Techniques%20of%20asset/liability%20management:%20Futures,%20options,%20and%20swaps

1
Techniques of asset/liability management
Futures, options, and swaps

• Outline
• Financial futures
• Options
• Interest rate swaps

2

• Futures contract
• Standardized agreement to buy or sell a specified
  quantity of an asset on a specified date at a set
  price. Pricing and delivery occur at two points
  in time.
• Buyer is in a long position, and seller is in a
  short position. The buyer of the contract is to
  receive delivery of the good and pay for it,
  while the seller of the contract promises to
  deliver the good and receive payment. The
  payment price is determined at the initial time
  of the contract.

3

• Suppose you know that you will need 5,000 bushels
  of corn in one year and want to lock in the price
  of corn today.
• You (long position trader) find a seller (short
  position trader) who agrees to sell at 4/bushel
  (strike price) in one year(settlement or
  expiration date) .
• On expiration date, corn is selling for
  5/bushel. You would pay the previously
  agreed-upon 4/bushel for 5,000 bushels, 20,000,
  to the seller and the seller has to deliver the
  5,000 bushels of corn.
• Your gain is 5,000, which is equal to the
  sellers loss.

4

• Standardization tells traders exactly what is
  being traded and the conditions of the
  transactions Uniformity promotes market
  liquidity.
• Exchange clearinghouse is a counterparty to each
  contract. Default risk on futures (but not
  forward) contracts is minimized by the role of
  the exchange clearinghouse in all futures
  contracts. The exchange clearinghouse is, in
  effect, the counterparty in each transaction.
• Marked-to-market at the end of each day. Futures
  contracts are evaluated daily at their market
  values and gains or losses are added to or
  subtracted from the margin balance each day.

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• Margin Account (Stocks)
• Margin Account A brokerage account in which,
  subject to limits, securities can be bought and
  sold on credit.
• Margin Equity in account / Value of securities
• the portion of the value of an investment that is
  not borrowed.
• Initial Margin the minimum margin that must be
  supplied on a security purchase. Initial margin
  of 50 has been set by the Fed.

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• Maintenance Margin the minimum margin that must
  be present at all times in a margin account.
  Typically 30.
• When the margin in account drops below the
  maintenance margin, the broker issue a margin
  call.
• Investors receiving this margin call should add
  new cash or securities to the margin account.
  Otherwise, your securities are sold and the
  margin loan will be repaid.

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• You have 10,000
• Initial margin is 50 maintenance is 30
• The maximum margin loan is 10,000.
• You buy 1,000 shares at 18
• Margin 10,000/18,000 55.56
• Price falls to 10
• Total value of stock is 10,000 You borrowed
  8,000, so your equity is 2,000.
• Margin 2,000 / 10,000 20

8

• You have 5,000 and buy 400 WMT at 25 each.
• Initial margin is 50 maintenance is 30
• Your account balance sheet is as follows
• Assets Liabilities
• 400 WMT 10,000 Margin Loan 5,000
• _at_ 25/share ______ Equity 5,000
• Total 10,000 Total 10,000
• Your margin is 5,000/10,000 50

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• Margin call occurs at what price?
• Value of your stock
• Margin loan Equity
• Value 400 x P
• Equity Value of stock margin loan
• 400 x P - 5,000
• Maintenance margin
• Equity / Value of stock .3
• (400 x P - 5,000) / (400 x P) 0.3
• P 17.86. At any price below 17.86, you will
  be subject to a margin call.

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• Margin account (Futures)
• Bob buys one futures contract of corn at
  2/bushel (1 contract 5,000 bushels). The
  initial margin was 1,000. The next day the price
  of corn falls by 3 cent a bushel. So, Bob has
  just lost ( ).
• At the end of the day, the daily settlement
  process marks Bobs margin account to market by
  taking 150 out of his account leaving a balance
  of 850. Now, assume the maintenance margin level
  is 75. If Bobs margin balance falls to or below
  750, he will get a ( ) and have to bring his
  account back up to the initial 1,000.
• Suppose during the next day, corn again falls 3
  cent per bushel. Bobs margin account balance
  now falls to ( ), and he gets a margin call to
  deposit 300 in variation margin. The deposit of
  300 will bring his account back up to the
  initial level of 1,000.

