Techniques of asset/liability management:
Futures, options, and swaps
• Outline
– Financial futures
– Options
– Interest rate swaps
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]
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.
Payoffs for futures contracts
Payoff
Payoff
F0 = Contract price at time 0
F1 = Future price at time 1
F1
Buy futures
0
F
F0
Sell futures
F
0
F0
-F1
Gain if interest rates
fall and prices rise of
debt securities.
Gain if interest rates
rise and prices fall of
debt securities.
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
Loans:
Inflows
Outflows
CDs:
Inflow
Outflows
Net cash flows
0
90
180
270
360
$1,000.00
$909.09
$909.09
0
$922.43 $935.98 $949.71
$922.43 $935.98 $949.71 $963.65
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].
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
T-bill futures (sold)
Receipts
T-bill (spot market
purchase)
Payments
Net cash flows
0
90
180
270
360
$985.54 $985.54 $985.54
$985.54 $985.54 $985.54
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).
Balance sheet hedging example
If interest rates increase by 2% in the next year (after the initial issue of
CDs), the bank’s net cash flows will be affected as follows:
Day
Loans:
Inflows
Outflows
CDs:
Inflow
Outflows
Net cash flows
0
90
180
270
360
$1,000.00
$909.09
$909.09
0
$922.43
$922.43
0
$940.35
$940.35
0
$958.62
$958.62 $977.24
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.
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
T-bill futures (sold)
Receipts
T-bill (spot market
Purchase)
Payments
Net cash flows
0
90
180
270
360
$985.54 $985.54 $985.54
$980.94 $980.94
$4.60
$4.60
$980.94
$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.
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.
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
A perfect futures short hedge
Month
June
Cash Market
Securities firm makes a
commitment to purchase
$1 million of munis bonds
yielding 8.59% (based
on current munis’ cash
price at 98-28/32) for
$988,750.
Futures Market
Sells 10 December munis bond
index futures at 96-8/32 for
$962,500.
October Securities firm purchases
and then sells $1 million of
munis bonds to investors
at a price of 95-20/32 for $956,250.
Buys 10 December munis bond
index futures at 93, or $930,000,
to yield 8.95%.
Loss: (32,500)
Gain: $32,500
An imperfect futures short hedge
Date
Cash 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/YrX+1 Sell $5 million corporate bonds
at 79.0:
Principal = $3,950,00
Loss: ($415,625)
Futures Market
Buy $5 million T-bond futures
at 79-21/32: :
Contract value = $3,951,563
Gain: $381,250
Complications in using
financial futures
• Accounting and regulatory guidelines.
• Macro hedge of the bank’s 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.
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).
Option Payoffs to Buyers
Payoff
Gross payoff
Call Option
Net payoff
Buy for $4 with
exercise price $100
“In the money”
$100
-4
$104
Price of security
Premium =
$4
NOTE: Sellers earn premium if option not
exercised by buyers.
Option
Payoffs
to
Buyers
Payoff
Net payoff
Put Option
Gross profit
Buy put for $5 with
exercise price of $40.
“In the money”
0
-4
$35
$40
Price of security
Premium = $5
NOTE: Sellers earn premium if option not
exercised by buyers.
Interest rate swaps
BEFORE
Firm 1
Fixed rate assets
Variable rate liabilities
AFTER
Firm 1
Fixed rate assets
Fixed rate liabilities
•
•
•
•
•
•
•
Firm 2
Variable rate assets
Fixed rate liabilities
Firm 2
Variable rate assets
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
Interest rate SWAP
13.1%
Libor
Bank
Bank makes
debt
payments
Firm A
Libor + 1%
Starting conditions:
Firm A borrows floating rate
bank loan at Libor + 1%
(premium for risk)
Firm B
12%
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
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.