and the officially required exchange
    rate is L11.44.
  • Assume the British Firm wants to undertake a
    project in the US requiring an outlay of
    100,000,000.

76
Parallel Loan Market
  • The cost of the project at the official exchange
    rate is 100,000,0000/1.44 L69,444,000
  • The cost of the project at the free market
    exchange rate is 100,000,0000/1.60 L62,500,000
  • The firm is paying an extra L7,000,000

77
Parallel Loan Market
  • The British firm lends L62,500,000 pounds to the
    US subsidiary operating in England at a floating
    rate based on LIBOR and The US firm lends
    100,000,000 to the British firm at a fixed rate
    of 7 in the US the official exchange rate is
    avoided.
  • The result is a basic fixed for floating currency
    swap. (In this case each loan is separate
    default on one loan does not constitute default
    on the other).

78
Synthetic Fixed Rate Debt
  • A firm with an existing floating rate debt can
    easily transform it into a fixed rate debt via an
    interest rate swap.
  • By receiving floating and paying fixed, the firm
    nets just a spread on the floating transaction
    creating a fixed rate debt (the rate paid on the
    swap plus the spread)

79
Synthetic Floating Rate Debt
  • Combining a fixed rate debt with a pay floating /
    receive fixed rate swap easily transforms the
    fixed rate. Again the fixed rates cancel out (or
    result in a spread) leaving just a floating rate.

80
Synthetic Callable Debt
  • Consider a firm with an outstanding fixed rate
    debt without any call option.
  • It can create a call option. If it had a call
    option in place it would retire the debt if
    called. Look at this as creating a new financing
    need (you need to finance the retirement of the
    debt.)
  • You want the ability to call the bond but not the
    obligation to do so.

81
Synthetic Callable Debt
  • Buying a receiver swapation allows the firm to
    receive a fixed rate, canceling out its current
    fixed rate obligation.
  • It will pay a new floating rate as part of the
    swap (similar to financing the call with new
    floating rate debt).

82
Synthetic non callable Debt
  • Basically the earlier example swapations.

83
Synthetic Dual Currency Debt
  • Dual Currency bond principal payments are
    denominated in one currency and coupon payments
    denominated in another currency.
  • Assume you own a bond that makes its payments in
    US dollars, but you would prefer the coupon
    payments to be in another currency with the
    principal repayment in dollars.
  • A fixed for fixed currency swap would allow this
    to happen

84
Synthetic Dual Currency Debt
  • Combine a receive fixed German marks and pay US
    dollars swap with the bond.
  • The dollars received from the bond are used to
    pay the dollar commitment on the swap. You then
    just receive the German Marks.

85
All in Cost
  • The IRR for a given financing alternative, it
    includes all costs including administration,
    flotation , and actual cash flows.
  • The cost is simply the rate that makes the PV of
    the cash flows equal to the current value of the
    borrowing.

86
Compare two alternative proposals
  • A 10 year semiannual 7 coupon bond with a
    principal of 40 million priced at par
  • A loan of 40 million for 10 years at a floating
    rate of LIBOR 30 Bps reset every six months
    with the current LIBOR rate of 6.5. Plus a swap
    transforming the loan to a fixed rate commitment.
    The swap will require the firm to pay 6.5 fixed
    and receive floating.

87
All in cost
  • The bond has a all in cost equal to its yield to
    maturity, 7
  • Assuming the firm must pay 400,000 to enter into
    the swap so it only nest 39,600,000. Today.
    The net interest rate it pays is 6.8 implying
    semiannual payments of (.068/2)(40,000,000)
    1,360,000 plus a final payment of 40,000,000.
    This implies a rate of .034703 every six months
    or .069406 every year.

