Products and Markets

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Products and Markets

• Financial Innovations and Product Design II

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Measuring Interest Rates

• Compounding m-times per annum (annual,
  semiannual, quarterly etc.)
• Continuous compounding

mn
R m
A 1
eRn
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Measuring Interest Rates

• Conversion formulas
• Rc continuously compounded rate
• Rm same rate with compounding m times per year

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Interest Rate Markets

• Types of rates
• Treasury Rate
• Applicable to borrowing by a government in its
  own currency
• LIBOR
• London InterBank Offer Rate
• Interest rates charged in trading between banks
• Repo Rate
• Sale and repurchase at a slightly higher price
• Most common overnight repos

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Interest Rate Markets

• Zero Rates
• Zero-coupon rate
• The n-year ZR is the rate of interest earned on
  an investment that starts today and lasts for n
  years with no cash flows in between
• Also referred to as the n-year spot rate

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Interest Rate Markets

• Bond pricing

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Interest Rate Markets

• Bond pricing
• Using zero rates
• Using bond yields
• Bond yields are bond specific!

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Interest Rate Markets

• Par Yield
• The par yield for a certain maturity is the
  coupon rate that causes the bond price to equal
  its face value
• Example using zero rates from the previous
  example solves

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Interest Rate Markets

• Bootstrap Method
• A method to extract the zero rates from prices of
  instruments that trade

Bond
Time to
Annual
Bond
Principal
Maturity
Coupon
Price
(dollars)
(years)
(dollars)
(dollars)
Zero rates
Three-month Six-month 1 year
10,127 10,469 10,536
100
0.25
0
97.5
100
0.50
0
94.9
100
1.00
0
90.0
100
1.50
8
96.0
100
2.00
12
101.6
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Interest Rate Markets

• Bootstrap Method
• 1,5 year zero rate?
• Solution yields R 10,681
• Calculation of the 2 year zero rate is similar, R
  10,808

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Interest Rate Markets

• Forward rates
• Future zero rates implied by the current term
  structure of interest rates

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Interest Rate Markets

• Forward rates
• Future zero rates implied by the current term
  structure of interest rates

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Interest Rate Markets

• Forward rate agreement
• OTC agreement that a certain interest rate will
  apply to a certain principal during a specified
  future period of time

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Interest Rate Markets

• Term structure theories
• What determines the shape of the zero curve?
• Expectations theory long-term interest rates
  reflect expected future short-term interest rates
• Segmentation theory no relationship between
  short-, medium- and long-term interest rates
• Liquidity preference theory forward rates should
  always be higher than expected future zero rates

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Interest Rate Markets

• Day count conventions
• Define the way interest accrues over time
• Interest earned between two dates
• Actual/actual used for Treasury bonds
• 30/360 used for corporate and municipal bonds
• Actual/360 used for T-bills and other money
  market instruments

Number of days between dates Number of days in
reference period
x Interest earned in reference period
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Interest Rate Markets

• Quotations
• Bonds
• Quoted price is for a bond with a face value of
  100
• Quoted in dollars and thirty-seconds of a dollar
• Example
• quoted price 90-05 90 5/32 90,15625
• The price paid by the purchaser cash price
• Cash price Quoted price Accrued interest
  since last coupon date

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Interest Rate Markets

• Quotations
• Treasury Bills
• If Y is the cash price of a T-Bill that has n
  days to maturity, the quoted price (discount
  rate) is
• This discount rate is not the same as the rate of
  return earned on the T-Bill dollar return/cost

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Interest Rate Markets

• Treasury bond futures
• Long-term interest rate futures contract
• Any government bond that has more than 15 years
  to maturity on the first day of the delivery
  month and that is not callable within 15 years
  from that day can be delivered.
• Because any bond that satisfies the conditions
  can be delivered, a parameter called conversion
  factor is applied to obtain the price received
  by the party with the short position.

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Interest Rate Markets

• Treasury bond futures
• The cash received then equals
• Conversion factor
• It is approximately equal to the value of the
  bond on the assumption that the yield curve is
  flat at 6 with semiannual compounding
• Cheapest-to-deliver bond
• Since many bonds can be delivered, the CTD bond
  will be the one that ensured that following
  quation is minimized

(Quoted futures price x Conversion factor)
Accrued interest
Quoted price (Quoted futures price x Conversion
factor)
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Interest Rate Markets

• Treasury bond futures
• Wild card play
• Taking advantage of different trading times in
  the T-bond futures market and the T-bond spot
  market.

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Interest Rate Markets

• Eurodollar futures
• Eurodollar a dollar deposited in a U.S. or
  foreign bank outside the U.S.
• Eurodollar interest rate the rate earned on
  Eurodollars deposited by one bank with another
  bank
• Three-month ED futures contracts are futures on
  the three-month ED interest rate, they have
  maturities in March, June, Sept., Dec. For up to
  10 years in the future.

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Interest Rate Markets

• Eurodollar futures
• If Q is the quoted price for a EDF contract, the
  value of the contract is given by
• Q is set so that on delivery day Q 1 R, where
  R is the 3 month ED interest rate on that day.

