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

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

• Outline
• Financial futures
• Options
• Interest rate swaps

2
Financial futures

• Using financial futures markets to manage
  interest rate risk.
• Futures contract
• Standardized agreement to buy or sell a specified
  quantity of a financial instrument on a specified
  data at a set price.
• Buyer is in a long position, and seller is in a
  short position.
• Note pricing and delivery occur at two points
  in time.
• Trading on CBOT, CBOE, and CME, as well as
  European and Asian exchanges.
• Exchange clearinghouse is a counterparty to each
  contract (lowers default risk).
• Margin is a small commitment of funds for
  performance bond purposes.
• Marked-to-market at the end of each day.
• Example A trader buys on Oct. 2, 2000 one Dec.
  2000 T-bill futures contact at 94.83 (or
  discount yield of 5.17). The contract value is
  1 million and maturity is 13 weeks. If the
  discount rate on T-bills rose 2 basis points
  (i.e., 25 per basis point or 100 per year/4
  quarters), the buyer would lose 50 in the margin
  account.
• The settlement price is
• 986,880.63 1,000,000 - 91(.0519 x
  1,000,000)/360

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Using interest rate futures to hedge a dollar gap
position

• Long (or buy) and short (or sell) hedges.
• If the bank has a positive dollar gap, and
  interest rates fall, buy a futures contract.
  When interest rates fall in the future, losses in
  the gap position are offset by gains in the
  futures position.
• Suppose that the bank has a negative dollar gap,
  and interest rates are expected to rise in the
  future. Now go short in futures contracts.
• 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.

4
Payoffs for futures contracts
F0 Contract price at time 0 F1 Future price
at time 1
Payoff
Payoff
Sell futures
F1
Buy futures
F
0
0
F
F0
F0
-F1
Gain if interest rates fall and prices rise of
debt securities.
Gain if interest rates rise and prices fall of
debt securities.
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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
• 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., 909.09
• (1.06)0.25, where 0.25 90 days/360 days.

6
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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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.

9
Using interest rate futures to hedge a duration
gap

• Assume that a bank has a positive duration gap
  as follows
• Days to maturity Assets Liabilities
• 90 500 3,299.18
• 180 600
• 270 1,000
• 360 1,400
• Also assume that single-payment loans at 12 are
  rolled over during one year only (i.e., all loans
  mature at the end of the year). Liabilities pay
  10.
• Present value of loans 3,221.50
  500/(1.12)1/4 600/(1.12)1/2
  1,000/(1.12)3/4 1,400/(1.12)
• Present value of liabilities 3,221.50
  3,299.18/(1.10)1/4
• Duration of assets 0.73 years
• Duration of liabilities 0.25 years.

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Using interest rate futures to hedge a duration
gap

• Solution Sell (short) 3-month T-bill futures
  until the duration of assets falls to 0.25.
• Dp Drsa Df Nf FP/ Vrsa
• Dp duration of cash and futures assets
  portfolio
• Drsa duration of rate sensitive assets
• Vrsa market value of rate sensitive assets
• Df duration of futures contract
• Nf number of futures contracts
• FP futures price
• Assuming that 3-month T-bills are yielding 12
  (price 100/1.121/4 97.21)
• 0.25 0.73 0.25 (Nf) 97.21/3,221.50
• Nf 64

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A perfect futures short hedge

• Month Cash Market Futures Market
• June Securities firm makes a Sells 10 December
  munis bond
• commitment to purchase index futures at
  96-8/32 for
• 1 million of munis bonds 962,500.
• yielding 8.59 (based
• on current munis cash
• price at 98-28/32) for
• 988,750.
• October Securities firm purchases Buys 10
  December munis bond
• and then sells 1 million of index futures at
  93, or 930,000,
• munis bonds to investors to yield 8.95.
• at a price of 95-20/32 for 956,250.
  
• Loss (32,500) Gain 32,500

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An imperfect futures short hedge

• Date Cash Market Futures
  Market
• October/YrX Purchase 5million corporate
  bonds Sell 5 million T-bonds
• maturing Aug. 20005, 8 coupon
  futures contracts at
• at 87-10/32
  86-21/32
• Principal 4,365,625
  Contract value 4,332,813
• March/YrX1 Sell 5 million corporate bonds
  Buy 5 million T-bond futures
  at 79.0
  at 79-21/32 Principal
  3,950,00 Contract
  value 3,951,563
• Loss (415,625) Gain
  381,250

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Complications in using financial futures

• Accounting and regulatory guidelines.
• Macro hedge of the banks entire portfolio --
  cannot defer gains and losses on futures, so
  earnings are less stable with this hedge
  strategy.
• Micro hedge linked to a specific asset -- can
  defer gains and losses on futures until contracts
  mature.
• Basis risk is the difference between the cash and
  futures prices. These two prices are not
  normally perfectly correlated (e.g., corporate
  bond rates in a cash position versus T-bill
  futures rates).
• Bank gaps are dynamic and change over time.
• Futures options allow the execution of the
  futures position only to hedge losses in the cash
  position. Gains in the cash position are not
  offset by losses in the futures position.

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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.
• Put Option Right to sell -- pay premium to
  seller for this right.
• Note Seller of option must buy or sell as
  arranged in the option, so the seller gets a
  premium for this risk. The premium is the price
  of the option. The Black-Scholes option pricing
  model can be used to figure out the premium (or
  price) of an option.
• Long position The buyer of the option, who
  gains if the price of the option increases.
• Short position The seller of the option, who
  earns the premium if the option is not exercised
  (because it is not valuable to the buyer 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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Interest rate swaps

• BEFORE
• Firm 1 Firm 2
• Fixed rate assets Variable
  rate assets
• Variable rate liabilities Fixed rate
  liabilities
• AFTER
• Firm 1 Firm 2
• Fixed rate assets Variable rate assets
• Fixed rate liabilities Variable rate
  liabilities
• Started in 1981 in Eurobond market
• Long-term hedge
• Private negotiation of terms
• Difficult to find opposite party
• Costly to close out early
• Default by opposite party causes loss of swap
• Difficult to hedge interest risk due to problem
  of finding exact opposite mismatch in assets or
  liabilities

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Interest rate SWAP
Bank
13.1
Libor
Bank makes debt payments
Firm A
Firm B
Libor 1
12
Starting conditions Firm A borrows floating
rate bank loan at Libor 1 (premium for
risk)
Starting conditions Firm B borrows fixed rate
12 bonds (AAA bonds with no premium for risk)
Results (A) Firm A has total or all-in fixed
rate obligation of 12 0.1(bank service fee
1.0 (premium over Libor) 13.1. (B) Firm
B has floating rate obligation to pay LIBOR rate
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Hedging strategies

• Use swaps for long-term hedging.
• Use futures and options for short-term hedges.
• Use futures to lock-in the price of cash
  positions in securities
• For example, a corporate treasurer has a payroll
  due in 5 days and wants to fix the value of
  marketable securities being held to meet the
  payroll -- a short hedge gives downside price
  protection in this case.
• Use options to minimize downside losses on a cash
  position and take advantage of possible
  profitable price movements in your cash position
• For example, you have a cash position in bonds
  and believe that interest rates are more likely
  to rise than fall -- -- you could buy by a put
  option on bonds -- if rates do rise, you are in
  the money on the option and offset losses in the
  cash position in bonds -- however, if rates fall,
  you do not exercise the option and make price
  gains on the cash position in bonds.
• Use options on futures to protect against losses
  in a futures position and take advantage of price
  gains in a cash position.
• Use options to speculate on price movements in
  stocks and bonds and put a floor on losses.