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• Marking to market (Financial futures)
• Suppose on day 1 the seller entered into a 90-day
  contract to deliver 20-year T-Bonds at 97. The
  next day, because of a rise in interest rates,
  the futures contract, which now has 89 days to
  maturity, is trading at 96 when the market
  closes.
• Marking to market requires the prices of all
  contracts to be marked to market at each nights
  closing price.
• As a result, the price of the contract is lowered
  to 96 per 100 of face value, but in turn for
  this lowering of the price from 97 to 96, the
  buyer has to compensate the seller 1 per 100 of
  face value.
• Thus, given a 100,000 contract, there is a cash
  flow payment of 1,000 on that day from the buyer
  to the seller.
• Note that if the price had risen to 98, the
  seller would have had to compensate the buyer
  1,000.

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• Q What is meant by a short position in financial
  futures? A long position? How is each affected by
  changes in interest rates?
• A financial futures contract is a standardized
  agreement to buy or sell a specified quantity of
  a financial instrument at a set price.
• A short position represents the sale of a futures
  contract. A long position represents the purchase
  of a futures contract.
• Since interest rates and the prices of fixed
  income instruments move inversely, a short
  position will benefit if interest rates increase
  but will be harmed by falling interest rates.
• Conversely, a long position will benefit from
  falling rates and will be harmed by rising rates.

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Using interest rate futures to hedge a dollar gap
position

• Q How would a bank use interest rate futures to
  hedge a positive dollar gap? A negative dollar
  gap?
•  
• ANSWER A bank with a positive dollar gap would
  benefit on-balance-sheet from rising interest
  rates but would lose from falling interest rates.
  It would hedge this risk by taking a long or buy
  position in the financial futures market.
• If, conversely, the bank has a negative dollar
  gap it would take a short position in the futures
  market.

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• Q How would a bank use interest rate futures to
  hedge a positive duration gap? A negative
  duration gap?
•  
• ANSWER With a positive duration gap, a bank
  would experience a decline in the market value of
  equity if interest rates increased (because the
  market value of assets would fall more than the
  market value of liabilities). It could help this
  exposure by taking a short position in financial
  futures. With such a position, increases in
  interest rates would produce gains in the futures
  market position that could be used to offset the
  losses in the cash market position.
• In contrast, a bank with a negative duration gap
  would hedge with a long position in the futures
  market.

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• Number of contracts to purchase in a hedge
• (V/F) x (MC/ MF) b
• V value of cash flow to be hedged
• F face value of futures contract
• MC maturity of cash assets
  
• MF maturity of futures contacts
• b variability of cash market to futures market.
• Example A bank wishes to use 3-month futures to
  hedge a 48 million positive dollar gap over the
  next 6 months. Assume the correlation
  coefficient of cash and futures positions as
  interest rates change is 1.0.
• N (48/1) x (6/3) 1 96 contracts.

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Balance sheet hedging example

• Consider the problem of a bank with a negative
  dollar gap facing an expected increase interest
  rates in the near future.
• Assume that bank has assets comprised of only
  one-year loans earning 10 and liabilities
  comprised of only 90-day CDs paying 6. If
  interest rates do not change

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• Day 0 90 180 270 360
• Loans
• Inflows 1,000.00
• Outflows 909.09
  
• CDs
• Inflow 909.09
  922.43 935.98 949.71
• Outflows 922.43
  935.98 949.71 963.65
• Net cash flows 0 0 0 0
  36.35
• Notice that for loans 1,000/(1.10) 909.09.
  Also notice that CDs are rolled over every 90
  days at the constant interest rate of 6 e.g.,
  922.43 909.09(1.06)0.25, where 0.25 90
  days/360 days.

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• As a hedge against this possibility, the bank may
  sell 90-day financial futures with a par of
  1,000. To simplify matters, we will assume only
  one T-bill futures contract is needed. In this
  situation the following entries on its balance
  sheet would occur over time.

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Balance sheet hedging example

• As a hedge against this possibility, the bank may
  sell 90-day financial futures with a par of
  1,000. To simplify matters, we will assume only
  one T-bill futures contract is needed. In this
  situation the following entries on its balance
  sheet would occur over time.
• Day 0 90 180 270 360
• T-bill futures (sold)
• Receipts 985.54
  985.54 985.54
• T-bill (spot market
• purchase)
• Payments 985.54 985.54
  985.54
• Net cash flows 0 0 0
• It is assumed here that the T-bills pay 6 and
  interest rates will not change (i.e.,
  1,000/(1.06)0.25 985.54).

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• If interest rates increase by 2 in the next year
  (after the initial issue of CDs), the banks net
  cash flows will be affected as follows

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Balance sheet hedging example

• If interest rates increase by 2 in the next year
  (after the initial issue of CDs), the banks net
  cash flows will be affected as follows
• Day 0 90 180 270 360
• Loans
• Inflows 1,000.00
• Outflows 909.09
• CDs
• Inflow 909.09 922.43 940.35
  958.62
• Outflows 922.43
  940.35 958.62 977.24
• Net cash flows 0 0
  0 0 22.76
• Thus, the net cash flows would decline by 13.59.
  In terms of present value, this loss equals
  13.59/1.10 12.35.

