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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