Chapter 7 and 8


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  • Increase rate on assets will increase NIM Increase rate on liabilities, decrease NIM Increase dollar amounts of funds (net assets) will increase NIM because rate on assets is higher than rate on liability Shifting earnings mix to higher paying assets or to cheaper sources of funds will increase NIM
  • Also known as funding gap, maturity gap Negative means the liabilities are more sensitive to interest rate changes than the assets
  • Target NIM can be around the same or can be changed (usually higher).
  • If we are hedging for next month, rising rates help us. However, if we think rates will rise after that, then rising rates will hurt us due to the negative dollar gap. The table suggests that management has consciously or unconsciously made decisions reflecting a belief that rates will rise in the ST (next 30 days) but fall after that.
  • Changes in the spread is often reflected in the change in the shape of the yield curve. Volume relates to bank growing or shrinking earning assets with scale of operations Change in mix is related to whether mgt wants fixed vs variable rates on assets and liabilities, between shorter and longer liabilities, and between higher and lower yield products.
  • Using earlier example. Interest income rises at 2% but a larger amount of liabilities are also growing at 2% rate. That means income will fall when interest rates rise.
  • Dollar gap assumes they are all repriced on the same day, which is not true. For example, a bank could have a zero 30-day gap, but with daily liabilities and 30-day assets NIM would react to changes in interest rates over time. A solution is to divide the assets and liabilities into maturity buckets (i.e., incremental gap) and manage each bucket separately. Of course, it is possible that liabilities are less correlated with interest rate movements than assets, or vice versa. Dollar gap may be set to increase NIM if interest rates increase, but equity values may decrease if the value of assets fall more than liabilities fall (i.e., the duration of assets is greater than the duration of liabilities). While GAP$ can adjust NIM for changes in interest rates, it does not consider effects of such changes on asset, liability, and equity values.
  • T-bill futures used to be the most popular but it has switched. T-bond value is based on underlying value of the bond; T-bill and Eurodollar time deposit futures are based upon interest rates.
  • Chicago Board of Trade Chicago Board Option Exchange Chicago Mercantile Exchange
  • Change: down 11 basis points from yesterday’s settle price.
  • Money in excess of the margin required may be withdrawn from the account. Bring margin account back up to $2,000
  • T-bill futures and Eurodollar time deposits are valued differently from the T-bond. 5.17% is discount on an annualized basis. We calculate the quarterly yield here. 91/360 = 25.28% of a year .2528 x .0517 = .013069 .013069 x $1,000,000 = $13,069, or this much discount from the $1 Million
  • 1 basis point = $25
  • Use 10% discount rate from loans.
  • Thought process: Worst case is rates rise. So what type of hedge can we get into that will increase in value when rates rise. When rates rise, value drops. So sell today and buy back at a lower price later. See a futures contract. Three contracts needed in this case.
  • $1,014.79 = $1,000 x (1 + .06/365 x 90) $1,034.50 = $1,014.49 x (1 + .08/365 x 90) $1,054.90 = $1,034.50 x (1 + .08/365 x 90) $1,075.71 = $1,054.90 x (1 + .08/365 x 90)
  • Interest rate changes from 6% to 8% during the first quarter. Spot price has dropped to $980.94.
  • Income from assets and liabilities dropped from $36.36 to $22.08 but with the hedge, the net loss is only $1.12 – smaller loss than with no hedge.
  • Cash flow means the size of the dollar gap.
  • Bank is concerned rates may fall, hurting NIM.
  • Sell short: sell at current high price then sell when prices drop when rates increase.
  • Multiplied by TL/TA because $volume of assets outweighs the $volume of liabilities (otherwise the bank is insolvent). The larger the duration gap, the more sensitive net worth is to changes in interest rates.
  • This is a positive duration gap. How will increasing interest rates affect net worth?
  • Notice the cash market is a purchase and the futures is a sale. If interest rates rise on purchase, the value of the munis drop. o hedge that, we sell futures to capture a gain if interest rates rise.
  • Macro hedges (hedging entire portfolio) must be accounted for with daily marked-to-market, making earnings variable. Micro hedges (hedging specific assets) need only be marked-to-market at end of quarter, making earnings more stable Basis risk: the rates on the futures and on the asset/liability are not identical. When interest rates move, the future and the asset/liability rates both move, preventing a perfect hedge. Changes in assets and liabilities after the hedge has been made changes the type and size of hedge needed Margin calls can cause liquidity problems.
  • If interest rates rise then underlying bond value falls making value of option rise.
