Chapters 7 and 8 AssetLiability Management

1
Chapters 7 and 8Asset/Liability Management
2
Key topics

• Asset, liability, and funds management
• Interest rate risk for corporations a reminder
• Market rates and interest rate risk for banks
• Measuring interest rate sensitivity and the
  dollar gap
• Duration gap analysis
• Simulation and asset/liability management
• Correlation among risks

3
Asset-liability management strategies

• Asset management control of the composition of
  a banks assets to provide adequate liquidity and
  earnings and meet other goals.
• Liability management control over a banks
  liabilities (usually through changes in interest
  rates offered) to provide the bank with adequate
  liquidity and meet other goals.

4
Asset-liability management strategies

• Funds management balanced approach
• Control volume, mix, return (cost) of assets
  and liabilities
• Coordinate control of assets and liabilities
• Maximize returns and minimize costs of managing
  assets and liabilities

5
Asset-liability management
Bank interest revenues Bank interest costs Marke
t value of bank assets Market value of
bank liabilities
Banks net interest margin dollar gap
Managing the banks response to changing interest
rates
Banks investment value, profitability, and risk
Banks net worth (equity) duration gap
From Rose textbook
6
Rate effects on income
Assets
Claims
Asset _at_ 8 100 Total
100
Liability _at_ 4 90 Equity
10 Total 100
7
Rate effects on income
Assets
Claims
Asset _at_ 8 100 Total
100
Liability _at_ 6 90 Equity
10 Total 100
Fixed interest loan but variable interest
liability
8
Rate effects on equity value
9
Bond Valuation

• The value of an asset is the present value of its
  future cash flows.
• V PV (future cash flows)
• Size, timing, and riskiness of the cash flows.

10
Bond Valuation, Continued

• Bond has 30 years to maturity, an 100 annual
  coupon, and a 1,000 face value
• Time 0 1 2 3 4 30
• Coupons 100 100 100 100 100
• Face Value 1,000
• How much is this bond worth? Depends on
• current level of interest rates
• riskiness of firm

11
Bond Valuation, Continued

• What if we require a 20 rate of return?
• FV 1000
• PMT 100
• i 20
• n 30
• PV -502.11
• Discount Bond

• What if we require a 5 rate of return?
• FV 1000
• PMT 100
• i 5
• n 30
• PV -1,768.62
• Premium Bond

12
Interest Rate Risk and Time to Maturity
Bond values ()
2,000
1,768.62
30-year bond
Time to Maturity
Interest rate 1 year 30
years 5 1,047.62 1,768.62
10 1,000.00 1,000.00 15 956.52 671.70
20 916.67 502.11
1,500
1-year bond
1,047.62
1,000
916.67
502.11
500
Interest rates ()
20
5
10
15
Value of a Bond with a 10 Coupon Rate for
Different Interest Rates and Maturities
13
Yield curve
U.S. Treasury Securities
14
Yield curve and maturity gap

• Most banks have positive maturity gaps assets
  have longer maturities than do liabilities
• How does yield curve affect
• Net interest income?
• Best equity value?

15
Interest rate risk for banks

• In the short-term, interest rates change the
  amount of net interest income bank earns.
• Changing market values of assets and liabilities
  affect total equity capital.

16
Fund management for income

• In general, fund management is a short-run tool
  days, weeks
• NIM (avg. 3.5) depends on
• interest rates on assets and liabilities
• dollar amount of funds
• the earning mix (higher paying assets or cheaper
  funds)

17
Dollar gap and income
Dollar gap interest sensitive assets interest
sensitive liabilities
18
Dollar gap and income
Dollar gap interest sensitive assets interest
sensitive liabilities
19
Dollar gap and income
Dollar gap interest sensitive assets interest
sensitive liabilities (15
20 40) (20 40 55)
75 - 115 -40
20
Dollar gap and income
21
Dollar gap and income
Ratio 1 means asset-sensitive bank
22
Important Gap Decisions

• Choose time over which NIM is managed
• Choose target NIM
• To increase NIM
• Develop correct interest rate forecast
• Reallocate assets and liabilities to increase
  spread
• Choose volume of interest-sensitive assets and
  liabilities

23
Gap, interest rates, and profitability

• Incremental gaps measure the gaps for different
  maturity buckets (e.g., 0-7 days, 8-30 days,
  31-90 days, and 91-365 days).
• Cumulative gaps add up the incremental gaps from
  maturity bucket to bucket.

