chicago financial asset management by tnw53257

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									    Chapters 7 and 8
Asset/Liability Management




                             1
                     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




                                                         2
     Asset-liability management
              strategies
• Asset management – control of the
  composition of a bank’s assets to provide
  adequate liquidity and earnings and meet
  other goals.

• Liability management – control over a bank’s
  liabilities (usually through changes in interest
  rates offered) to provide the bank with
  adequate liquidity and meet other goals.


                                                 3
    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



                                                   4
            Asset-liability management

                        Bank interest
                         revenues           Bank’s net
                                         interest margin:
                        Bank interest       dollar gap
  Managing                 costs                            Bank’s investment
  the bank’s                                                value, profitability,
 response to             Market value                            and risk
   changing             of bank assets
interest rates
                                          Bank’s net
                        Market value
                                          worth (equity):
                          of bank
                                          duration gap
                         liabilities




                                                                              5
   From Rose textbook
     Rate effects on income
            Assets                      Claims


    Asset @ 8%       $100       Liability @ 4%   $90

                                Equity           $10

    Total            $100       Total            $100


                       Total Interest Income Total Interest Expense
Net Interest Margin 
                                  Average Earning Assets
                       Total Interest Income Total Interest Expense
                     
                         Total Securities  Net Loans and Leases
                       $100  .08  $90  .04
                     
                               $100
                       $8.0  3.6
                     
                         $100
                      4.4%                                            6
      Rate effects on income
            Assets                       Claims


    Asset @ 8%       $100        Liability @ 6%    $90

                                 Equity            $10

    Total            $100        Total            $100

                       Total Interest Income Total Interest Expense
Net Interest Margin 
                                   Average Earning Assets
                       $100  .08  $90  .06
                     
                               $100
                       $8.0  5.4
                     
                         $100
                      2.6%


Fixed interest loan but variable interest liability                    7
Rate effects on equity value




                               8
               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.




                                                      9
       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


                                                  10
          Bond Valuation, Continued

• What if we require a 5% • What if we require a 20%
  rate of return?           rate of return?

•   FV      +1000        •   FV       +1000
•   PMT     +100         •   PMT      +100
•   i       5            •   i        20
•   n       30
                         •   n        30
•   PV      -1,768.62
                         •   PV       -502.11
• Premium Bond
                         • Discount Bond

                                                  11
     Interest Rate Risk and Time to Maturity
Bond values ($)


   2,000
           $1,768.62
                           30-year bond                                                   Time to Maturity
   1,500
                                                                       Interest rate        1 year       30 years
                                                                           5%          $1,047.62      $1,768.62
           $1,047.62                      1-year bond                     10            1,000.00       1,000.00
   1,000
                                                             $916.67
                                                                          15             956.52         671.70
                                                                          20             916.67         502.11
     500                                                     $502.11




                                                                       Interest rates (%)
                       5         10         15          20

       Value of a Bond with a 10% Coupon Rate for Different Interest Rates and Maturities


                                                                                                             12
Yield curve




                           13
U.S. Treasury Securities
   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?


                                       14
    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.



                                             15
  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)
                                               16
              Dollar gap and income

Dollar gap = interest sensitive assets – interest sensitive liabilities

        Assets                      Liabilities and Equity Capital

        Vault cash           NRS    Demand deposits          NRS

        ST securities        RSA    NOW accounts             NRS
                                    Money market
        LT securities        NRS                             RSL
                                    deposits
        Variable-rate loan   RSA    ST savings               RSL

        ST loans             RSA    LT savings               NRS

        LT loans             NRS    Fed funds borrowing      RSL

        Other assets         NRS    Equity capital           NRS

                                                                     17
                     Dollar gap and income
Dollar gap = interest sensitive assets – interest sensitive liabilities


Assets                              Liabilities and Equity

Vault cash             NRS   $20 Demand deposits             NRS    $5

ST securities          RSA    15 NOW accounts                NRS     5
                                    Money market
LT securities          NRS    30                             RSL    20
                                    deposits
Variable-rate loan     RSA    40 ST savings                  RSL    40

ST loans               RSA    20 LT savings                  NRS    60

LT loans               NRS    60 Fed funds borrowing         RSL    55

Other assets           NRS    10 Equity                      NRS    10
                                                                     18
                             $195                                  $195
                Dollar gap and income

Dollar gap = interest sensitive assets – interest sensitive liabilities
           = ($15 + $20 + $40) – ($20 + $40 + $55)
           = $75 - $115
           = -$40




                                                                   19
                 Dollar gap and income

Gap               Cause       Rates…   Profits…
Positive          RSA$>RSL$   Rise     Rise
   (Asset)                    Fall     Fall
Negative          RSA$<RSL$   Rise     Fall
   (Liability)                Fall     Rise
Zero              RSA$=RSL$   Rise     No effect
                              Fall     No effect




                                                   20
Dollar gap and income

                               RSA$
interest  sensitivity ratio 
                               RSL$
                                $75
                             
                               $115
                              0.652



Ratio > 1 means asset-sensitive bank

                                       21
     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
                                                       22
 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.