  • Chapter 7 and 8

    1. 1. Chapters 7 and 8 Asset/Liability Management
    2. 2. Key topics <ul><li>Asset, liability, and funds management </li></ul><ul><li>Interest rate risk for corporations – a reminder </li></ul><ul><li>Market rates and interest rate risk for banks </li></ul><ul><li>Measuring interest rate sensitivity and the dollar gap </li></ul><ul><li>Duration gap analysis </li></ul><ul><li>Simulation and asset/liability management </li></ul><ul><li>Correlation among risks </li></ul>
    3. 3. Asset-liability management strategies <ul><li>Asset management – control of the composition of a bank’s assets to provide adequate liquidity and earnings and meet other goals. </li></ul><ul><li>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. </li></ul>
    4. 4. Asset-liability management strategies <ul><li>Funds management – balanced approach </li></ul><ul><ul><li>Control volume, mix, & return (cost) of assets and liabilities </li></ul></ul><ul><ul><li>Coordinate control of assets and liabilities </li></ul></ul><ul><ul><li>Maximize returns and minimize costs of managing assets and liabilities </li></ul></ul>
    5. 5. Asset-liability management Managing the bank’s response to changing interest rates Bank interest revenues Bank interest costs Market value of bank assets Market value of bank liabilities Bank’s net interest margin: dollar gap Bank’s net worth (equity): duration gap Bank’s investment value, profitability, and risk From Rose textbook
    6. 6. Rate effects on income Asset @ 8% $100 Total $100 Liability @ 4% $90 Equity $10 Total $100 Assets Claims
    7. 7. Rate effects on income Asset @ 8% $100 Total $100 Liability @ 6% $90 Equity $10 Total $100 Assets Claims Fixed interest loan but variable interest liability
    8. 8. Rate effects on equity value
    9. 9. Bond Valuation <ul><li>The value of an asset is the present value of its future cash flows. </li></ul><ul><li>V = PV (future cash flows) </li></ul><ul><li>Size, timing, and riskiness of the cash flows. </li></ul>
    10. 10. <ul><li>Bond has 30 years to maturity, an $100 annual coupon, and a $1,000 face value </li></ul><ul><li>Time 0 1 2 3 4 …30 </li></ul><ul><li>Coupons $100 $100 $100 $100 $100 </li></ul><ul><li>Face Value $1,000 </li></ul><ul><li>How much is this bond worth? Depends on </li></ul><ul><ul><li>current level of interest rates </li></ul></ul><ul><ul><li>riskiness of firm </li></ul></ul>Bond Valuation, Continued
    11. 11. Bond Valuation, Continued <ul><li>What if we require a 5% rate of return? </li></ul><ul><li>FV +1000 </li></ul><ul><li>PMT +100 </li></ul><ul><li>i 5 </li></ul><ul><li>n 30 </li></ul><ul><li>PV -1,768.62 </li></ul><ul><li>Premium Bond </li></ul><ul><li>What if we require a 20% rate of return? </li></ul><ul><li>FV +1000 </li></ul><ul><li>PMT +100 </li></ul><ul><li>i 20 </li></ul><ul><li>n 30 </li></ul><ul><li>PV -502.11 </li></ul><ul><li>Discount Bond </li></ul>
    12. 12. Interest Rate Risk and Time to Maturity Bond values ($) Interest rates (%) 1-year bond 30-year bond $1,768.62 $916.67 $1,047.62 $502.11 5 10 15 20 2,000 1,500 1,000 500 Value of a Bond with a 10% Coupon Rate for Different Interest Rates and Maturities <ul><li>Interest rate 1 year 30 years </li></ul><ul><li>5% $1,047.62 $1,768.62 </li></ul><ul><li>10 1,000.00 1,000.00 </li></ul><ul><li>15 956.52 671.70 </li></ul><ul><li>20 916.67 502.11 </li></ul><ul><ul><ul><ul><ul><li>Time to Maturity </li></ul></ul></ul></ul></ul>
    13. 13. Yield curve U.S. Treasury Securities
    14. 14. Yield curve and maturity gap <ul><li>Most banks have positive maturity gaps: assets have longer maturities than do liabilities </li></ul><ul><li>How does yield curve affect </li></ul><ul><ul><li>Net interest income? </li></ul></ul><ul><ul><li>Best equity value? </li></ul></ul>
    15. 15. Interest rate risk for banks <ul><li>In the short-term, interest rates change the amount of net interest income bank earns. </li></ul><ul><li>Changing market values of assets and liabilities affect total equity capital . </li></ul>
