Fixed Income Securities - Fundamentals of Swaps

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					Module-I

                 Part-VI-A
           Fundamentals of Swaps




2/8/2012          Prof. Rushen Chahal
Introduction
   What is a swap?
          It is basically an exchange of two payment
           streams that are different from each other.
   Why do parties enter into a swap?
          To acquire one stream of payments and to
           dispose off another stream.



2/8/2012                 Prof. Rushen Chahal
Introduction (Cont…)
   What is an interest rate swap?
          It is a contract where two counterparties
           commit themselves to exchange, over an
           agreed time period, two streams of
           payments, each calculated using a different
           type of interest rate, but with the same
           notional principal.



2/8/2012                 Prof. Rushen Chahal
Introduction (Cont…)
   Are there other types of swaps?
   Yes
          In the case of a currency swap the two
           streams of payment are denominated in
           different currencies.
          In an equity swap one stream is calculated
           based on an equity price.
          In a commodity swap one stream is
           calculated based on a commodity price.
2/8/2012                 Prof. Rushen Chahal
Illustration
   Citibank and HSBC agree to exchange
    over a period of two years, two streams
    of cash flows at six monthly intervals.
 Citibank will calculate its payments
    based on a fixed interest rate of 6% per
    annum.
 HSBC will calculate its payments based
    on the 6M LIBOR that is prevailing at
    the start of the six monthly period for
    which the payment is being computed.
2/8/2012            Prof. Rushen Chahal
Terms
   Counterparties: Citibank and HSBC
   Maturity: 2 Years
   Interest Rate (1): Fixed 6% per annum
    Citibank pays HSBC
   Frequency of payment: Semi-annual
   Interest Rate (2): 6M LIBOR
    HSBC pays Citibank
   Frequency of payment: Semi-annual
   Notional Principal: 100 MM USD
2/8/2012            Prof. Rushen Chahal
Illustration (Cont…)
   The interest rate is normally fixed at the
    start of the period to which it applies.
 But the payment calculated using this

    rate is made at the end of the period.
 This is what is meant by `determined in
    advance and paid in arrears.’
 We can also have a system of

    `determined in arrears and paid in
    arrears.’
2/8/2012            Prof. Rushen Chahal
       Summary of Cash Flows
Time          Days in    Fixed Rate Amount             LIBOR    Amount
              the 6M                payable                     payable
              interval              by                          by HSBC
                                    Citibank
0             -          6%          -                 5.75     -

6M            181        6%          2975343           6.125%   2851370

12M           184        6%          3024658           6%       3087671

18M           181        6%          2975343           5.5%     2975343

24M           184        -           3024658           -        2772603

TOTAL         -          -           12000000          -        11686987
       2/8/2012                  Prof. Rushen Chahal
Sample Calculations
   Cash Outflow for Citibank after 6
    months:
    0.06 x 100,000,000 x 181
                                 ------ =
    2,975,343
                                  365
 Cash Outflow for HSBC after 12
    months:
    0.06125 x 100,000,000 x 184
2/8/2012          Prof. Rushen Chahal
Notional Principal
   In the case of an interest rate swap
    only the interest is exchanged.
   There is no exchange of principal.
   The principal is specified purely for the
    computation of interest.
   Hence it is termed as a `notional
    principal’.

2/8/2012           Prof. Rushen Chahal
Off-Balance-Sheet
   Since the principal is not exchanged the
    swap does not impact the balance
    sheets of the counterparties.
   Hence interest rate swaps are referred
    to as off-balance-sheet transactions.




2/8/2012           Prof. Rushen Chahal
Netting
   In our illustration the counterparties
    were required to make payments to
    each other on the same date.
   Hence the payments are usually netted
    and only a single amount representing
    the difference is exchanged.