                                          23
   Choosing time to manage dollar gap

                       Day    Day    Day     Day
               1 day                                  Total
                       2-7    8-30   31-90   91-360
  Assets
maturing or
 repriced
                $50    $25    $20    $10      $10     $115
  within
 Liabilities
maturing or
  repriced
                $30    $20    $20    $40      $35     $145
   within

Incremental
    gap
               +$20    +$5     $0    -$30     -$25    -$30


Cumulative
   gap
               +$20    +$25   +$25    -$5     -$30
                                                       24
            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
                                                 25
 Gap, interest rates, and profitability
• The change in dollar amount of net interest
  margin (NIM) is:



   ΔNIM  RSA$ (i)  RSL$ (i)  Gap$  (i)




                                                  26
 Gap, interest rates, and profitability

An increase in interest rates adversely affects
NIM because there are more RSL$ than
RSA$

  ΔNIM  RSA$  (i )  RSL$  (i )  Gap $  (i )
        $75  .02  $115  .02  $40  .02
          $0.80


                                                       27
 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).


                                             28
      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).

                                                        29
    Aggressive fund management

• Increase RSA$           • Increase RSL$
  – More Fed fund sales     – Borrow Fed funds
  – Buy marketable          – Issue CDs in
    securities                different sizes and
  – Make deposits in          maturities
    other banks




                                                    30
    Interest rate risk strategy?
• Depends on risk preferences and skills
  of the management team




                                       31
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.
                                           32
  Solution to correlation problem:
         Standardized gap
Assume GAP$ = RSA$ - RSL$
                 = $200 (com’l paper) - $500 (CDs)
                 = -$300
Assume the CD rate is 105% as volatile as 90-day T-
Bills, while the com’l paper rate is 30% as volatile.

Now calculate the
Standardized Gap = 0.30 ($200) - 1.05 ($500)
                  = $60 - $525
                  = -$460
                                                    33
Much more negative!
         Dollar gap analysis

       Dollar gap = RSA$ - RSL$


RSA$ > RSL$ = Positive gap

RSL$ > RSA$ = Negative gap

Impacts on net interest income



                                  34
Practice




           35
Hedging dollar gap

         • Background on
           futures

         • How to hedge dollar
           gap




                            36
              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.

                                                 37
                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


                                            38
Rose textbook
  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.
                                                   39
      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   98-16 188,460
Sept 99-25 100-18 99-16 99-24      -     11     102-05   99-10 42,622
Dec 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
                                                                  40
             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


                                                 41
      Change in Margin Account
         Value of   Change in
Day                              Margin Account
         Contract     Value

 0      $950,000                        $2,000

 1      $950,625      $625              $2,625

 2      $950,725      $100              $2,725

 3      $949,825      -$900             $1,825

 4      $948,325     -$1,500            $325

 5      $947,825      -$500     -$175   Margin Call!
                                                  42
                        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%
                                               discount yield  $1,000,000
       settlement price  $1,000,000 91 days 
                                                        360 days
                                               0.0517 $1,000,000
                        $1,000,000 91 days 
                                                    360 days
                        $1,000,000- $13,069
                        $986,931

                                                                             43
                     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:

                                             discount yield  $1,000,000
  settlement price  $1,000,000 91 days 
                                                      360 days
                                             0.0519 $1,000,000
                   $1,000,000 91 days 
                                                  360 days
                   $986,881                                           44
                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.
                                               45
Rose textbook
     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?
                                                             46
     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)1=$36.36
                                                               47
        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
                                                            48
Dollar gap hedging example

PV of net gain on assets and liabilities   $36.36

PV of gain on futures contracts            $   0

        Net gain                           $36.36




                                                    49
     Dollar gap hedging example
If interest rates increase by 2% (after the initial issue of CDs),
    bank’s 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



                                                                   50
        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

                                                                           51
      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             52
     Futures contracts to trade

                For dollar gap

                             V MC 
       number of contracts      b
                             F MF 
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.
                                                    53
 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.
                           V M 
      number of contracts   C   b
                            F MF 
                           $80M 6 months
                                        1.00
                           $1M 3 months 
                         80  2  1.00
                         160 contracts
                                                     54
    Example: Less than perfect
           correlation
Assume the correlation coefficient of cash and
futures position as interest rates change is 0.5.
                            V MC 
      number of contracts      b
                            F MF 
                          $80M 6 months
                                       0.5
                          $1M 3 months 
                        80  2  0.5
                        80 contracts