24
Choosing time to manage dollar gap
25
NIM Influenced By

• Changes in interest rates up or down
• Changes in the spread between assets and
  liabilities
• Changes in the volume of interest-sensitive
  assets and liabilities
• Changes in the mix of assets and liabilities

26
Gap, interest rates, and profitability

• The change in dollar amount of net interest
  margin (?NIM) is

27
Gap, interest rates, and profitability
An increase in interest rates adversely affects
NIM because there are more RSL than RSA
28
Managing interest rate risk with dollar gaps

• Defensive fund management guard against changes
  in NIM (e.g., near zero gap).
• Aggressive fund management
  seek to increase NIM in
  conjunction with interest rate
  forecasts (e.g., positive or
• negative gaps).

29
Aggressive fund management

• Forecasts important to bank strategy
• If interest rates are expected to increase in the
  near future, the bank can exploit a positive
  dollar gap.
• If interest rates are expected to decrease in the
  near future, the bank could exploit a negative
  dollar gap (as rates decline, deposit costs fall
  more than interest income, increasing profit).

30
Aggressive fund management

• Increase RSA
• More Fed fund sales
• Buy marketable securities
• Make deposits in other banks

• Increase RSL
• Borrow Fed funds
• Issue CDs in different sizes and maturities

31
Interest rate risk strategy?

• Depends on risk preferences and skills of the
  management team

32
Problems with dollar gap management

• Time horizon problems related to when assets and
  liabilities are repriced.
• Assumed correlation of 1.0 between market rates
  and rates on assets and liabilities
• Focus on net interest income rather than
  shareholder wealth.

1 2 3
33
Solution to correlation problem Standardized gap
Assume GAP RSA - RSL
200 (coml paper) - 500 (CDs)
-300 Assume the CD rate is 105 as
volatile as 90-day T-Bills, while the coml paper
rate is 30 as volatile. Now calculate the
Standardized Gap 0.30 (200) - 1.05 (500)
60 - 525
-460 Much more
negative!
34
Dollar gap analysis
Dollar gap RSA - RSL
RSA RSL Positive gap RSL RSA
Negative gap Impacts on net interest income
35
Practice
36
Hedging dollar gap

• Background on futures
• How to hedge dollar gap

37
Financial futures

• Futures contract
• Standardized agreement to buy or sell a specified
  quantity of a financial instrument on a specified
  date at a set price.
• Purpose to shift risk of interest rate changes
  from risk-averse parties (e.g., commercial banks)
  to speculators willing to accept risk.

38
Popular financial futures contracts

• U.S. Treasury bond futures
• U.S. Treasury bill futures
• 3-month Eurodollar time deposits (most popular in
  world)
• 30-day Federal funds futures
• 1-month LIBOR futures contract

Rose textbook
39
Details of financial futures trading

• Buyer is in a long position, and seller is in a
  short position.
• 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.
• Pricing and delivery occur at two points in time.

40
WSJ Futures Price Quotations

• INTEREST RATE
• Lifetime
  Open Open High Low Settle Change High
  Low Interest
• TREASURY BONDS (CBT) 100,000, pts. 32nds of
  100
• June 100-20 101-11 100-07 100-10 - 13
  104-03 98-16 188,460Sept 99-25 100-18
  99-16 99-24 - 11 102-05 99-10
  42,622Dec 99-00 99-24 98-24 98-30 - 10
  101-11 98-06 5,207
• Futures contract for September
• 99 24/32 .9975
• 0.9975 x 100K 99,750

41
Margin Account

• Participants in futures contracts use margin
  accounts which are marked-to-market daily.
• Assume a financial manager buys a T-bill futures
  contract with initial margin account of 2,000.
• Contracts is initially priced at 950K

42
Change in Margin Account
43
T-Bill futures

• Trader buys on Oct. 2, 2007 one Dec. 2007 T-bill
  futures contract at 94.83. The contract value
  is 1 million and maturity is 13 weeks (91 days
  13 weeks x 7 days).
• Discount yield is 100 94.83 5.17 or 5.17

44
T-Bill futures

• Suppose discount rate on T-bills rises 2 basis
  points to 5.19
• Drop in value in margin account realized that
  day
• 1,000,000 x (.0002/4) qtrs per year 50
• The final settlement price is based on a futures
  price of 94.81 (94.83-0.02), or a change of
  50 from the price on the earlier slide

45
Hedging with Futures

• Selling price on futures contract reflects
  investors expectations of interest rates and
  underlying security value at due date
• Hedging requires bank to take opposite position
  in futures market from its current position
  (dollar gap) today.