2/8/2012          Prof. Rushen Chahal
       Illustration
Settlement        Amount           Amount            Net Amount
Date              Payable by       Payable by        Payable by
                  Citibank         HSBC              Citibank
6M                2975343          2851370           123973

12M               3024658          3087671           -63013

18M               2975343          2975343           0

24 M              3024658          2772603           252055

                  12000000         11686987          313013
       2/8/2012                Prof. Rushen Chahal
Netting
   Netting of payments reduces the delivery risk.
   What is delivery risk?
   It is a default risk that can arise when an
    exchange of payments does not occur
    simultaneously.
   Thus a delay exposes the counterparty
    making the earlier payment to the risk that
    the other party may not honour its
    commitment.
2/8/2012             Prof. Rushen Chahal
Netting (Cont…)
   In order to facilitate netting, the
    frequency and timing of fixed rate
    payments will usually match the
    frequency and timing of the floating
    rate counter payments.




2/8/2012           Prof. Rushen Chahal
Frequency of Payments
   The frequency of the floating rate
    payments is usually set by the tenor of
    the benchmark rate that is used in the
    swap.
 Thus if 6M LIBOR is used as the
    benchmark then the payments will be
    made semi-annually, whereas if 3M
    LIBOR were to be used, the payments
                   quarterly.
    would be madeProf. Rushen Chahal
2/8/2012
Terms
   A swap agreement ought to contain the
    following details
          The names of the counterparties
          The maturity date of the swap
          The fixed interest rate
          The benchmark for the floating rate
          The notional principal amount
          And the frequency of payments
2/8/2012                 Prof. Rushen Chahal
Frequency of Payments
   In our illustration, both fixed as well as
    floating rate payments were made on a semi-
    annual basis.
          Such a swap is called a semi/semi.
          Longer term swaps can even be annual/semi.
   Short-term swaps can often be
    quarterly/quarterly.
   In some cases fixed payments are made
    annually and floating payments are received
    quarterly.
          These are called annual/threes swaps.

2/8/2012                   Prof. Rushen Chahal
Purpose of a Swap
   Let us consider the swap between
    Citibank and HSBC.
 What did it achieve?

 In the case of Citibank the fixed interest
    rate payments were known from the
    outset.
 But in the case of HSBC since LIBOR id
    variable, the cash outflows were subject
    to uncertainty, except for the first six
    months.
2/8/2012            Prof. Rushen Chahal
Purpose (Cont…)
   Citibank is paying fixed and receiving
    floating.
          Hence it is subject to the risk that the
           LIBOR will fall during the life of the Swap.
   HSBC is paying floating and receiving
    fixed.
          It is therefore exposed to the risk that the
           LIBOR will rise during the life of the swap.
2/8/2012                  Prof. Rushen Chahal
Purpose (Cont…)
   Thus an interest rate swap exposes
    both the counterparties to interest rate
    risk.
 Such swaps may therefore be used for

    speculation or for profiting from an
    expected interest rate change by
    deliberately taking risk.
 Or they may be used for hedging
    against another source of interest rate
2/8/2012            Prof. Rushen Chahal
Speculation
   Assume that Citibank is anticipating
    rates to rise whereas HSBC is expecting
    that rates will fall.
   Thus a swap which requires Citibank to
    pay fixed and HSBC to pay floating, can
    be used as a speculative mechanism by
    both the parties.

2/8/2012          Prof. Rushen Chahal
Hedging
   Assume that Citibank has already
    borrowed on a floating rate basis.
   It can use the swap with HSBC to
    hedge interest rate risk.
          If rates rise it will have to pay more
           interest on its original borrowings, but will
           receive a net cash inflow from the swap.


2/8/2012                  Prof. Rushen Chahal
Hedging (Cont…)
   Assume that HSBC has already made a
    loan on floating rate basis.
   If so it can use the swap to hedge.
   If interest rates were to fall it would
    receive less on its original investment
    but will receive a cash inflow from the
    swap.