 We can lower our futures positions when the correlation
 is not perfectly positive.
                                                    55
     Payoffs for futures contracts
          Long Hedge                             Short Hedge
Payoff                                 Payoff         F0 = Contract price at time 0
                                                      F1 = Future price at time 1

    Buy futures                                            Sell futures

                    Gain                     Gain
0                                       0                                 F
                              F1   F        F1
            F0                                          F0




    Buy futures expecting                        Sell futures expecting
    interest rates to fall                       interest rates to rise
    increasing the value of                      lowering the price of
    the future contract.                         the futures.
                                                                          56
Practice




           57
                         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                                                      58
                      Duration
  • Average
    maturity of
    future cash
    flows (assets
    or liabilities)

  • Average time
    needed to
    recover the
    funds
    committed to
    investment
Rose                             59
             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


                                                             60
            Calculating duration
        n
           Expected CF in Period t
               (1 YTM)   t
                                    Period t
   D t 1

           Current Market Value or Price




Rose                                            61
                        Calculating duration
                         Period t      E(CF)        PV of E(CF)     PV of E(CF) x t

                            1              $100            $90.91            $90.91

                            2              $100            $82.64           $165.29
       Expected
       interest
                            3              $100            $75.13           $225.39
       income from
       loan
                            4              $100            $68.30           $273.21

                            5              $100            $62.09           $310.46

       Repayment of
                            5            $1,000           $620.92         $3,104.61
       loan principal
                         Price or
                                         $1,000                           $4,169.87
                         value

                            D = $4,169.87/$1,000 = 4.17 years
                                                                                62
Rose
                    Duration gap analysis

                                         i                                        i 
Net Worth   Avg. D  Total Assets              Avg. D  Total Liabilities 
                                       (1  i)  
                                                                                   (1  i) 
                                                                                            

                                           i
                   Net Worth   DGAP            TA
                                         (1  i )


        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.
                                                                                         63
             Duration gap analysis
                       Duration                               Duration
Assets                  (Years)     Claims                     (Years)


Cash           $100      0.00       CD, 1 year         $600     1.00
Business loans 400       1.25       CD, 5 year          300     5.00
                                     Total liabilities $900     2.33
Mortgage loans   500     7.00
                                    Equity            $100
Total        $1,000      4.00
                                    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
                                                                            64
                    Duration gap analysis

    Assume an interest rate of 8% and a change of 1% point
                                            i                                        i 
Net Worth   Avg. D  Total Assets                 Avg. D  Total Liabilities 
                                          (1  i)  
                                                                                      (1  i ) 
                                                                                                
                                 .01                         .01 
             4.00  $1,000              2.33  $900 
                               1  .08  
                                                             1  .08 
                                                                      
            $37.04  $19.42
            $17.62

                                                           Δi
                                 ΔNet Worth  DGAP              TA
                                                          (1 i)
                                                          .01
                                               1.903          $1,000
                                                        1  .08
                                               $17.62
                                                                                             65
           Duration gap and net worth

Gap              Cause            Rates…   Net Worth…
Positive         DA > DLx TL/TA   Rise     Falls
   (Asset)                        Fall     Rise
Negative         DA < DLx TL/TA   Rise     Rise
   (Liability)                    Fall     Fall
Zero             DA = DLx TL/TA   Rise     No effect
                                  Fall     No effect




                                                        66
    Duration gap management
• Defensive
  – Immunize net worth
    of bank
  – Duration gap ~ 0

• Aggressive
  – Use forecast of
    interest rate
    changes to manage
    bank net worth
                              67
Aggressive duration gap management

  If interest rates ↑, - duration gap, + Δ equity

  If interest rates ↓, + duration gap, + Δ equity




                                                68
        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
                                          69
  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%.

                                                   70
   Duration gap hedging example
                     Duration                            Duration
Assets                (Years)   Claims                    (Years)

Loans:
90-day        $500     0.25     CD, 90-day   $3,299.18     0.25
180-day        600     0.50
270-day      1,000     0.75
360-day      1,400     1.00

Total       $3,500     0.736


 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                71
  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




                                                        72
  Duration gap hedging example
                               N f FP
          D p  D rsa    Df 
                               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
                                               73
Duration gap hedging example
  Assume T-bills are yielding 12% so price is:
       Price = $100/(1.12).25 = $97.21

                               N f FP
          D p  D rsa    Df 
                               Vrsa
                              N f $97.21
          0.25  0.73  0.25
                              $3,221.50
          N f  64
      Df = 0.25 because T-bills are 90 days
      Negative 64 means to sell T-bill futures
                                                 74
Duration gap hedging example

              D p  D rsa
       Vrsa
                Df
Nf 
               FP
              0.25  0.73
    $3,221.50
                0.25
           $97.21
   63.63



                            75
   A perfect futures short hedge
 Month            Cash Market                   Futures Market
June      Bank makes commitment to        Sells 10 December munis
          purchase $1 million of muni     bond index futures at 96-8/32
          bonds yielding 8.59% (based     for $962,500.
          on current munis’ cash price
          at 98-28/32) for $988,750.