10.000100 0,25(100 Q)
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Interest Rate Markets

• Duration
• A measure of how long on average the holder of a
  bond has to wait before receiving cash payments.
• The duration can be used to estimate bond price
  changes as a result of yield changes

B bond price y yield
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Interest Rate Markets

• Duration
• When y is expressed with compounding m times per
  year, the Modified duration should be used
• Duration of a portfolio weighted average of the
  durations of the individual bonds in the
  portfolio, with the weights being proportional to
  the bond prices

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Interest Rate Markets

• Duration
• Hedging using duration
• Hedging against interest rate risk by matching
  the durations of assets and liabilities

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Interest Rate Markets

• Duration
• Problems
• Hedging works only when there are parallel shifts
  in the yield curve
• Unaccurate for larger yield changes

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Interest Rate Markets

• Convexity
• Eliminates some of the unaccuracy caused by the
  duration when estimating price changes resulting
  from larger yield changes

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Swaps

• Swap
• An agreement between two companies to exchange
  cash flows at specified future times according to
  specified rules

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Swaps

• Interest rate swap
• One company agrees to pay cash flows equal to
  interest at a predetermined fixed rate on a
  notional principal and in return receives
  interest at a floating rate on the same notional
  principal
• The notional principal itself is not exchanged
• Plain vanilla swap

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Swaps

• Interest rate swap
• Assets and liabilities can be converted from
  fixed rate to floating rate vice versa
• Trasforming a liability (example)
• Microsoft borrows at LIBOR 10 bps
• Intel borrows at 5,2 fixed
• Microsoft Intel enter into a swap
• Microsoft pays 5 and receives LIBOR
• Intel pays LIBOR and receives 5

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Swaps

• Interest rate swap
• Trasforming a liability
• Result
• Intel pays LIBOR 20bps
• Microsoft pays 5,1 fixed

5
5.2
Intel
MS
LIBOR0.1
LIBOR
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Swaps

• Interest rate swap
• Financial intermediary
• Usually two nonfinancial companies do not get in
  touch directly to arrange a swap deal each deal
  with a financial intermediary (FI)
• The FI enters into two offsetting swap
  transactions with the two companies and earns
  about 3-4bps
• Because the FI has two separate contracts, it
  bears the default risk of one of the companies in
  the swap and still has to honor the remaining
  contract

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Swaps

• Interest rate swap
• Financial intermediary
• Large FIs act as market makers, i.e. they are
  prepared to enter into a swap without an
  offsetting swap with another counterparty
• Result
• Microsoft pays 5,115
• Intel pays LIBOR 21,5bps
• The FI earns 3bps

4.985
5.015
5.2
F.I.
Intel
MS
LIBOR0.1
LIBOR
LIBOR
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Swaps

• Interest rate swap
• Why are swaps so popular?
• Comparative advantage argument some companies
  have a comparative advantage in floating rate
  markets whereas others have a comparative
  advantage in fixed rate markets

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Swaps

• Interest rate swap
• Why are swaps so popular?
• Result
• AAA now pays LIBOR 5bps (compared to LIBOR
  30bps)
• BBB now pays 10,95 fixed (compared to 11,2)

9.95
10
AAA
BBB
LIBOR1
LIBOR
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Swaps

• Interest rate swap
• Criticism of the comparative advantage argument
• The fixed rate remains the same throughout the
  life of the swap whereas the floating rate is
  reset at constant intervals
• This creates a problem to the company that
  transforms its floating rate obligation into a
  fixed rate
• The amount fixed rate interest paid depends on
  the way the original floating rate is reset, i.e.
  if BBB was downgraded to a lower credit rating
  this would be reflected in a higher floating rate
  and thus increasing the amount of interest BBB
  has to pay

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Swaps

• Interest rate swap
• Valuation using bonds
• The value of a swap can be characterized as the
  difference between two bonds one paying a fixed
  coupon and one paying a floating rate coupon
• The value of a swap to a company receiving
  floating and paying fixed is then

Vswap Bfl - Bfix
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Swaps

• Interest rate swap
• Valuation using bonds
• Value of a floating-rate bond?
• Immediately after payment date, Bfl principal
• Between payments
• k floating-rate payment that will be made on
  the next payment date
• L notional principal
• t1 time until the next payment date

-r1t1
Bfl (Lk)e
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Swaps

• Interest rate swap
• Swap rates the average of Bid and Offer rates
  quoted by market makers in the swap market
• Bid rate the fixed rate in a contract where the
  market maker will pay fixed and receive floating
• Offer rate the fixed rate in a contract where
  the market maker will pay floating and receive
  fixed
• Swap rates can be used to determine zero rates
• Consider a new swap where the fixed rate equals
  the swap rate, then we have

Bfl Bfix
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Swaps

• Interest rate swap
• Swap rates can be used to determine zero rates
• The floating-rate bond will be worth par
• Thus, the fixed-rate bond will be worth par as
  well the swap rate is the par yield of the
  fixed-rate bond
• As a result, zero rates can be extracted using
  the bootstrap method
• Swap rates are used to calculate the zero curve
  for longer maturities

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Swaps

• Currency swap
• In its simplest form it involves exchanging
  principal and interest payments in one currency
  for principal and interest payments in another
  currency
• The principal amounts are usually exchanged at
  the beginning and at the end of the swaps life

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Swaps

• Currency swap
• Example
• Swap between IBM and BP
• IBM pays a fixed rate of interest 11 in Pounds
  and receives a fixed rate of interest of 8 in
  dollars

IBMs cash flows
Dollars
Pounds


Year
------millions------
2001
15.00
10.00
1.20
2002
1.10
1.20
1.10
2003
2004
1.20
1.10
1.20
1.10
2005
2006
16.20
-11.10
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Swaps

• Currency swaps
• Valuation
• Using bonds if S0 is the exchange rate (number
  of domestic currency per unit of foreign
  currency), BD the value of the domestic bond, BF
  the value of the foreign bond (in foreign
  currency units), the value to the party receiving
  domestic currency and paying foreign currency is
• Using forwards the swap is decomposed into a
  series of forward contracts

Vswap BD S0BF
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Swaps

• Credit risk
• A swap is worth zero to a company initially
• At a future time its value is liable to be either
  positive or negative
• The company has credit risk exposure only when
  its value is positive
• While market risks can be hedged by entering into
  offsetting contracts, credit risks are less easy
  to hedge

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Thank You for Your Attention!