    16. 16. Fund management for income <ul><li>In general, fund management is a short-run tool – days, weeks </li></ul><ul><li>NIM (avg. 3.5%) depends on </li></ul><ul><ul><li>interest rates on assets and liabilities </li></ul></ul><ul><ul><li>dollar amount of funds </li></ul></ul><ul><ul><li>the earning mix (higher paying assets or cheaper funds) </li></ul></ul>
    17. 17. 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 LT securities NRS Money market deposits RSL 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
    18. 18. 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 LT securities NRS 30 Money market deposits RSL 20 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 $195 $195
    19. 19. Dollar gap and income Dollar gap = interest sensitive assets – interest sensitive liabilities = ($15 + $20 + $40) – ($20 + $40 + $55) = $75 - $115 = -$40
    20. 20. Dollar gap and income Gap Cause Rates… Profits… Positive RSA$>RSL$ Rise Rise (Asset) Fall Fall Negative RSA$<RSL$ Rise Fall (Liability) Fall Rise Zero RSA$=RSL$ Rise No effect Fall No effect
    21. 21. Dollar gap and income Ratio > 1 means asset-sensitive bank
    22. 22. Important Gap Decisions <ul><li>Choose time over which NIM is managed </li></ul><ul><li>Choose target NIM </li></ul><ul><li>To increase NIM : </li></ul><ul><ul><li>Develop correct interest rate forecast </li></ul></ul><ul><ul><li>Reallocate assets and liabilities to increase spread </li></ul></ul><ul><li>Choose volume of interest-sensitive assets and liabilities </li></ul>
    23. 23. Gap, interest rates, and profitability <ul><li>Incremental gaps measure the gaps for different maturity “buckets” (e.g., 0-7 days, 8-30 days, 31-90 days, and 91-365 days). </li></ul><ul><li>Cumulative gaps add up the incremental gaps from maturity bucket to bucket. </li></ul>
    24. 24. Choosing time to manage dollar gap 1 day Day 2-7 Day 8-30 Day 31-90 Day 91-360 Total Assets maturing or repriced within $50 $25 $20 $10 $10 $115 Liabilities maturing or repriced within $30 $20 $20 $40 $35 $145 Incremental gap +$20 +$5 $0 -$30 -$25 -$30 Cumulative gap +$20 +$25 +$25 -$5 -$30
    25. 25. NIM Influenced By: <ul><li>Changes in interest rates up or down </li></ul><ul><li>Changes in the spread between assets and liabilities </li></ul><ul><li>Changes in the volume of interest-sensitive assets and liabilities </li></ul><ul><li>Changes in the mix of assets and liabilities </li></ul>
    26. 26. Gap, interest rates, and profitability <ul><li>The change in dollar amount of net interest margin (  NIM) is: </li></ul>
    27. 27. Gap, interest rates, and profitability An increase in interest rates adversely affects NIM because there are more RSL$ than RSA$
    28. 28. Managing interest rate risk with dollar gaps <ul><li>Defensive fund management: guard against changes in NIM (e.g., near zero gap). </li></ul><ul><li>Aggressive fund management: seek to increase NIM in conjunction with interest rate forecasts (e.g., positive or </li></ul><ul><li>negative gaps). </li></ul>
    29. 29. Aggressive fund management <ul><li>Forecasts important to bank strategy </li></ul><ul><ul><li>If interest rates are expected to increase in the near future, the bank can exploit a positive dollar gap. </li></ul></ul><ul><ul><li>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). </li></ul></ul>
    30. 30. Aggressive fund management <ul><li>Increase RSA$ </li></ul><ul><ul><li>More Fed fund sales </li></ul></ul><ul><ul><li>Buy marketable securities </li></ul></ul><ul><ul><li>Make deposits in other banks </li></ul></ul><ul><li>Increase RSL$ </li></ul><ul><ul><li>Borrow Fed funds </li></ul></ul><ul><ul><li>Issue CDs in different sizes and maturities </li></ul></ul>
    31. 31. Interest rate risk strategy? <ul><li>Depends on risk preferences and skills of the management team </li></ul>