October   Bank purchases and then         Buys 10 December munis
          sells $1 million of munis       bond index futures at 93, or
          bonds to investors at a price   $930,000, to yield 8.95%.
          of 95-20/32 for $956,250


          Loss: ($32,500)                 Gain: $32,500


                                                                  76
An imperfect futures short hedge
 Month            Cash Market                Futures Market
October   Purchase $5 million           Sell $5 million T-bonds
          corporate bonds maturing      futures contracts at 86-
          Aug. 2005, 8% coupon at 87-   21/32:
          10/32:
                                        Contract value = $4,332,813
          Principal = $4,365,625
March     Sell $5 million corporate     Buy $5 million T-bond
          bonds at 79.0:                futures at 79-1/32:

          Principal = $3,950,000        Contract value = $3,951,563



          Loss: ($415,625)              Gain: $381,250


                                                                   77
    Complications using financial
              futures
•   Not used for speculation
•   Accounting for macro vs. micro hedges
•   Basis risk
•   Hedge need changes after hedge made
•   Liquidity effects



                                       78
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.                79
             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.

                                                           80
       Option players
                                  BANK buys
           Sells option
                                    option

        Collects               Pays premium;
        premium; gives         gets right to buy
Call
        right to buy from      from her
        her
        Collects               Pays premium;
        premium; gives         gets right to sell
Put     right to sell to her   to her


                                                81
  Option buyer actions
          Price rises           Price falls

       Buyer has right to   Buyer has right to
       buy at set price     buy a set price so
Call   so gains from        loses premium.
       buying then
       selling.
       Buyer has right to   Buyer has right to
       sell at set price    sell at set price
Put    so loses             so buys at lower
       premium.             price & sells at
                            set price
                                              82
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


                                83
     Relevant types of options
• Treasury bills
• Eurodollar futures
• Currencies




                                 84
     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.
                                                                     85
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
                      $36 $40    Price of security
-4

         Premium = $4

NOTE: Sellers earn premium if option not exercised by buyers.   86
  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
                                         87
        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.   88
     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.


                                                89
                 Needed Information
                                    Today       30 Days from
                                                    Now
Cash rates                          9.75%          11.25%
90-day Eurodollar Futures Rates     9.60%          11.00%
90-day Eurodollar, $1M Contract         Points of 100%
Futures Option (Put, pts of 100%)
Striking Price
   8875                             .00009          .0001
   8900                             .0005            .01
   8925                             .0009            .25
   8950                              .003            .50
   8975                              .007            .75
   9000                              .009           1.00
   9025                              .01            1.25
                                                            90
   9050                              .10            1.50
                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 firm’s
borrowing.

                                                                91
            Interest Rates Fall
If interest rates had fallen, then the value of the option
would have fallen also. The firm would have:

1) let the option expire, losing the $750 premium
2) 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.




                                                     92
                  Swaps
• Agreement between 2 parties to
  exchange (or swap) specified cash
  flows at specified intervals in the future

• Series of forward contracts




                                           93
                    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


                                               94
             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
                                                          95
               Swap Example
• Bank A                      • Bank B
  – Portfolio of fixed rate     – Portfolio of variable
    mortgages                     rate loans
  – Agrees to pay Bank          – Issued 11% $100 M
    B a fixed 11% per             Eurodollar bond
    year on $100 M              – Agrees to make
    every 6 months                variable rate
                                  payments on $100 M
                                  to Bank A at 35 basis
                                  points below LIBOR.

                                                    96
                     Swap example
                                       Fixed rate   Net pmt     Net pmt
                 Floating rate pmt
                                       pmt          from Bank   from Bank
Date    LIBOR    ½ x (LIBOR-.35%)
                                       ½ x (11%)    B to Bank   A to Bank
                 of $100 M                          A           B
                                       of $100 M

6/05    8.98%            --                --          --           --

                                       .055 x
                 ½ x (.0843-.0035) x
11/05   8.43%                          $100M =                  $1,460,000
                 100M=$4,040,000
                                       $5,500,000

                 ½ x (.1154-.0035) x
6/06    11.54%                         $5,500,000    $95,000
                 100M=$5,595,000

                 ½ x (.0992-.0035) x
11/06    9.92    100M=$4,785,000       $5,500,000               $715,000

                                                                   97
                  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.



                                                         98
          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.
                               99
               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.


                                       100
Solution



   • The firms arrange
     parallel loans for the
     initial investment
     and use the
     proceeds from the
     project to repay the
     loan.
                       101
            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.

                                                       102
  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.

                                                    103
   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.
                                                                  104
Questions?




             105

								
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