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Balance sheet hedging example

• We next show the effect of this interest rate
  increase on net cash flows from the short T-bill
  futures position
• Day 0 90 180 270 360
• T-bill futures (sold)
• Receipts 985.54
  985.54 985.54
• T-bill (spot market
• Purchase)
• Payments 980.94
  980.94 980.94
• Net cash flows
  4.60 4.60 4.60
• The total gain in net cash flows is 13.80. In
  present value terms, this equals 4.60/(1.10).25
  4.60/(1.10).50 4.60/(1.10).75 13.16. Thus,
  the gain on T-bill futures exceeds the loss on
  spot bank loans and CDs.

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Options

• Definition Right but not obligation to buy or
  sell at a specified price (striking price) on
  or before a specified date (expiration date).
• Call option Right to buy -- pay premium to
  seller for this right.
• A July call option on Motorola stock with
  exercise price of 50 gives the owner of the call
  option to buy this stock for a price of 50
  before expiration in July.
• The holder of the call is not required to
  exercise the option. Only when the stock price
  exceeds the exercise price of 50, the holder
  will exercise the call option.

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• Put Option Right to sell -- pay premium to
  seller for this right.
• An October put option on Motorola stock with
  exercise price of 50 gives the owner of the put
  option to sell this stock for a price of 50 at
  any time before expiration in October.
• A put option will be exercised only if the stock
  price is less than the exercise price of 50.
• Note Seller of option must sell or buy as
  arranged in the option, so the seller gets a
  premium for this risk. The premium is the price
  of the option.

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Option Payoffs to Buyers
Payoff
Gross payoff
Call Option
Net payoff
Buy for 4 with exercise price 100
In the money
100
104
-4
Price of security
Premium 4
NOTE Sellers earn premium if option not
exercised by buyers.
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Option Payoffs to Buyers
Payoff
Net payoff
Put Option
Gross profit
Buy put for 5 with exercise price of 40.
In the money
0
Price of security
40
35
-4
Premium 5
NOTE Sellers earn premium if option not
exercised by buyers.
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• Options on futures contracts (futures options)
• Give the holder the right, but not the obligation
  to enter into a futures contract on an underlying
  security or commodity at a later date and at a
  predetermined price.
• Purchasing a call on a futures allows for the
  acquisition of a long position in the futures
  market, while exercising a put would create a
  short futures position.
• The writer of the call would be obligated to
  enter into the short side of the futures contract
  if the option holder decided to exercise the
  contract, while the seller of the put might be
  forced into a long futures contract.

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• When the bank hedges by buying put options on
  futures, if interest rates rise and bond prices
  fall, the exercise of the put results in the bank
  delivering a futures contract to the writer at an
  exercise price higher than the cost of the bond
  future currently trading on the futures exchange.
• If interest rates fall while bond and futures
  prices rise, the buyer of the futures put option
  will not exercise the put, and the losses on the
  futures put option are limited to the put
  premium.

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• Q) What is a futures options contract? Compare
  and contrast a futures options contract with a
  futures contract.
•  
• ANSWER A futures options contract is an option
  contract in which the deliverable is a futures
  contract, such as the Treasury bill futures
  contract. As with all options contracts, the
  holder has the right but not the obligation to
  take delivery (call option) or make delivery (put
  option).

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• Q) Suppose that your bank has a commitment to
  make a fixed rate loan in three months at the
  existing rate. In order to hedge against the
  prospect of rising interest rates, the bank takes
  a position in the futures options markets. What
  position should it take? The relevant information
  is as follows
•  
• T-bill futures prices 89
• Put option 90
• Premium 2500
•  
• What will be the net gain to the bank if T-bill
  futures prices fall to 85? Increase to 93?

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• If T-bill futures prices fall to 85, the put
  option could be exercised at 90 for a gain of 5,
  or 50,000. After paying the premium, the net
  gain would be 47,500.
• If T-bill futures prices rise to 93, the put
  option would not be exercised. The loss would
  equal the premium paid for the option, or 2,500.

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• Q) Explain how futures options contracts can be
  used to hedge interest rate risk.
•  
• ANSWER A bank that would be harmed if interest
  rates increased could hedge this risk by selling
  call options on futures or buying put option on
  futures.
• In contrast, if the bank was in a position in its
  portfolio where it would lose if interest rates
  fell it could hedge by buying a call option on
  futures or selling a put option.