2/8/2012           Prof. Rushen Chahal
Advantages
   Before swaps became available interest
    rate risk had to be managed using
    assets and liabilities in the form of cash
    instruments.
   For instance assume that a bank
    anticipates a fall in interest rates.
   It could make a medium term fixed rate
    loan and fund it by taking a series of
    consecutive short term deposits.
2/8/2012           Prof. Rushen Chahal
Advantages (Cont…)
   For instance if it were to rollover a
    series of short term deposits, it would
    be
    effectively borrowing at a floating rate
    and lending at a fixed rate.
 If rates were to fall as expected it

    would pay a lower rate of interest on its
    deposits would continue to receive a
                                  from
    fixed rate of interest Chahal its loan.
2/8/2012             Prof. Rushen
Advantages (Cont…)
   An interest rate swap where the bank
    receives fixed and pays floating can be
    used to achieve the same result.
   The swap would yield the same profit
    would there would be no transfer f
    principal and consequently no impact
    on the balance sheet.

2/8/2012           Prof. Rushen Chahal
Advantages (Cont…)
   Since a swap is an off-balance-sheet
    transaction as opposed to the
    alternative entailing the use of assets
    and liabilities, it offers several
    advantages.
          There is less credit risk.
               Only interest payments are at risk whereas in
                the case of assets and liabilities the full
                principal is at risk.
2/8/2012                     Prof. Rushen Chahal
Advantages (Cont…)
          Swaps are subject to lower capital
           adequacy requirements because they
           involve less credit risk.
          Swaps involve lower transaction costs
           because less money is being transferred
           and funded.
          They offer greater flexibility.



2/8/2012                 Prof. Rushen Chahal
Types of Interest Rate Swaps
   Coupon swaps
       What we have just seen is a coupon swap.
       It entails the exchange of a payment based on a
        fixed rate in return for a payment based on a
        floating rate.
   Basis swaps
        In these swaps both streams of payment are
         calculated using a floating rate index.
      For instance one stream could be based on the

         LIBOR whereas the other could be based on the
2/8/2012
         prevailing commercial paper rate.
                          Prof. Rushen Chahal
Types (Cont…)
          Asset swaps
              If one of the payment streams is funded with
               interest received from an asset, the swap and
               the asset as a whole are called an asset swap.
              There is no change in the swap mechanism per
               se.
              Strictly speaking we could also have liability
               swaps.
              But this term is rarely used.
              Thus swaps used in conjunction with a liability
               are merely referred to as interest rate swaps.
2/8/2012                     Prof. Rushen Chahal
Types (Cont…)
          Term swap
              A swap with an original maturity of more than
               two years is called a term swap.
          Money market swap
              A swap with an original maturity of up to one
               year is called a money market swap.
          Currency swap
              It is a swap where each stream on interest is
               denominated in a different currency.
              These swaps also involve an exchange of
               principal.
2/8/2012                     Prof. Rushen Chahal
Terminology
   The counterparties to a swap are called
    payers or receivers.
 In the case of a coupon swap, the party
    paying on a fixed rate basis is said to be
    the `payer in the swap’ and the other
    counterparty is the `receiver in the
    swap’.
 In the case of a basis swap we cannot
    use this convention since both the cash
                   Prof. based
    flow streams are Rushen Chahal on floating
2/8/2012
Terminology (Cont…)
   Thus it is a god practice in the case of
    basis swaps to describe each
    counterparty in terms of both the rate it
    pays as well as the rate it receives.
   In the inter-bank swap market the
    terms buyer and seller are used in the
    case of coupon swaps.
          Buyers are payers and sellers are receivers.
2/8/2012                 Prof. Rushen Chahal
Terminology (Cont…)
   In most coupon swaps the 6M LIBOR is the
    standard index for the floating rate.
   Thus these swaps can be defined purely in
    terms of the fixed rate of interest.
   For example in the case of the Citibank-HSBC
    swap, the price of the swap would have been
    quoted as 6% per annum, which is nothing
    but the fixed rate.
   The price of a coupon swap is also called the
    swap rate.
2/8/2012             Prof. Rushen Chahal
Terminology (Cont…)
   In most markets swap rates are quoted as
    full percentage figures.
   Example in our case the rate was 6%.
   This is called an all-in price.
   However in certain inter-bank swap markets,
    particularly the US dollar market, the
    convention of quoting the price on an all-in
    basis has been replaced by the convention of
    quoting the differential between the all-in
    rate and an accepted benchmark rate.
2/8/2012            Prof. Rushen Chahal
Terminology (Cont…)
   The benchmark rate is usually the rate on the
    government bond with a remaining period to
    maturity closest to that of the swap.
 The difference between the all-in price and
    the benchmark rate is called the swap
    spread..
 For instance assume that the all-in price is
    5.5% for a 5 year swap and that 5 year T-
    notes are yielding 5.3% per annum.
 The swap price will be quoted as 20 basis
    points.
2/8/2012              Prof. Rushen Chahal
Terminology (Cont…)
   The trade date or the fixing date is the date
    on which the terms are agreed upon.
          The following terms have to be agreed upon
               The maturity
               The swap rate
               The floating rate index
               The payment frequency
               The notional principal
   On this date the counterparties contractually
    commit themselves to the transaction.
2/8/2012                        Prof. Rushen Chahal
Terminology (Cont…)
   The value date is the date on which the
    interest payments start to accrue.
   For swaps involving only the domestic
    currency the value date is usually the
    same as the trade date.
   For foreign currency swaps the value
    date is usually two days after the trade
    date.
2/8/2012           Prof. Rushen Chahal
Terminology (Cont…)
   The date on which the floating rate is re-fixed
    for the next period is called
          The re-fixing or re-pricing or reset date.
   The date on which the interest is paid for the
    preceding period is called the effective date.
   The effective dates are calculated from the
    value date.
          For domestic currency swaps the effective dates
           are the same as the re-fixing dates.
          For currency swaps the effective date is two
           business days after the re-fixing date.
2/8/2012                     Prof. Rushen Chahal
Swaps versus Other
Derivatives
   Swaps are traded on a bilateral basis in
    decentralized markets.
 Thus swaps are OTC instruments.