    32. 32. Problems with dollar gap management <ul><li>Time horizon problems related to when assets and liabilities are repriced. </li></ul><ul><li>Assumed correlation of 1.0 between market rates and rates on assets and liabilities </li></ul><ul><li>Focus on net interest income rather than shareholder wealth. </li></ul>1 2 3
    33. 33. Solution to correlation problem: Standardized gap <ul><ul><ul><li>Assume GAP$ = RSA$ - RSL$ </li></ul></ul></ul><ul><ul><ul><li>= $200 (com’l paper) - $500 (CDs) </li></ul></ul></ul><ul><ul><ul><li>= -$300 </li></ul></ul></ul><ul><ul><ul><li>Assume the CD rate is 105% as volatile as 90-day T-Bills, while the com’l paper rate is 30% as volatile. </li></ul></ul></ul><ul><ul><ul><li>Now calculate the </li></ul></ul></ul><ul><ul><ul><li>Standardized Gap = 0.30 ($200) - 1.05 ($500) </li></ul></ul></ul><ul><ul><ul><li>= $60 - $525 </li></ul></ul></ul><ul><ul><ul><li>= -$460 </li></ul></ul></ul><ul><ul><ul><li>Much more negative! </li></ul></ul></ul>
    34. 34. Dollar gap analysis Dollar gap = RSA$ - RSL$ RSA$ > RSL$ = Positive gap RSL$ > RSA$ = Negative gap Impacts on net interest income
    35. 35. Practice
    36. 36. Hedging dollar gap <ul><li>Background on futures </li></ul><ul><li>How to hedge dollar gap </li></ul>
    37. 37. Financial futures <ul><li>Futures contract </li></ul><ul><ul><li>Standardized agreement to buy or sell a specified quantity of a financial instrument on a specified date at a set price. </li></ul></ul><ul><ul><li>Purpose to shift risk of interest rate changes from risk-averse parties (e.g., commercial banks) to speculators willing to accept risk. </li></ul></ul>
    38. 38. Popular financial futures contracts <ul><li>U.S. Treasury bond futures </li></ul><ul><li>U.S. Treasury bill futures </li></ul><ul><li>3-month Eurodollar time deposits (most popular in world) </li></ul><ul><li>30-day Federal funds futures </li></ul><ul><li>1-month LIBOR futures contract </li></ul>% % % Rose textbook
    39. 39. Details of financial futures trading <ul><li>Buyer is in a long position, and seller is in a short position. </li></ul><ul><li>Trading on CBOT, CBOE, and CME, as well as European and Asian exchanges. </li></ul><ul><li>Exchange clearinghouse is a counterparty to each contract (lowers default risk). </li></ul><ul><li>Margin is a small commitment of funds for performance bond purposes. </li></ul><ul><li>Marked-to-market at the end of each day. </li></ul><ul><li>Pricing and delivery occur at two points in time. </li></ul>
    40. 40. WSJ Futures Price Quotations <ul><li>INTEREST RATE </li></ul><ul><li> Lifetime Open Open High Low Settle Change High Low Interest </li></ul><ul><li>TREASURY BONDS (CBT)— $100,000, pts. 32nds of 100% </li></ul><ul><li>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 </li></ul><ul><li>Futures contract for September: </li></ul><ul><li>99 + 24/32 = .9975 </li></ul><ul><li>0.9975 x $100K = $99,750 </li></ul>
    41. 41. Margin Account <ul><li>Participants in futures contracts use margin accounts which are marked-to-market daily. </li></ul><ul><li>Assume a financial manager buys a T-bill futures contract with initial margin account of $2,000. </li></ul><ul><li>Contracts is initially priced at $950K </li></ul>
    42. 42. Change in Margin Account Day Value of Contract Change in Value Margin Account 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!
    43. 43. T-Bill futures <ul><li>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). </li></ul><ul><li>Discount yield is $100 – $94.83 = $5.17 or 5.17% </li></ul>
    44. 44. T-Bill futures <ul><ul><ul><li>Suppose discount rate on T-bills rises 2 basis points to 5.19% </li></ul></ul></ul><ul><ul><ul><li>Drop in value in margin account realized that day: </li></ul></ul></ul><ul><ul><ul><li>$1,000,000 x (.0002/4) qtrs per year = $50 </li></ul></ul></ul><ul><ul><ul><li>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: </li></ul></ul></ul>
