Commerce 4FJ3

1
Commerce 4FJ3

• Fixed Income Analysis
• Week 10
• Interest Rate Futures

2
Forward Contracts

• Any contract that legally binds two parties to
  engage in a specific transaction at some point in
  the future at a pre-specified price is a forward
  contract
• Can be negotiated individually
• Not usually transferable
• Subject to counterparty risk

3
Forward Payoff

• A forward contract does not have a direct payoff,
  the transaction that was negotiated takes place
• Implied payoff or cost the company has agreed to
  sell a bond forward for 1,160 and the bond is
  selling at 1,200 at the time of delivery, there
  is an opportunity cost of 40

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Futures

• Similar to a forward contract in the fact that it
  binds both parties to a specific transaction in
  the future but
• A futures contract is standardized with respect
  to the quantity, quality, time, and location
• Contracts are traded on organized exchanges
• No specific link between the buyer and seller
• Gains or losses are realized on a daily basis

5
Futures Trading

• When a futures contract is traded on an exchange
  the price is recorded as well as the identities
  of the two parties
• The link between buyer and seller is broken
• The buyer now has a contract to buy the asset
  from the clearinghouse and the seller has a
  contract to sell to the clearinghouse

6
Futures Trading

• If either party takes the opposite position later
  that position is netted against their previous
  contract and their position is reversed or closed
  out
• A trader that sells an asset is said to be short
  in that asset while a buyer is referred to as
  long in the asset

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Delivery

• If a contract is held to maturity (less than 1
  on average are), the clearinghouse matches buyers
  and sellers based on their stated preferences for
  delivery options and informs each party of the
  delivery details
• Often closed out before maturity to allow the
  investor to set their own details

8
Marking to Market

• To protect against the credit risk, futures
  contracts are marked to market at the end of each
  trading day
• This rewrites the contract so that the price is
  set to the settlement price and any gain or loss
  is paid in cash
• The settlement price is usually the closing price
  of that contract but may differ if a contract has
  very low volume

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Marking to Market Example

• You enter a futures contract to buy a bond issued
  by XYZ for 95.20/100 face value
• The settlement price is 95.00 (FV1,000)
• your contract is rewritten to buying at 95.00
• you must pay the difference of 2.00 to the
  clearinghouse
• The next day price rise to 95.75 you will be
  paid 7.50 by the clearinghouse

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Reason for Marking to Market

• Marking to market significantly reduces the
  counter-party risk (one party being unable or
  unwilling to fulfil their obligations)
• To be able to meet the marking to market
  requirements investors are required to maintain a
  margin account
• Margin requirements are typically 5-10

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Margins

• Initial margin how much you must deposit when
  you open a position
• Maintenance margin the lowest level that your
  margin account can fall to before you are
  required to deposit more
• Variation margin the amount that you must
  deposit within 24 hours or your position will be
  closed out

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Leverage

• Consider two investment options
• buy 1 bond for 1,000, cost 1,000
• enter futures contracts for 20,000 face value of
  those bonds, initial margin 1,000
• Return if price rises to 1,025
• 25 increase in market value 2.5 return
• 500 net marking to market 50 return

13
Use of Leverage

• Can be used by speculators
• Can be used to offset price risk
• A portfolio has a potential large loss if
  interest rates increase
• The portfolio can be rebalanced to reduce the
  price risk, at the cost of transaction costs
• Selling a few bond futures could generate large
  profits if interest rates increase

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Currently Traded Contracts

• A few of the most traded contracts are
• US T-Bill futures
• Eurodollar CD futures
• US treasury bond futures
• US treasury note futures
• US agency note futures
• CBOT 10-year municipal note index futures

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US T-Bill futures

• Traded on the International Money Market of the
  Chicago Mercantile Exchange (IMM)
• Underlying asset is a US T-bill with a face value
  of 1,000,000 and a maturity of 13 weeks
  (typically 91 days) from the delivery date
• The delivered T-bill can either be newly issued
  or seasoned
• Delivery dates are synchronized with regularly
  scheduled T-bill auctions