 In contrast futures contracts and listed

    options are exchange traded
    instruments.
 On an exchange the clearinghouse

    becomes the buyer for every seller and
    the seller for every buyer.
2/8/2012            Prof. Rushen Chahal
Swaps vs. Others (Cont…)
   Both the parties have to provide daily
    collateral called margins.
 The role of the clearinghouse and the

    margining mechanism minimizes the
    risk of default.
 In OTC markets there is no

    clearinghouse, and margining is not
    compulsory.
 So
2/8/2012 default risk is a major concern.
                      Prof. Rushen Chahal
Swaps vs. Others (Cont…)
   Futures contracts and listed options are
    standardized instruments.
   Standardization reduces transactions costs
    and provides greater liquidity.
   OTC contracts are however customized.
   Activity in exchange traded products is limited
    to certain instruments.
   However OTC products like swaps are
    available for any currency and for any tenor
    provided a counterparty can be found.
2/8/2012             Prof. Rushen Chahal
Swaps vs. Others (Cont…)
   Futures and listed options are usually
    available only for short to medium
    terms.
   Swaps on the other hand can extend as
    far as 20 years into the future.




2/8/2012          Prof. Rushen Chahal
Trading Swaps
   The swap market is an OTC market.
   Trading is conducted primarily by
    telephone.
   Indicative prices are disseminated over
    screen services by agencies like
    Reuters.


2/8/2012           Prof. Rushen Chahal
Negotiations
   Key financial details are agreed verbally
    between dealers.
   Key details are then confirmed y an
    exchange of telexes or faxes within 24
    hours.
   Full contract documentation is agreed,
    signed, and exchanged subsequently.