    45. 45. Hedging with Futures <ul><li>Selling price on futures contract reflects investors’ expectations of interest rates and underlying security value at due date </li></ul><ul><li>Hedging requires bank to take opposite position in futures market from its current position (dollar gap) today. </li></ul>Rose textbook
    46. 46. Dollar gap hedging example <ul><li>Bank with a negative dollar gap </li></ul><ul><ul><li>More rate sensitive liabilities than assets </li></ul></ul><ul><li>Hoping rates will decline but afraid that rates will increase </li></ul><ul><ul><li>increase interest expense more than interest income making net interest margin drop </li></ul></ul><ul><li>Bank has assets comprised of only one-year $1000 loans earning 10% and liabilities comprised of only 90-day CDs paying 6%. </li></ul><ul><li>What cash flows do we expect if interest rates do NOT change? </li></ul>
    47. 47. Dollar gap hedging example <ul><li>Day 0 90 180 270 360 </li></ul><ul><li>Loans: </li></ul><ul><li>Inflows $1,100 </li></ul><ul><li>Outflows $1,000 </li></ul><ul><li>CDs: </li></ul><ul><li>Inflow $1000 $1014.67 $1029.56 $1044.67 </li></ul><ul><li>Outflows $1014.67 $1029.56 $1044.67 $1060 </li></ul><ul><li>Net C.F. 0 0 0 0 $ 40.00 </li></ul><ul><li>FV of loans = $1,000 x (1.10) = $1,100 </li></ul><ul><li>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]. </li></ul><ul><li>PV ($40) = $40/(1.10) 1 =$36.36 </li></ul>
    48. 48. Dollar gap hedging example <ul><li>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 </li></ul><ul><li>Day 0 90 180 270 360 </li></ul><ul><li>T-bill futures (sold) </li></ul><ul><li>Receipts $985.54 $985.54 $985.54 </li></ul><ul><li>T-bill (spot market </li></ul><ul><li>purchase) </li></ul><ul><li>Payments $985.54 $985.54 $985.54 </li></ul><ul><li>Net cash flows 0 0 0 </li></ul><ul><li>It is assumed here that the T-bills pay 6% and bank managers are wrong -- interest rates do NOT change </li></ul>
    49. 49. 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
    50. 50. Dollar gap hedging example <ul><li>If interest rates increase by 2% (after the initial issue of CDs), bank’s net cash flows will change as follows: </li></ul><ul><li>Day 0 90 180 270 360 </li></ul><ul><li>Loans: </li></ul><ul><li>Inflows 1,100.00 </li></ul><ul><li>Outflows $1,000 </li></ul><ul><li>CDs: </li></ul><ul><li>Inflow $1000 $1014.49 $1034.50 $1054.90 </li></ul><ul><li>Outflows $1014.49 $1034.50 $1054.90 $1075.71 </li></ul><ul><li>Net C.F. 0 0 0 0 $ 24.29 </li></ul><ul><li>6% 8% 8% </li></ul><ul><li>PV ($24.29) = $24.29/(1.10) 1 = $22.08 </li></ul>
    51. 51. Dollar gap hedging example <ul><li>Effect of 2% interest rate increase on net cash flows from short T-bill futures position: </li></ul><ul><li>Day 0 90 180 270 360 </li></ul><ul><li>T-bill futures (sold) </li></ul><ul><li>Receipts $985.54 $985.54 $985.54 </li></ul><ul><li>T-bill (spot market Purchase) </li></ul><ul><li>Payments $980.94 $980.94 $980.94 </li></ul><ul><li>Net cash flows $4.60 $4.60 $4.60 </li></ul><ul><li>$980.94 = $1000/(1.08) .25 </li></ul><ul><li>Total gain is $13.80 ($4.60 x 3) </li></ul><ul><li>PV = 4.60/(1.10) .25 + 4.60/(1.10) .50 + 4.60/(1.10) .75 = $13.16 </li></ul>
    52. 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. 53. Futures contracts to trade <ul><li>V = value of cash flow to be hedged </li></ul><ul><li>F = face value of futures contract </li></ul><ul><li>M C = maturity of cash assets </li></ul><ul><li>M F = maturity of futures contacts </li></ul><ul><li>b = variability of cash market to futures market. </li></ul>For dollar gap
    54. 54. Example: Perfect correlation <ul><ul><ul><li>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. </li></ul></ul></ul><ul><ul><ul><li>Assume the correlation coefficient of cash and futures positions as interest rates change is 1.0. </li></ul></ul></ul>
    55. 55. Example: Less than perfect correlation <ul><ul><ul><li>Assume the correlation coefficient of cash and futures position as interest rates change is 0.5. </li></ul></ul></ul>We can lower our futures positions when the correlation is not perfectly positive.