Rose textbook
46
Dollar gap hedging example

• Bank with a negative dollar gap
• More rate sensitive liabilities than assets
• Hoping rates will decline but afraid that rates
  will increase
• increase interest expense more than interest
  income making net interest margin drop
• Bank has assets comprised of only one-year 1000
  loans earning 10 and liabilities comprised of
  only 90-day CDs paying 6.
• What cash flows do we expect if interest rates do
  NOT change?

47
Dollar gap hedging example

• Day 0 90 180 270
  360
• Loans
• Inflows
  1,100
• Outflows 1,000
  
• CDs
• Inflow 1000 1014.67
  1029.56 1044.67
• Outflows 1014.67
  1029.56 1044.67 1060
• Net C.F. 0 0
  0 0 40.00
• FV of loans 1,000 x (1.10) 1,100
• CDs are rolled over every 90 days at the constant
  interest rate of 6 e.g., 1000 x (1.06)0.25,
  where 0.25 90 days/360 days.
• PV (40) 40/(1.10)136.36

48
Dollar gap hedging example

• Bank concerned interest rates will rise,
  making income fall. As hedge, bank sells today
  90-day financial futures with a par of 1,000.
  Sells at a discount 1000/(1.06).25
• 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
  bank managers are wrong -- interest rates do NOT
  change

49
Dollar gap hedging example
PV of net gain on assets and liabilities 36.36 P
V of gain on futures contracts
0 Net gain
36.36
50
Dollar gap hedging example

• If interest rates increase by 2 (after the
  initial issue of CDs), banks net cash flows
  will change as follows
• Day 0 90 180
  270 360
• Loans
• Inflows
  1,100.00
• Outflows 1,000
• CDs
• Inflow 1000 1014.49 1034.50
  1054.90
• Outflows 1014.49 1034.50
  1054.90 1075.71
• Net C.F. 0 0 0 0
  24.29
• 
  6 8 8
• PV (24.29) 24.29/(1.10)1 22.08

51
Dollar gap hedging example

• Effect of 2 interest rate increase on net cash
  flows from 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
• 980.94 1000/(1.08).25
• Total gain is 13.80 (4.60 x 3)
• PV 4.60/(1.10).25 4.60/(1.10).50
  4.60/(1.10).75 13.16

52
Dollar gap hedging example
PV of net effect of hedging against increase in
interest rates No change in interest rates
36.36 0 36.36 Interest rates
increase by 2, with hedge 22.08
13.16 35.24 Reduction in income without
hedge 36.36 - 22.08 14.28
53
Futures contracts to trade
For dollar gap

• 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.

54
Example Perfect correlation
A bank wishes to use 3-month T-bill futures to
hedge an 80 million positive dollar gap over the
next 6 months. Buy futures. Assume the
correlation coefficient of cash and futures
positions as interest rates change is 1.0.
55
Example Less than perfect correlation
Assume the correlation coefficient of cash and
futures position as interest rates change is 0.5.
We can lower our futures positions when the
correlation is not perfectly positive.
56
Payoffs for futures contracts
Short Hedge
Long Hedge
Payoff
Payoff
F0 Contract price at time 0 F1 Future price
at time 1
Gain
Gain
Buy futures
Sell futures
F
0
0
F
F1
F1
F0
F0
Sell futures expecting interest rates to rise
lowering the price of the futures.
Buy futures expecting interest rates to fall
increasing the value of the future contract.
57
Practice
58
Duration
A measure of the maturity and value
sensitivity of a financial asset that considers
the size and the timing of all its expected cash
flows.
Rose
59
Duration

• Average maturity of future cash flows (assets or
  liabilities)
• Average time needed to recover the funds
  committed to investment