88
BF Goodrich and RabobankAn early swap example
  • In the early 1980s BF Goodrich needed to raise
    new funds, but its credit rating had been
    downgraded to BBB-. The firm needed 50,000,000
    to fund continuing operations.
  • They wanted long term debt in the range of 8 to
    10 years and a fixed rate. Treasury rates were
    at 10.1 and BF Goodrich anticipated paying
    approximately 12 to 12.5
  • taken from Kolb - Futures Options and Swaps

89
Rabobank
  • Rabobank was a large Dutch banking organization
    consisting of more than 1,000 small agricultural
    banks. The bank was interested in securing
    floating rate financing on approximately
    50,000,000 in the Eurobond market.
  • With a AAA rating Rabobank could issue fixed rate
    in the Eurobond market for approximately 11 and
    for a floating rate of LIBOR plus .25

90
The Intermediary
  • Salomon Brothers suggested a swap agreement to
    each party.
  • This would require BF Goodrich to issue the first
    public debt tied to LIBOR in the United States.
    Salomon Brothers felt that there would be a
    market for the debt because of the increase in
    deposits paying a floating rate due to
    deregulation.

91
Problems
  • Rabobank was interested in the deal,but fearful
    of credit risk. A direct swap would expose it to
    credit risk. Without an active swap market it
    was common for swaps to be arranged between the
    two counter parties.
  • The two finally reached an agreement to use
    Morgan Guaranty as an intermediary.

92
The agreement
  • BF Goodrich issued a noncallable 8 year floating
    rate note with a principal value of 50,000,000
    paying the 3 month LIBOR rate plus .5
    semiannually. The bond was underwritten by
    Salomon.
  • Rabobank issued a 50,000,000 non callable 8 year
    Eurobond with annual payments of 11
  • Both entered into a swap with Morgan Guaranty

93
The swaps
  • BF Goodrich promised to pay Morgan Guaranty
    5,500,000 each year for eight years (matching the
    coupon on the Rabobanks debt). Morgan agreed to
    pay BF Goodrich a semi annual rate tied to the 3
    month LIBOR equal to .5(50,000,000)(3 mo
    LIBOR-x)
  • x represents an undisclosed discount
  • Rabobank received 5,500,000 each year for 8
    years and paid semi annul payments of LIBOR-x

94
The intermediary role
  • The two swap agreements were independent of each
    other eliminating the credit risk concerns of
    Rabobank.
  • Morgan received a one time fee of 125,000 paid
    by BF Goodrich plus an annual fee of 8 to 37 Bp
    (40,000 to 185,000) also paid by BF Goodrich.

95
BF Goodrich
  • Assuming that the discount from LIBOR was 50 Bp
    and that the service fee was 22.5 BP (the
    midpoint of the range). BF Goodrich paid an all
    in cost of 11.9488 annually compared to 12 to
    12.5 if they had issued the debt on their own.

96
Rabobanks Position
  • At the time of financing it would have paid LIBOR
    plus 25 to 50 Bp. Given that it paid no fees and
    the fixed rate canceled out it ended up paying
    LIBOR - x.

97
Securing financing
  • BF Goodrich was able to secure financing via its
    use of the swaps market, this is a common use of
    the market.
  • The example provides a good illustration of the
    idea of the comparative advantage arguments we
    discussed earlier.

98
A Second Example of securing financing
  • It is possible for swaps to increases
    accessibility two the debt market
  • Mexcobre (Mexicana de Corbre) is the copper
    exporting subsidiary of Grupo Mexico. In the
    late 1980s it would have had a difficult time
    borrowing in international credit markets due to
    concerns or default risk
  • However it was able to borrow 210 million for 38
    months from a group of banks led by Paribas
  • from Managing Financial Risk by Smithson, Smith
    and Wilford

99
The original loan
  • The banks lent the firm 210 Million at a fixed
    rate of 11.48. The debt replaced borrowing from
    the Mexican government which had cost the firm
    23.
  • A Belgian company Sogem agreed to buy 4,000 tons
    of copper per month at the prevailing spot rate
    from Mexcobre making payments into an escrow
    account in New York that was used to service the
    debt with any extra funds returned to Mexcobre.