2/8/2012           Prof. Rushen Chahal
Negotiations (Cont…)
   Because of the delay is documentation,
    swaps are sometimes said to be dealt
    on an as of basis.
   However a contract is assumed to be
    struck based on the initial verbal
    agreement between dealers without
    waiting for the exchange of
    confirmations or documentation.
2/8/2012          Prof. Rushen Chahal
Negotiations (Cont…)
   In the case of coupon swaps which are
    quoted in terms of a spread over a
    benchmark yield, the dealers will agree on
    the spread first.
 They will then break of negotiations to check

    whether they have credit lines to each other.
 If there are no credit problems they will
    resume negotiations and agree on the
    benchmark yield.
 The spread will be added to the benchmark
2/8/2012              Prof. Rushen Chahal
        Illustration of All-in Prices
   New Zealand Dollar Swaps

            Maturity              Semi-annual Rate
            1 year                8.00-7.85
            2 years               8.25-8.05
            3 years               8.50-8.30
            4 years               8.85-8.65
            5 years               9.05-8.85
            7 years               9.25-9.05
        2/8/2012       Prof. Rushen Chahal
    Illustration of Swap Spreads
US Dollars     Spread                        Annual Interest
                                             A/360
2 years        21/25                         5.70-5.75

3 years        40/45                         6.23-6.28

5 years        46/51                         7.01-7.05

7 years        46/51                         7.46-7.51

10 years       47/52                         7.93-7.97
    2/8/2012           Prof. Rushen Chahal
Two-way Prices
   As can be seen, two swap rates are
    quoted for each maturity.
 Such prices are quoted between

    professional dealers and consist of a
    buying and selling price for the
    instrument.
 However the terms buying and selling

    can be ambiguous in the case of swaps.
 So                Prof. Rushen paying and
2/8/2012 we use the terms Chahal
Two-way Prices (Cont…)
   When you have two prices, which is
    being paid and which is received?
 The logic is that the dealer hopes to

    make a profit if he undertakes a fixed-
    floating swap with one party and a
    floating-fixed swap with the other.
 Thus he would like to pay the lower

    fixed rate and receive the higher fixed
    rate.
2/8/2012            Prof. Rushen Chahal
Two-way Prices (Cont…)
   For instance the all-in prices for the 5
    year NZ Dollar swap is 9.05-8.85.
   Thus the dealer will demand 9.05% if
    he is receiving the fixed rate and will
    part with 8.85%if he is paying the fixed
    rate.


2/8/2012           Prof. Rushen Chahal
Two-way Prices (Cont…)
   What about quotations in terms of spreads?
   For instance a 5 year USD swap is quoted as
    46/51.
   This means that when the dealer is paying
    fixed he will give 46 basis points over the
    yield on the most liquid 5 year T-note.
   If he is receiving fixed he will demand 51
    basis points over the 5 year T-note yield.
   The equivalent all-in rates are 7.01% and
    7.05%.
2/8/2012            Prof. Rushen Chahal
Swap Documentation
   What is a contract?
   It is evidence of an agreement between
    the counterparties to a transaction.
   It should provide a detailed definition of
    a transaction in respect of:
   Financial terms and conditions
          That is the rights that the parties enjoy or
           the obligations that they have accepted.
2/8/2012                  Prof. Rushen Chahal
Documentation (Cont…)
   The legal framework should be spelt
    out.
          What are the rights of enforcement
           according to law if there is a default by a
           counterparty.
          In this context the definition of default
           must be clearly spelt out
          The methods of computing damages
           should be clearly stated
2/8/2012                  Prof. Rushen Chahal
Documentation (Cont…)
   In the early days, swap documentation
    was extremely complex because the
    instrument was new and there was a
    need to provide adequate financial and
    legal definitions.
   There was a lack of legal precedent and
    little in the way of `custom and usage’.
   Contracts therefore contained extensive
    legal opinion.
2/8/2012           Prof. Rushen Chahal
Documentation (Cont…)
   Contracts were long winded and often
    took months to finalize.
 An attempt has been made

    subsequently to standardize the
    documentation.
 Initial efforts were on a bilateral basis

    between active market players.
 Subsequently multilateral initiatives
                   by market
    were launched Prof. Rushen Chahal associations.
2/8/2012
Documentation (Cont…)
   The two principal multilateral initiatives
    have originated from:
   The British Bankers’ Association (BBA)
   The International Swap Dealers’
    Association (ISDA)



2/8/2012            Prof. Rushen Chahal
BBA Documentation
   In 1985 the BBA promulgated its
    BBAIRS Terms or the Recommended
    Terms and Conditions for London
    Interbank Interest Rate Swaps
   They were intended to apply to money
    market swaps traded interbank in
    London.