Rose
60
Duration gap analysis
Duration gap Dollar-weighted -
Dollar-weighted x Total liabilities
duration of asset duration of
bank Total assets
portfolio liabilities
Asset duration Liability duration Positive
gap Liability duration Asset duration
Negative gap Effects on net worth
61
Calculating duration
Rose
62
Calculating duration
Rose
63
Duration gap analysis
Where do we get the average duration? It is the
average duration of the assets or liabilities
weighted by their value relative to total value
of assets or liabilities.
64
Duration gap analysis
Duration (Years)
Duration (Years)
Assets
Claims
Cash 100 0.00 Business
loans 400 1.25 Mortgage loans 500
7.00 Total 1,000
4.00
CD, 1 year 600 1.00 CD,
5 year 300 5.00
Total liabilities 900
2.33 Equity 100 Total claims
1,000
DA(100/1,000) x 0.00 (400/1,000) x 1.25
(500/1,000) x 7.00 4.00 (.1)(0.00)
(.4)(1.25) (.5)(7.00) 4.00 DL(600/900) x
1.00 (300/900) x 5.00 2.33
(.6667)(1.00) (.3333)(5.00) 2.33 DGAP 4.00
2.33 (9/10) 1.903
65
Duration gap analysis
Assume an interest rate of 8 and a change of 1
point
66
Duration gap and net worth
67
Duration gap management

• Defensive
• Immunize net worth of bank
• Duration gap 0
• Aggressive
• Use forecast of interest rate changes to manage
  bank net worth

68
Aggressive duration gap management

• If interest rates ?, - duration gap, ? equity
• If interest rates ?, duration gap, ? equity

69
Duration gap hedging

• Positive gap
• Reduce duration of assets
• Increase duration of liabilities
• Short position in financial futures
• Negative gap
• Increase duration of assets
• Decrease duration of liabilities
• Long position in financial futures

70
Duration gap hedging example

• Assume bank has positive duration gap
• Days to maturity Assets Liabilities
• 90 500 3,299.18
• 180 600
• 270 1,000
• 360 1,400
• Assets are single-payment loans at 12
• Liabilities are 90-day CDs paying 10.

71
Duration gap hedging example
Duration (Years)
Duration (Years)
Assets
Claims
Loans 90-day 500
0.25 180-day 600 0.50 270-day
1,000 0.75 360-day
1,400 1.00 Total
3,500 0.736
CD, 90-day 3,299.18 0.25
DA(500/3,500) x 0.25 (600/3,500) x 0.50
(1,000/3,500) x 0.75 (1,400/3,500) x
1.00 0.736
PV (loans) 500/(1.12).25 600/(1.12).50
1,000/(1.12).75 1,400/(1.12)1 3,221.50
PV (CDs) 3,299.18/(1.10).25 3,221.50
72
Duration gap hedging example

• Duration gap 0.736 years 0.250 years 0.486
  years
• Positive duration gap!
• Interest rates rise and net worth declines!
• Sell 3-month T-bill futures until duration of
  assets 0.25 years, the duration of the
  liabilities

Sell!
73
Duration gap hedging example

• 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

74
Duration gap hedging example
Assume T-bills are yielding 12 so price
is Price 100/(1.12).25 97.21
Df 0.25 because T-bills are 90 days Negative 64
means to sell T-bill futures
75
Duration gap hedging example
76
A perfect futures short hedge
77
An imperfect futures short hedge
78
Complications using financial futures

• Not used for speculation
• Accounting for macro vs. micro hedges
• Basis risk
• Hedge need changes after hedge made
• Liquidity effects

79
Hedging with Options

• Alternative to financial futures contracts
• Option contract gives buyer the right but not the
  obligation to purchase a single futures contract
  for a specified period at a specified striking
  price.

80
Option Terminology

• Call option a contract that gives the owner the
  right to buy an asset at a fixed price for a
  specified time.
•  
• Put option a contract that gives the owner the
  right to sell an asset at a fixed price for a
  specified time.
•  
• Strike or exercise price the fixed price agreed
  upon in the option contract.
• Expiration date the last date of the option
  contract.

81
Option players
82
Option buyer actions
83
Big Differences

• Biggest difference between futures option and
  futures contract
• Premium paid for option is most that can be lost
  in futures option.
• Loss can be unlimited for futures contract

84
Relevant types of options

• Treasury bills
• Eurodollar futures
• Currencies

85
Option Payoffs to Buyers of Calls
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.
86
Option Payoffs to Buyers of Puts
Payoff
Net payoff
Put Option
Gross profit
Buy put for 4 with exercise price of 40.
In the money
0
Price of security
40
36
-4
Premium 4
NOTE Sellers earn premium if option not
exercised by buyers.
87
Dollar gap and futures options

• Negative dollar gap means net interest income
  falls if interest rates rise
• Protect against rising interest rates
• Buy an interest rate put option
• Interest rates rise net interest income falls
  but value of put rises
• Interest rates fall net interest income rises
  but value of put falls

88
Futures Option Example

• Most recent cash flow forecast indicates in 30
  days bank needs to borrow 3 million for 3
  months.
• Current yield curve is relatively flat with
  short-term rates at 9.75.
• Rate seems reasonable so bank would like to
  lock-in the rate.