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Quoted Yields

• T-bills are quoted on the annualized yield on a
  bank discount basis

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T-Bill Futures Prices

• Quoted on an index basisindex price 100 - (Yd
  x 100)
• Given a current quote of 3.75 for T-bills index
  price 100 - (3.75) 96.25
• Given a futures price of 92.50 the yield is

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Invoice Price

• This is how much is paid for the t-bill if it is
  delivered
• Invoice price 1,000,000 - D
• Find the invoice price if the final settlement
  price is 92.50

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Price of a Basis Point

• The change in price of the underlying bond for a
  change of one basis point is
• 0.0001 x 1,000,000 x 91/360 25.28
• Market participants often refer to the value of a
  basis point as 25 in spite of the fact that the
  typical T-Bill has a maturity of 91 days

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Eurodollar CD Futures

• Traded on both the IMM of the Chicago Mercantile
  Exchange, and the London International Financial
  Futures Exchange
• Debt obligation tied to foreign banks instead of
  US treasury
• Discount is based LIBOR, London interbank offered
  rate

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Eurodollar Futures

• Also 1,000,000 face value and quoted on an index
  basis, but standardized at 90 days
• Value of a basis point 25
• Cash settlement contract, no delivery if held to
  maturity, parties settle in cash

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Treasury Bond Futures

• Underlying asset hypothetical 100,000 face
  value, 20-year, 6 coupon bond
• Physical settle The CME Group allows the seller
  to deliver one of several Treasury bonds that the
  CME Group declares is acceptable for delivery,
  with adjustments
• List is printed before trading begins

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Exhibit 26-1 Treasury Bonds Acceptable for
Delivery and Conversion Factors
Coupon Maturity Date Mar. 2011 Jun. 2011 Sep. 2011 Dec. 2011 Mar. 2012 Jun. 2012 Sep. 2012 Dec. 2012 Mar. 2013
6 3/4 08/15/26 1.0741 1.0735 ----- ----- ----- ----- ----- ----- -----
6 1/2 11/15/26 1.0500 1.0494 1.0490 ----- ----- ----- ----- ----- -----
6 5/8 02/15/27 1.0630 1.0625 1.0618 1.0613 ----- ----- ----- ----- -----
6 3/8 08/15/27 1.0385 1.0382 1.0377 1.0375 1.0370 1.0368 ----- ----- -----
6 1/8 11/15/27 1.0130 1.0127 1.0127 1.0125 1.0125 1.0123 1.0123 ----- -----
5 1/2 08/15/28 0.9466 0.9472 0.9475 0.9481 0.9485 0.9490 0.9494 0.9500 0.9504
5 1/4 11/15/28 0.9194 0.9200 0.9208 0.9213 0.9221 0.9227 0.9235 0.9242 0.9250
5 1/4 02/15/29 0.9187 0.9194 0.9200 0.9208 0.9213 0.9221 0.9227 0.9235 0.9242
6 1/8 08/15/29 1.0136 1.0136 1.0134 1.0134 1.0132 1.0132 1.0130 1.0130 1.0127
6 1/4 05/15/30 1.0281 1.0278 1.0277 1.0274 1.0273 1.0270 1.0269 1.0265 1.0264
5 3/8 02/15/31 0.9281 0.9287 0.9291 0.9297 0.9301 0.9307 0.9311 0.9318 0.9322
4 1/2 02/15/36 0.8078 0.8087 0.8095 0.8105 0.8113 0.8123 0.8132 0.8142 0.8151
4 3/4 02/15/37 ----- ----- ----- ----- 0.8398 0.8406 0.8413 0.8421 0.8427
5 02/15/37 ----- ----- ----- ----- ----- 0.8718 0.8725 0.8730 0.8737
4 3/8 02/15/38 ----- ----- ----- ----- ----- ----- ----- ----- 0.7918
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Treasury Bond Futures Details

• Price quoted per 100 of face value
• Price quoted in 1/3296-13 means (96 13/32)
  96.40625
• Invoice price Contract size (face value) x
  settlement price x conversion factor
  accrued interest

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Treasury Bond Delivery Example

• Settlement price 102-12
• Conversion factor of delivered bond 1.157
• Invoice price 100,000 x 102.375 x 1.157
  accrued interest 118,447.88 accrued
  interest
• The buyer does not know the exact price they have
  to pay until the bond is delivered