2/8/2012         Prof. Rushen Chahal
BBA Documentation (Cont…)
   They provided the following:
          Financial terms and conditions
          Sample confirmations
          Rights of enforcement in the event of default
   In addition to the documentation, the BBAIRS Terms
    also set out conventions for conducting negotiations.
   These terms have now been largely superseded by
    the more comprehensive documentation drafted by
    ISDA.
   But the mechanism for fixing LIBOR which was
    devised as a part of BBAIRS Terms continues to play
    a central role in the settlement of swaps.
2/8/2012                       Prof. Rushen Chahal
BBAIRS Interest Settlement Rate
   The BBA arranged for Telerate to
    calculate and publish on a daily basis a
    list of BBAIRS Interest Settlement Rates
    for each monthly maturity between one
    and twelve months for 9 currencies.




2/8/2012           Prof. Rushen Chahal
ISDA Documentation
   In 1985 ISDA published a Code of
    Standard Wording, Assumptions and
    Provisions for Swaps known as the
    ISDA Swaps Code.
   This was a menu from which
    counterparties could draw when
    drafting a contract for US Dollar swaps.

2/8/2012           Prof. Rushen Chahal
ISDA Documentation (Cont…)
   The Code dealt mainly with financial
    terms and conditions such as calculation
    of interest and termination payments.
   It was subsequently revised and
    expanded to address rights of
    enforcement and credit provisions.


2/8/2012          Prof. Rushen Chahal
ISDA Documentation (Cont…)
   In 1987 ISDA published two master
    contracts.
        For USD interest rate swaps – The Interest
         Rate Swap Agreement (Rate Swap Master
         Agreement)
      For interest rate and currency swaps in or

         between a variety of currencies – the
         Interest Rate and Currency Exchange
         Agreement (Rate and Currency Swap
2/8/2012 Master agreement)
                        Prof. Rushen Chahal
ISDA Documentation (Cont…)
   Once an ISDA Master Contract is in
    place between two counterparties, the
    details of new swaps are simply added
    as appendices.
   Thus there will always be a single
    contract in place between two
    counterparties regardless of the number
    of swaps transacted.
2/8/2012          Prof. Rushen Chahal
ISDA Documentation (Cont…)
   A master agreement is designed to net
    the profits and losses being made on all
    the swaps outstanding between the
    same two counterparties.




2/8/2012           Prof. Rushen Chahal
The Primary Market: The Role of
Banks
   In the early days of the swap market,
    the intermediaries were investment
    banks with fairly limited resources.
 They tried to avoid exposure to default
    risk by assuming the role of an agent
    rather than a principal in swap
    transactions.
 Hence they merely helped arrange such
    transactions between the
                    for which
    counterparties,Prof. Rushen Chahal they were
2/8/2012
2/8/2012   Prof. Rushen Chahal
The Role of Banks (Cont…)
   As the market developed it became
    necessary for swap intermediaries to
    assume the role of principals.
   There were two reasons for this.
          End users desired anonymity
          Secondly they were reluctant to deal with
           non-bank counterparties because of the
           default risk.
2/8/2012                 Prof. Rushen Chahal
The Role of Banks (Cont…)
   Intermediaries initially began to
    maintain matched books.
   That is, they would arrange a swap only
    if there was a more or less equal and
    opposite swap that was immediately
    available as a hedge.
   Such a matching swap is known as a
    reversal.
2/8/2012          Prof. Rushen Chahal
The Role of Banks (Cont…)
   While running a matched book, the
    intermediary is exposed to default risk
    from both sides.
   Consequently they would charge a risk-
    related dealing spread in the form of a
    difference between the fixed interest
    rate paid to one user and that received
    from the other user.
2/8/2012          Prof. Rushen Chahal
The Role of Banks (Cont…)
   Due to competition, arrangement fees
    have become rare unless the swap
    structure is unusual and complex.
   Swaps have now become an active tool
    for asset-liability management.
   Intermediaries have now become
    market makers, that is, they provide
    continuous two-way quotes.
2/8/2012         Prof. Rushen Chahal
The Role of Banks (Cont…)
   Such market makers stand ready to
    accept temporary exposures to a
    position, until they are able to find a
    matching swap.