    56. 56. Payoffs for futures contracts Payoff Payoff 0 0 F 1 F F Buy futures Sell futures Buy futures expecting interest rates to fall increasing the value of the future contract. Sell futures expecting interest rates to rise lowering the price of the futures. F 0 F 0 F 0 = Contract price at time 0 F 1 = Future price at time 1 F 1 Long Hedge Short Hedge Gain Gain
    57. 57. Practice
    58. 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. 59. Duration <ul><li>Average maturity of future cash flows (assets or liabilities) </li></ul><ul><li>Average time needed to recover the funds committed to investment </li></ul>Rose
    60. 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. 61. Calculating duration Rose
    62. 62. Calculating duration Rose Period t E(CF) PV of E(CF) PV of E(CF) x t Expected interest income from loan 1 $100 $90.91 $90.91 2 $100 $82.64 $165.29 3 $100 $75.13 $225.39 4 $100 $68.30 $273.21 5 $100 $62.09 $310.46 Repayment of loan principal 5 $1,000 $620.92 $3,104.61 Price or value $1,000 $4,169.87 D = $4,169.87/$1,000 = 4.17 years
    63. 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. 64. Duration gap analysis 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 Assets Claims Duration (Years) Duration (Years) D A =($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 D L =($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. 65. Duration gap analysis Assume an interest rate of 8% and a change of 1% point
    66. 66. Duration gap and net worth Gap Cause Rates… Net Worth… Positive D A > D L x TL/TA Rise Falls (Asset) Fall Rise Negative D A < D L x TL/TA Rise Rise (Liability) Fall Fall Zero D A = D L x TL/TA Rise No effect Fall No effect
    67. 67. Duration gap management <ul><li>Defensive </li></ul><ul><ul><li>Immunize net worth of bank </li></ul></ul><ul><ul><li>Duration gap ~ 0 </li></ul></ul><ul><li>Aggressive </li></ul><ul><ul><li>Use forecast of interest rate changes to manage bank net worth </li></ul></ul>
    68. 68. Aggressive duration gap management <ul><ul><li>If interest rates ↑ , - duration gap, + Δ equity </li></ul></ul><ul><ul><li>If interest rates ↓ , + duration gap, + Δ equity </li></ul></ul>
    69. 69. Duration gap hedging <ul><li>Positive gap </li></ul><ul><ul><li>Reduce duration of assets </li></ul></ul><ul><ul><li>Increase duration of liabilities </li></ul></ul><ul><ul><li>Short position in financial futures </li></ul></ul><ul><li>Negative gap </li></ul><ul><ul><li>Increase duration of assets </li></ul></ul><ul><ul><li>Decrease duration of liabilities </li></ul></ul><ul><ul><li>Long position in financial futures </li></ul></ul>
    70. 70. Duration gap hedging example <ul><li>Assume bank has positive duration gap: </li></ul><ul><ul><li>Days to maturity Assets Liabilities </li></ul></ul><ul><ul><li> 90 $ 500 $3,299.18 </li></ul></ul><ul><ul><li>180 600 </li></ul></ul><ul><ul><li>270 1,000 </li></ul></ul><ul><ul><li> 360 1,400 </li></ul></ul><ul><ul><li>Assets are single-payment loans at 12% </li></ul></ul><ul><ul><li>Liabilities are 90-day CDs paying 10%. </li></ul></ul>
    71. 71. Duration gap hedging example 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 Assets Claims Duration (Years) Duration (Years) D A =($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 <ul><ul><li>PV (loans) = $500/(1.12) .25 + $600/(1.12) .50 + $1,000/(1.12) .75 + $1,400/(1.12) 1 = $3,221.50 </li></ul></ul><ul><ul><li>PV (CDs) = $3,299.18/(1.10) .25 = $3,221.50 </li></ul></ul>
    72. 72. Duration gap hedging example <ul><ul><li>Duration gap = 0.736 years – 0.250 years = 0.486 years </li></ul></ul><ul><ul><li>Positive duration gap! </li></ul></ul><ul><ul><li>Interest rates rise and net worth declines! </li></ul></ul><ul><ul><li>Sell 3-month T-bill futures until duration of assets = 0.25 years, the duration of the liabilities </li></ul></ul>Sell!