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Treasury Bond Delivery Options

• The seller has a few options when actually
  delivering the bond
• Quality option (swap option) can deliver one of
  the listed acceptable bonds
• Timing option can deliver on any day of the
  contract delivery month
• Wild card option notice of intent to deliver,
  must be given 1 day in advance, as late as 800
  p.m. Chicago time

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Cheapest to Deliver

• Given a choice sellers will want to figure out
  which issue is the cheapest to deliver
• Face value of issue is set at 100,000 but actual
  price is affected by conversion ratio
• Find implied repo rate
• Highest repo rate is the cheapest to deliver

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US Treasury Note Futures

• 2, 5, and 10 year maturity contracts
• Underlying asset 100,000 face value or 200,000
  for 2 year, 6 coupon rate
• Smaller basket of acceptable bonds available due
  to more restrictive definitions of an acceptable
  issue

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US Agency Note Futures

• Traded on CBOT and CME (2006)
• Underlying asset is 100,000 debenture from
  either Fannie Mae or Freddie Mac
• Both exchanges have 5 10 year maturities
• Coupon rate 6 on CBOT, 6.5 on CME

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Municipal Index Futures

• CBOT 10-year municipal note index futures
• Mentioned on page 596, 8th Edition
• Underlying asset a basket of up to 250 municipal
  bonds which meet certain rules, 10-40 years
  remaining maturity, coupon rate between 3 and
  9, etc.
• Cash settlement contract

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Pricing of Futures Contracts

• Theoretical model based on carry cost pricing and
  arbitrage arguments
• Tactic
• buy the underlying asset using borrowed funds
• enter a futures contract to fix the selling price
• sell at delivery date and repay the loan
• if money can be made, there will be excess demand
  for the bond and supply of the future

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Cash and Carry Trade Example

• 20-year, 12 coupon par bond, borrowing rate of
  8, futures price of 107 for delivery in 3
  months
• No cost to establish borrow to buy bond
• Invoice price 107 3 (accrued interest)
• Bank loan 100 2 (interest)
• Net profit 110 - 102 8 per 100 of face

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Theoretical Price

• Assuming short sales, we can also do the reverse,
  so we can get a theoretical price
• profit 0 proceeds - outlay
• F P(1 t(r - c))F futures price P Current
  bond pricet time to delivery r financing
  costc current yield on underlying bond
• (r - c) called cost of carry

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Theoretical Price Problems

• Interim cash flows from marking to market make
  the strategy risky
• Financing rate borrowing and lending rates may
  be different
• Multiple issues may be deliverable
• Delivery date unknown
• Underlying may be a basket of bonds, tracking
  error may result

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Adjusted Model

• The simple model may be adjusted to handle some
  of those problems
• P(1 t(rb - c)) F P(1 t(rl - c))to
  account for different rates
• F P(1 t(r - c)) - delivery optionsto account
  for delivery options

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Bond Portfolio Management

• The bond portfolio manager can use future
  contracts to
• Speculate on the movement of interest rates
• Control the interest risk of a portfolio
• Create synthetic securities for yield enhancement
• Create a temporary substitute for rebalancing or
  switching from bonds to stocks

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Controlling the Duration of a Portfolio

• Instead of rebalancing a manager can use futures
  to match duration
• The contract size and duration must be known to
  find the hedge ratio
• Dollar duration Duration x value of portfolio

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Hedging

• Hedging is nothing more than a special case of
  interest rate risk management where the target
  duration is zero
• In hedging an individual bond position with
  futures, the hedger is taking a futures position
  as a temporary substitute for transactions to be
  made in the cash market at a later date

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Hedging Risks

• The difference between the cash price and the
  futures price is the basis. The risk that the
  basis will change in an unpredictable way is
  called basis risk
• Typically, the bond to be hedged is not identical
  to the bond underlying the futures contract. This
  type of hedging is referred to as cross hedging

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Bonds vs. Stocks

• A pension fund manager wanting to change the
  allocation between stocks and bonds can
• Buy bonds and sell stocks
• Use interest-rate futures and stock index futures
• transactions costs are lower
• market impact costs are avoided or reduced
• activities of the portfolio managers employed by
  the pension fund manager are not disrupted