100
Quarterly payments of 11.48 interest plus
principal
Banks
Escrow
Excess cash if it builds up
210 million loan
Cash based on Spot Price
4,000 tons of copper per month
Mexcobre
SOGEM
101
Swaps
  • Swaps were added between Paribas and the escrow
    account to hedge the price risk of copper and
    between Paribas and the banks to change the banks
    position to a floating rate

102
Paribas
Spot Price per ton
Floating
Fixed
2,000 per ton
Quarterly payments of 11.48 interest plus
principal
Banks
Escrow
Excess cash if it builds up
Cash per ton based on Spot Price
210 million loan
4,000 tons of copper per month
Mexcobre
SOGEM
103
Duration of Interest Rate Swaps
  • A plain vanilla swap can be valued as a portfolio
    of two bonds, therefore the duration of the swap
    should equal the duration of the bond portfolio.
  • The duration can be either positive or negative
    depending on the side of the swap
  • Kolb, Futures Options and Swaps

104
Duration of Swaps
  • Duration of Receive Fixed Swap
  • Duration of Underlying coupon bond
  • - Duration of underlying floating Rate Bond
  • gt0
  • Duration of Pay Fixed Swap
  • Duration of underlying floating Rate Bond
  • - Duration of Underlying coupon bond
  • lt0

105
Example
  • Consider a swap with a semiannual fixed rate of
    7 and a floating rate that resets each six
    months.
  • The duration of the fixed rate side (assuming a
    100 notional principal) is 5.65139 years
  • Duration of Receive Fixed Swap
  • 5.65139-0.55.15369
  • Duration of Pay Fixed Swap
  • 0.5-5.65139-5.15369

106
Calculating Duration
  • Duration of floating rate security is equal to
    the time between resetting of the rate.
  • Therefore the duration of the swap actually
    depends upon the duration of the fixed rate side.
  • Receive Fixed rate swaps will then usually
    lengthen the duration of an existing position
    while pay fixed swaps will shorten the duration
    of an existing position.

107
Immunization with Swaps
  • Swaps can be used to hedge interest rate risk by
    impacting the duration of the assets and
    liabilities on the balance sheet.
  • Going to look at a fictional financial services
    firm FSF

108
Balance Sheet for FSF
  • Liabilities
  • 6mo money mkt 75,000,000
  • (avg yield 6)
  • Floating Rate Notes 40,000,000
  • (5 yr mat7.3 yld semi)
  • Coupon Bond 24,111,725
  • (10 yr semi 6.5 coup
  • 25,000,000 par, 7 YTM
  • Net worth 16,355,408
  • Total Liab NW 155,467,133
  • Assets
  • Cash 7,000,000
  • Marketable Sec 18,000,000
  • (6 mo mat Yield 7)
  • Amortizing loans 130,467,133
  • (10 yr avg mat
  • semiannual
  • 8 avg yield)
  • Total Assets 1555,467,133

109
Basic Duration
110
Duration
  • Assets
  • Duration
  • Cash 0.00
  • Marketable Sec 0.500
  • Amortizing loans 4.604562
  • Total Duration
  • (7,000,000/155,467,133)0.000
  • (18,000,000/155,467,133)0.500
  • (130,467,133/155,467,133)4.605
  • 3.922013
  • Liabilities
  • Duration
  • 6mo money mkt 0.5000
  • Floating Rate Notes 0.5000
  • Coupon Bond 7.453369
  • Total Duration
  • (75,000,000/155,467,133)0.500
  • (40,000,000/155,467,133)0.500
  • (24,111,725/155,467,133)7.45337
  • 1.705202

111
Hedging the portfolios separately
  • It is easy to use duration to hedge the interest
    rate risk of the portfolio.
  • The idea is to construct a portfolio with a
    duration of zero.
  • Let MVi be the market value and Di be the
    Duration of the assets (A), liabilities (L) or
    hedge vehicle (H) then
  • MVA(DA)MVH(DH) 0
  • and
  • MVL(DL)MVH(DH) 0