2/8/2012            Prof. Rushen Chahal
The Role of Brokers
   Dealers often trade in swaps through brokers.
   These brokers act as agents in locating a
    counterparty.
   But they do not actually participate in the
    transaction.
   In practice brokers continuously take prices
    from customers, and then select and
    broadcast the cheapest selling price and the
    highest buying price for each maturity.
2/8/2012            Prof. Rushen Chahal
The Role of Brokers (Cont…)
   The series of two-way prices broadcast
    by brokers back to the customers is
    called a Broker’s Run.
 If a customer were to accept one of the

    prices the broker will pass on the
    identity of the customer who originated
    the price.
 For this reason swap brokers are known
    as              Prof. brokers.
2/8/2012 Name-Passing Rushen Chahal
The Role of Brokers (Cont…)
   Brokers are paid a flat fee or brokerage
    commission which is related to the size
    of the deal (the notional principal) and
    maturity.
 Typical brokerage fees are flat basis
    points per annum from each
    counterparty.
 Brokerage is paid upfront in the form of
    the present value of the basis points
    earned over the life of the swap.
2/8/2012            Prof. Rushen Chahal
Forward Rate Agreements
   An FRA is noting but a forward contract
    on an interest rate.
   In the case of derivatives on debt
    instruments the payoff is determined by
    the price of the instrument and is
    consequently indirectly determined by
    the underlying interest rate.
   In contrast the payoff from a FRA is
    directly determined by the interest rate.
2/8/2012           Prof. Rushen Chahal
FRA (Cont…)
   The agreement would have to specify a
    notional principal and the terms on
    which the payment is to be made.
   Typically, the payoff is based on the
    LIBOR.
   The payoff is based on the difference
    between the prevailing value of LIBOR
    and the contract rate which was agreed
    upon at the outset.
2/8/2012          Prof. Rushen Chahal
FRA (Cont…)
   The method of computing interest is not
    standard.
 In some cases the year is assumed to have
    360 days.
 In other cases it is assumed to have 365
    days.
 The number of days for which the interest is
    computed is sometimes taken to be the
    actual number of days.
 In other cases it is computed assuming that
                     30 days.
    every month has Prof. Rushen Chahal
2/8/2012
Illustration
   A company wants to lock in a borrowing
    rate for a loan that it will take after 30
    days.
   The loan will be for a period of 90 days.
   The applicable rate will be the LIBOR
    prevailing after 30 days plus 1%.
   The year is assumed to have 360 days.

2/8/2012           Prof. Rushen Chahal
Illustration (Cont…)
   The company would like to protect itself
    against rising rates.
   Hence it would like a positive payoff
    from the FRA if rates were to rise.
   Hence it would need a long position in
    the FRA.
   Assume that the company agrees on a
    fixed rate of 10% for the FRA.
2/8/2012          Prof. Rushen Chahal
Illustration (Cont…)
   The payoff from the FRA would be:
   Notional Principal x (LIBOR – 0.10) x
    90

    ____

    360
 So if the LIBOR after 30 days were to

    exceed 10% the company would
2/8/2012         Prof. Rushen Chahal
Illustration (Cont…)
   Assume that the FRA is structured so
    that the payment will be made 120 days
    from today so as to coincide with the
    payment on the loan.
   The notional principal is 20 MM USD.