    73. 73. Duration gap hedging example <ul><ul><li>D p = duration of cash and futures assets portfolio </li></ul></ul><ul><ul><li>D rsa = duration of rate-sensitive assets </li></ul></ul><ul><ul><li>V rsa = market value of rate-sensitive assets </li></ul></ul><ul><ul><li>D f = duration of futures contract </li></ul></ul><ul><ul><li>N f = number of futures contracts </li></ul></ul><ul><ul><li>FP = futures price </li></ul></ul>
    74. 74. Duration gap hedging example D f = 0.25 because T-bills are 90 days Negative 64 means to sell T-bill futures Assume T-bills are yielding 12% so price is: Price = $100/(1.12) .25 = $97.21
    75. 75. Duration gap hedging example
    76. 76. A perfect futures short hedge Month Cash Market Futures Market June Bank makes commitment to purchase $1 million of muni bonds yielding 8.59% (based on current munis’ cash price at 98-28/32) for $988,750. Sells 10 December munis bond index futures at 96-8/32 for $962,500. October Bank 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
    77. 77. An imperfect futures short hedge Month Cash Market Futures Market October Purchase $5 million corporate bonds maturing Aug. 2005, 8% coupon at 87-10/32: Principal = $4,365,625 Sell $5 million T-bonds futures contracts at 86-21/32: Contract value = $4,332,813 March Sell $5 million corporate bonds at 79.0: Principal = $3,950,000 Buy $5 million T-bond futures at 79-1/32: Contract value = $3,951,563 Loss: ($415,625) Gain: $381,250
    78. 78. Complications using financial futures <ul><li>Not used for speculation </li></ul><ul><li>Accounting for macro vs. micro hedges </li></ul><ul><li>Basis risk </li></ul><ul><li>Hedge need changes after hedge made </li></ul><ul><li>Liquidity effects </li></ul>
    79. 79. Hedging with Options <ul><li>Alternative to financial futures contracts </li></ul><ul><li>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. </li></ul>
    80. 80. Option Terminology <ul><li>Call option — a contract that gives the owner the right to buy an asset at a fixed price for a specified time. </li></ul><ul><li>  </li></ul><ul><li>Put option — a contract that gives the owner the right to sell an asset at a fixed price for a specified time. </li></ul><ul><li>  </li></ul><ul><li>Strike or exercise price — the fixed price agreed upon in the option contract. </li></ul><ul><li>Expiration date — the last date of the option contract. </li></ul>
    81. 81. Option players Sells option BANK buys option Call Collects premium; gives right to buy from her Pays premium; gets right to buy from her Put Collects premium; gives right to sell to her Pays premium; gets right to sell to her
    82. 82. Option buyer actions Price rises Price falls Call Buyer has right to buy at set price so gains from buying then selling. Buyer has right to buy a set price so loses premium. Put Buyer has right to sell at set price so loses premium. Buyer has right to sell at set price so buys at lower price & sells at set price
    83. 83. Big Differences <ul><li>Biggest difference between futures option and futures contract: </li></ul><ul><li>Premium paid for option is most that can be lost in futures option. </li></ul><ul><li>Loss can be unlimited for futures contract </li></ul>
    84. 84. Relevant types of options <ul><li>Treasury bills </li></ul><ul><li>Eurodollar futures </li></ul><ul><li>Currencies </li></ul>
    85. 85. Option Payoffs to Buyers of Calls Payoff Premium = $4 Gross payoff Net payoff Price of security Call Option $100 $104 Buy for $4 with exercise price $100 “ In the money ” NOTE: Sellers earn premium if option not exercised by buyers. -4
    86. 86. Option Payoffs to Buyers of Puts Gross profit Net payoff Price of security Put Option Premium = $4 NOTE: Sellers earn premium if option not exercised by buyers. $40 $36 Buy put for $4 with exercise price of $40. Payoff “ In the money ” 0 -4
    87. 87. Dollar gap and futures options <ul><li>Negative dollar gap means net interest income falls if interest rates rise </li></ul><ul><li>Protect against rising interest rates </li></ul><ul><li>Buy an interest rate put option </li></ul><ul><li>Interest rates rise: net interest income falls but value of put rises </li></ul><ul><li>Interest rates fall: net interest income rises but value of put falls </li></ul>
    88. 88. Futures Option Example <ul><li>Most recent cash flow forecast indicates in 30 days bank needs to borrow $3 million for 3 months. </li></ul><ul><li>Current yield curve is relatively flat with short-term rates at 9.75%. </li></ul><ul><li>Rate seems reasonable so bank would like to “lock-in” the rate. </li></ul>Based on Short-term Financial Mgt, by Maness and Zietlow, 2002.
    89. 89. Eurodollar Futures Options <ul><li>Based on $1 million 3-month eurodollar deposit </li></ul><ul><li>Traded on the International Monetary Market of Chicago Mercantile Exchange. </li></ul><ul><li>Strike price is quoted as an index. So 9300 represents an index value of 93, which is related to a 7% annualized discount rate. </li></ul>
    90. 90. 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 Futures Option (Put, pts of 100%) Points 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 9050 .10 1.50
    91. 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 firm’s borrowing.