112
Swap notional value
  • Given the duration of the hedge (a swap) it is
    then possible to solve for a notional value (or
    market value) of the swap that would make the
    portfolio duration zero.
  • Previously we found the duration of a swap
  • Duration of Receive Fixed Swap
  • 5.65139-0.55.15369
  • Duration of Pay Fixed Swap
  • 0.5-5.65139-5.15369

113
Asset Hedge
  • The asset can then be hedged by solving for the
    notional value (MVH) of the pay fixed swap
  • MVA(DA)MVH(DH) 0
  • 155,467,133(3.922)(-5.15369)(MVH) 0
  • MVH118,365,451

114
Liability Hedge
  • The liabilities can then be hedged by solving for
    the notional value (MVH) of the receive fixed
    swap
  • MVL(DL)MVH(DH) 0
  • (-139,111,725)(1.705202)(5.15369)(MVH) 0
  • MVH46,048,651

115
Hedging Assets and Liabilities together
  • The entire balance sheet can be hedged with one
    interest rate swap by using GAP analysis.

116
Static GAP Analysis(The repricing model)
  • Repricing GAP
  • The difference between the value of interest
    sensitive assets and interest sensitive
    liabilities of a given maturity.
  • Measures the amount of rate sensitive (asset or
    liability will be repriced to reflect changes in
    interest rates) assets and liabilities for a
    given time frame.

117
GAP Analysis
  • Static GAP-- Goal is to manage interest rate
    income in the short run (over a given period of
    time)
  • Measuring Interest rate risk calculating GAP
    over a broad range of time intervals provides a
    better measure of long term interest rate risk.

118
Interest Sensitive GAP
  • Given the Gap it is easy to investigate the
    change in the net interest income (NII) of the
    financial institution.

119
Example
  • Over next 6 Months
  • Rate Sensitive Liabilities 120 million
  • Rate Sensitive Assets 100 Million
  • GAP 100M 120M - 20 Million
  • If rate are expected to decline by 1
  • Change in net interest income
  • (-20M)(-.01) 200,000

120
GAP Analysis
  • Asset sensitive GAP (Positive GAP)
  • RSA RSL gt 0
  • If interest rates h NII will h
  • If interest rates i NII will i
  • Liability sensitive GAP (Negative GAP)
  • RSA RSL lt 0
  • If interest rates h NII will i
  • If interest rates i NII will h
  • Would you expect a commercial bank to be asset or
    liability sensitive for 6 mos? 5 years?

121
Important things to note
  • Assuming book value accounting is used -- only
    the income statement is impacted, the book value
    on the balance sheet remains the same.
  • The GAP varies based on the bucket or time frame
    calculated.
  • It assumes that all rates move together.

122
Steps in Calculating GAP
  • Select time Interval
  • Develop Interest Rate Forecast
  • Group Assets and Liabilities by the time interval
    (according to first repricing)
  • Forecast the change in net interest income.

123
Alternative measures of GAP
  • Cumulative GAP
  • Totals the GAP over a range of of possible
    maturities (all maturities less than one year for
    example).
  • Total GAP including all maturities

124
Other useful measures using GAP
  • Relative Interest sensitivity GAP (GAP ratio)
  • GAP / Bank Size
  • The higher the number the higher the risk that is
    present
  • Interest Sensitivity Ratio

125
What is Rate Sensitive
  • Any Asset or Liability that matures during the
    time frame
  • Any principal payment on a loan is rate sensitive
    if it is to be recorded during the time period
  • Assets or liabilities linked to an index
  • Interest rates applied to outstanding principal
    changes during the interval

126
Unequal changes in interest rates
  • So far we have assumed that the change the level
    of interest rates will be the same for both
    assets and liabilities.
  • If it isnt you need to calculate GAP using the
    respective change.
  • Spread effect The spread between assets and
    liabilities may change as rates rise or decrease

127
Strengths of GAP
  • Easy to understand and calculate
  • Allows you to identify specific balance sheet
    items that are responsible for risk
  • Provides analysis based on different time frames.