Based on Short-term Financial Mgt, by Maness and
Zietlow, 2002.
89
Eurodollar Futures Options

• Based on 1 million 3-month eurodollar deposit
• Traded on the International Monetary Market of
  Chicago Mercantile Exchange.
• Strike price is quoted as an index. So 9300
  represents an index value of 93, which is related
  to a 7 annualized discount rate.

90
Needed Information
91
Example, Continued
Firm buys 3 90-day put futures options with a
striking price of 9050 for 750 3,000,000 x
(.1/4)/100, where 4 represents quarters. If
interest rates rise to 11 as expected in our
example info, then the value of the option rises
to 1.50 points of 100. The 3 options will be
worth 11,250 3,000,000 x (1.5/4)/100 and
the gain will be 10,500 11,250 -
750 offsetting losses on the increase in
interest rates for the firms borrowing.
92
Interest Rates Fall

• If interest rates had fallen, then the value of
  the option
• would have fallen also. The firm would have
• let the option expire, losing the 750 premium
• sold the option at a price less than 750
• In either case, the loss in the value of the
  option
• would have been offset by reduced costs of
  borrowing.

93
Swaps

• Agreement between 2 parties to exchange (or swap)
  specified cash flows at specified intervals in
  the future
• Series of forward contracts

94
Swaps

• 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 rate risk due to
  problem of finding exact opposite mismatch in
  assets or liabilities

95
Interest rate swaps

• BEFORE
• Bank 1 Bank 2
• Fixed rate assets Variable
  rate assets
• Variable rate liabilities Fixed rate
  liabilities
• Firm 1 has negative dollar gap
• Firm 2 has positive dollar gap
• AFTER
• Bank 1 Bank 2
• Fixed rate assets Variable rate assets
• Fixed rate liabilities Variable rate
  liabilities

96
Swap Example

• Bank A
• Portfolio of fixed rate mortgages
• Agrees to pay Bank B a fixed 11 per year on 100
  M every 6 months

• Bank B
• Portfolio of variable rate loans
• Issued 11 100 M Eurodollar bond
• Agrees to make variable rate payments on 100 M
  to Bank A at 35 basis points below LIBOR.

97
Swap example
98
Currency Swap

• Two firms agree to exchange a specific amount of
  one currency for a specific amount of another at
  specific dates in the future.
• Two multinational companies with foreign projects
  need to obtain financing.
• Firm A is based in England and has a U.S.
  project.
• Firm B is based in the U.S. and has an English
  project.

99
Exchange Rate Risk

• Both firms want to avoid exchange rate
  fluctuations.
• Both firms receive currency for investment at
  time zero and repay loan as funds are generated
  in the foreign project.

100
Constraints

• Both firms can avoid XR changes if they arrange
  for loans in the country of the project.
• Both firms can borrow
• more cheaply in home
• country.
•  

101
Solution

• The firms arrange parallel loans for the initial
  investment and use the proceeds from the project
  to repay the loan.

102
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
• Use options to minimize downside losses on a
  cash position and take advantage of possible
  profitable price movements in your cash position
• 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.

103
Problems with duration gap

• Overly aggressive management bets the bank.
• Duration analysis assumes (1) that the yield
  curve is flat and (2) shifts in the level of
  interest rates imply parallel shifts of the yield
  curve
• Average durations of assets and liabilities drift
  or change over time and not at the same rates
  (duration drift). Rebalancing can help to keep
  the duration gap in a target range over time.

104
Other issues in gap analyses

• Simulation models
• Examine different what if scenarios about
  interest rates and asset and liability mixes in
  gap management -- stress testing shows impacts on
  income and net worth.
• Correlation among risks
• Gap management can affect credit risk. For
  example, if a bank decides to increase its use of
  variable rate loans (to obtain a positive dollar
  gap in anticipation of an interest rate increase
  in the near future), as rates do rise, credit
  risk increases due to fact that some borrowers
  may not be able to make the higher interest
  payments.
• Gap management may make the bank less liquid.

105
Questions?