    92. 92. Interest Rates Fall <ul><li>If interest rates had fallen, then the value of the option </li></ul><ul><li>would have fallen also. The firm would have: </li></ul><ul><li>let the option expire, losing the $750 premium </li></ul><ul><li>sold the option at a price less than $750 </li></ul><ul><li>In either case, the loss in the value of the option </li></ul><ul><li>would have been offset by reduced costs of borrowing. </li></ul>
    93. 93. Swaps <ul><li>Agreement between 2 parties to exchange (or swap) specified cash flows at specified intervals in the future </li></ul><ul><li>Series of forward contracts </li></ul>
    94. 94. Swaps <ul><li>Started in 1981 in Eurobond market </li></ul><ul><li>Long-term hedge </li></ul><ul><li>Private negotiation of terms </li></ul><ul><li>Difficult to find opposite party </li></ul><ul><li>Costly to close out early </li></ul><ul><li>Default by opposite party causes loss of swap </li></ul><ul><li>Difficult to hedge interest rate risk due to problem of finding exact opposite mismatch in assets or liabilities </li></ul>
    95. 95. Interest rate swaps <ul><li>BEFORE </li></ul><ul><li>Bank 1 Bank 2 </li></ul><ul><li>Fixed rate assets Variable rate assets </li></ul><ul><li>Variable rate liabilities Fixed rate liabilities </li></ul><ul><li>Firm 1 has negative dollar gap </li></ul><ul><li>Firm 2 has positive dollar gap </li></ul><ul><li>AFTER </li></ul><ul><li>Bank 1 Bank 2 </li></ul><ul><li>Fixed rate assets Variable rate assets </li></ul><ul><li>Fixed rate liabilities Variable rate liabilities </li></ul>
    96. 96. Swap Example <ul><li>Bank A </li></ul><ul><ul><li>Portfolio of fixed rate mortgages </li></ul></ul><ul><ul><li>Agrees to pay Bank B a fixed 11% per year on $100 M every 6 months </li></ul></ul><ul><li>Bank B </li></ul><ul><ul><li>Portfolio of variable rate loans </li></ul></ul><ul><ul><li>Issued 11% $100 M Eurodollar bond </li></ul></ul><ul><ul><li>Agrees to make variable rate payments on $100 M to Bank A at 35 basis points below LIBOR. </li></ul></ul>
    97. 97. Swap example Date LIBOR Floating rate pmt ½ x (LIBOR-.35%) of $100 M Fixed rate pmt ½ x (11%) of $100 M Net pmt from Bank B to Bank A Net pmt from Bank A to Bank B 6/05 8.98% -- -- -- -- 11/05 8.43% ½ x (.0843-.0035) x 100M=$4,040,000 .055 x $100M = $5,500,000 $1,460,000 6/06 11.54% ½ x (.1154-.0035) x 100M=$5,595,000 $5,500,000 $95,000 11/06 9.92 ½ x (.0992-.0035) x 100M=$4,785,000 $5,500,000 $715,000
    98. 98. Currency Swap <ul><li>Two firms agree to exchange a specific amount of one currency for a specific amount of another at specific dates in the future. </li></ul><ul><li>Two multinational companies with foreign projects need to obtain financing. </li></ul><ul><ul><li>Firm A is based in England and has a U.S. project. </li></ul></ul><ul><ul><li>Firm B is based in the U.S. and has an English project. </li></ul></ul>
    99. 99. Exchange Rate Risk <ul><li>Both firms want to avoid exchange rate fluctuations. </li></ul><ul><li>Both firms receive currency for investment at time zero and repay loan as funds are generated in the foreign project. </li></ul>
    100. 100. Constraints <ul><li>Both firms can avoid XR changes if they arrange for loans in the country of the project. </li></ul><ul><li>Both firms can borrow </li></ul><ul><li>more cheaply in home </li></ul><ul><li>country. </li></ul><ul><li>  </li></ul>
    101. 101. Solution <ul><li>The firms arrange parallel loans for the initial investment and use the proceeds from the project to repay the loan. </li></ul>
    102. 102. Hedging strategies <ul><li>Use swaps for long-term hedging. </li></ul><ul><li>Use futures and options for short-term hedges. </li></ul><ul><li>Use futures to “lock-in” the price of cash positions in securities </li></ul><ul><li>Use options to minimize downside losses on a cash position and take advantage of possible profitable price movements in your cash position </li></ul><ul><li>Use options on futures to protect against losses in a futures position and take advantage of price gains in a cash position. </li></ul><ul><li>Use options to speculate on price movements in stocks and bonds and put a floor on losses. </li></ul>
    103. 103. Problems with duration gap <ul><ul><li>Overly aggressive management “bets the bank.” </li></ul></ul><ul><ul><li>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 </li></ul></ul><ul><ul><li>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. </li></ul></ul>
    104. 104. Other issues in gap analyses <ul><li>Simulation models </li></ul><ul><ul><li>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. </li></ul></ul><ul><li>Correlation among risks </li></ul><ul><ul><li>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. </li></ul></ul><ul><ul><li>Gap management may make the bank less liquid. </li></ul></ul>
    105. 105. Questions?