2/8/2012          Prof. Rushen Chahal
        Possible Scenarios
LIBOR          Payoff from Interest on   Total             Annualized   Annualized
               FRA         Loan          Effective         Cost with    Cost
                                         Interest          FRA          without
                                                                        FRA
6.00%          -200,000    350,000       550,000           11.63        7.29

8%             -100,000    450,000       550,000           11.63        9.44

10%            0           550,000       550,000           11.63        11.63

12%            100,000     650,000       550,000           11.63        13.85

14%            200,000     750,000       550,000           11.63        16.10

        2/8/2012                     Prof. Rushen Chahal
Sample Calculation
   LIBOR = 12%
   Payoff from FRA:
    20,000,000 x (0.12-0.10) x 90
                              ____
                               360
    = 100,000


2/8/2012          Prof. Rushen Chahal
Sample Calculation (Cont…)
 Interest due on loan:
  20,000,000 x 0.13 x 90
                       _____
                        360
= 650,000
 Effective interest paid = 650,000 –

  100,000 = 550,000
2/8/2012         Prof. Rushen Chahal
Sample Calculation (Cont…)
   Annualized Interest:
     20,000,000 + 550,000
( ___________________)365/90 – 1 =
    .1163
         20,000,000
 Annualized interest without the FRA:

   20,000,000 + 650,000
( __________________)365/90 – 1 = .1385
2/8/2012 20,000,000 Prof. Rushen Chahal
Illustration (Cont…)
   Regardless of the LIBOR after 90 days
    the cost of the loan with the FRA is
    11.63%.
   Without the FRA the cost of the loan
    will vary directly with the LIBOR.
   Thus the loan plus the FRA is essentially
    a risk free transaction.

2/8/2012           Prof. Rushen Chahal
Valuing a FRA
   To value a FRA we need to specify as to
    how the interest rate is expected to
    evolve over time.
 We will specify a binomial model for the
    evolution of the interest rate through
    time.
 That is given a particular rate, the next
    period the rate could either go up by a
    pre-specified factor, or down by a pre-
    specified factor. Rushen Chahal
2/8/2012            Prof.
A Binomial Tree                                16.45


                                   14.95

                  13.47                        13.06

                                     11.60
           12
                    10.17                        9.76

                                       8.35
    10.5
           8.74

                     6.96                        6.57
                                        5.20

                                                   3.46

2/8/2012              Prof. Rushen Chahal
A Binomial Tree (Cont…)
   At every stage the probability of an up
    move is 0.52 and that of a down move
    is 0.48.




2/8/2012           Prof. Rushen Chahal
Pricing a FRA
   An interest rate FRA that pays off at the
    expiration of the contract is said to payoff in
    arrears.
   In the earlier illustration we assumed that the
    FRA expired after 30 days but that the payoff
    was received after 120 days so as to coincide
    with the payment of interest on the loan.
   These are called delayed settlement FRAs.

2/8/2012             Prof. Rushen Chahal
A One Period In Arrears FRA
   The fixed interest rate should be such
    that the FRA has a zero value today
    since neither party has to pay to get
    into a FRA.
   So the if we set the expected payoff
    from the FRA equal to zero:
   .52(.12-k) + .48(.0874-k) = 0
    k = .1044
2/8/2012           Prof. Rushen Chahal
A Two-Period in Arrears FRA
   .52x.52x(.1347-k)+2X.52x.48x(.1017-k)
    + .48x.48x(.0696-k) = 0
    K = 0.1032




2/8/2012         Prof. Rushen Chahal
A Delayed Settlement One-
Period FRA
   In this case the payoff from the FRA is one
    period after its time of expiration.
   Thus all cash flows have to be discounted for
    one period at the applicable rate.
   So:
   .52(.12-k)       .48x(.0874-k)
   ________ + ____________ = 0k = .1041
       1.12               1.0874

2/8/2012             Prof. Rushen Chahal
A Delayed Settlement Two-
Period FRA
 .52x.52x(.1347-k) 2x.52x.48(.1017-k)
  _______________ + _______________
     1.1347            1.1017
 + .48x.48x(.0696-K)
    _______________ = 0 k =.1027
     (1.0696)


2/8/2012       Prof. Rushen Chahal

				
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