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• Caps
• Buying a cap means buying a call option on
  interest rates.
• If interest rates rise above the cap rate, the
  seller of the cap compensates the buyer in return
  of an up-front premium. The seller of the cap is
  obliged to pay the difference between LIBOR and
  the exercise or cap rate (times the fraction of
  the year, times the notional principal).
• As a result, buying an interest cap is like
  buying insurance against an increase in interest
  rates.

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• Suppose a bank buys a 9 cap at t0 with
  exercise dates at the end of the first year and
  end of the second year. Face value is 100M. If
  the actual interest rate at the end of year 1 is
  10, the cap holder is entitled to receive the
  difference between the current market interest
  rate and the strike price multiplied by the
  principal value of the contract. (10-9)(100M)
  1M
• If the interest rate is below the cap, the cap
  seller makes no payments to the buyer.

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• Floors
• a put option on interest rates. An interest rate
  floor is a contract that limits the exposure of
  the buyer to downward movements in interest
  rates.
• The seller of a floor makes settlement payments
  only when LIBOR is below the floor rate

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• Your bank is liability sensitive. To protect
  itself against rising interest rates, management
  purchased 10 caps from a large investment bank
  firm. Each contract had a notional value of
  1,000,000, a strike price (based on three-month
  Treasury bill rates) of 7 (rate was currently
  6), and a one-year maturity. Over the next year
  interest rates in Treasury bills fell, reaching
  3 at the end of the year, the cap expired
  without benefit, and the bank lost the full
  premium of 46,000. Did management error in its
  decision to purchase the cap?
• ANSWER No, the bank bought insurance against a
  negative event. The negative event did not occur.

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• Interest rate swaps
• An exchange of fixed interest payments for
  floating interest payments by two counterparties.
• The swap buyer agrees to make a number of fixed
  interest rate payments on periodic settlement
  dates to the swap seller.
• The seller agrees to make floating rate payments
  to the buyer on the same settlement dates.

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• Advantages of swap markets
• swap markets are very private since only the
  counterparties know that the swap is taking place
• swap markets have virtually no government
  regulation
• swap markets allow for custom designed contracts
  (size and maturity)

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• Limitations of swap markets
• it is difficult to find counterparites wanting to
  take the opposite side of a specific transaction
• swap agreements are difficult to alter and hard
  to terminate once they are initiated
• the counterparties are both exposed to default
  risk.

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• Consider two banks.
• Bank A has raised 100 million of its funds by
  issuing four-year medium-term notes with 10
  annual fixed coupons. On the asset side of its
  portfolio, the bank makes CI loans whose rates
  are indexed to LIBOR.
• Bank B has short-term CD with an average of
  duration of one year, and it has 100 million
  worth of fixed rate residential mortgages of long
  duration.
• Bank A has a positive dollar gap, while Bank B
  has a negative dollar gap.
• Bank A sells an IRS (makes floating-rate
  payments) and Bank B buys an IRS (makes
  fixed-rate payments)

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• Bank A sends annual payments indexed to one-year
  LIBOR2 (assuming one-year LIBOR is 8) to help
  the Bank B cover the cost of refinancing its one
  year CDs
• Bank B sends fixed annual payments of 10 for the
  notional principal of 100 M to the Bank A to
  allow the bank to cover fully the coupon interest
  payments on its note issue.

42

• Bank A and Bank B have the following
  opportunities for borrowing in the short-term
  (floating rate) and long-term (fixed rate)
  markets.
•  
• Bank A Bank B
• Floating Rate T-Bill 1.0 T Bill 2.0
• Fixed Rate 8 10.5
• Bank A has a positive gap and Bank B has a
  negative gap. Show that both banks can benefit
  from a swap in the sense of lowering their
  interest rate risk. Can they also lower their
  cost of funds?

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• Bank A wants to receive fixed and pay floating.
  Bank B wants to receive floating and pay fixed.
  If Bank A and Bank B exchange flows in this
  manner it will reduce the interest rate risk of
  both parties.
• Since the relative credit quality spreads are
  different in the two markets (Bank A has a 1
  advantage in the floating rate market and a 2.5
  advantage in the fixed rate market), both parties
  can lower their cost of funds through the swap as
  well as reduce their interest rate risk. Pick
  swap terms and show this to be true.
• One such is the following (but there are others).
  Bank A pays T-Bill and receives 8, and B
  receives T-Bill and pays 8. In this case, the
  cost of funds to A is T-Bill with the swap
  (versus T Bill 1.0 without the swap) and for B
  it is 10 with the swap (versus 10.5 without the
  swap).
•