128
Weaknesses of Static GAP
  • Market Value Effects
  • Basic repricing model the changes in market
    value. The PV of the future cash flows should
    change as the level of interest rates change.
    (ignores TVM)
  • Over aggregation
  • Repricing may occur at different times within the
    bucket (assets may be early and liabilities late
    within the time frame)
  • Many large banks look at daily buckets.

129
Weaknesses of Static GAP
  • Runoffs
  • Periodic payment of principal and interest that
    can be reinvested and is itself rate sensitive.
  • You can include runoff in your measure of rate
    sensitive assets and rate sensitive liabilities.
  • Note the amount of runoffs may be sensitive to
    rate changes also (prepayments on mortgages for
    example)

130
Weaknesses of GAP
  • Off Balance Sheet Activities
  • Basic GAP ignores changes in off balance sheet
    activities that may also be sensitive to changes
    in the level of interest rates.
  • Ignores changes in the level of demand deposits

131
Basic Duration Gap
  • Duration Gap

132
Basic DGAP
  • If the Basic DGAP is
  • If Rates h
  • i in the value of assets gt i in value of liab
  • Owners equity will decrease
  • If Rate i
  • h in the value of assets gt h in value of liab
  • Owners equity will increase

133
Basic DGAP
  • If the Basic DGAP is (-)
  • If Rates h
  • i in the value of assets lt i in value of liab
  • Owners equity will increase
  • If Rate i
  • h in the value of assets lt h in value of liab
  • Owners equity will decrease

134
Basic DGAP
  • Does that imply that if DA DL the financial
    institution has hedged its interest rate risk?
  • No, because the amount of assets gt amount of
    liabilities otherwise the institution would be
    insolvent.

135
DGAP
  • Let MVL market value of liabilities and MVA
    market value of assets
  • Then to immunize the balance sheet we can use the
    following identity

136
DGAP calculation
137
Hedging with DGAP
  • The net cash flows represented on the balance
    sheet have the same properties as a long position
    in a bond with a duration of 2.396201.
  • We can hedge using our equation from before and
    the duration of the interest rate swap.

138
Hedging with DGAP
  • Since the duration of our position is positive we
    want the duration of the hedge to be negative.
    This requires the pay fixed swap from before with
    a notional value equal to MVH below.
  • MVi(Di)MVH(DH) 0
  • 155,467,725(2.396201)(-5.151369)MVH0
  • MVH72,316,800

139
DGAP and owners equity
  • Let DMVE DMVA DMVL
  • We can find DMVA DMVL using duration
  • From our definition of duration

140

141
DGAP Analysis
  • If DGAP is ()
  • An h in rates will cause MVE to i
  • An i in rates will cause MVE to h
  • If DGAP is (-)
  • An h in rates will cause MVE to h
  • An i in rates will cause MVE to i
  • The closer DGAP is to zero the smaller the
    potential change in the market value of equity.

142
Weaknesses of DGAP
  • It is difficult to calculate duration accurately
    (especially accounting for options)
  • Each CF needs to be discounted at a distinct rate
    can use the forward rates from treasury spot
    curve
  • Must continually monitor and adjust duration
  • It is difficult to measure duration for non
    interest earning assets.

143
More General Problems
  • Interest rate forecasts are often wrong
  • To be effective management must beat the ability
    of the market to forecast rates
  • Varying GAP and DGAP can come at the expense of
    yield
  • Offer a range of products, customers may not
    prefer the ones that help GAP or DGAP Need to
    offer more attractive yields to entice this
    decreases profitability.

144
Changing Duration
  • You can also manipulate the duration of your cash
    flows. This allows you to lower your interest
    rate sensitivity instead of eliminating it.
  • Let DG be the desired duration gap, DG be the
    current duration gap, DS be the duration of the
    Swap, and MVH be the notional value of required
    for the swap.

145
Decreasing Duration GAP to One year
  • The negative sign just indicate that we need a
    pay fixed swap (the duration would then be
    negative making the MV positive)
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