1. Techniques of asset/liability management: Futures, options, and swaps Outline –Financial futures –Options –Interest rate swaps

2. Financial futures Using financial futures markets to manage interest rate risk. –Futures contract: Standardized agreement to buy or sell a specified quantity of a financial instrument on a specified data at a set price. Buyer is in a long position, and seller is in a short position. Note: pricing and delivery occur at two points in time. Trading on CBOT, CBOE, and CME, as well as European and Asian exchanges. Exchange clearinghouse is a counterparty to each contract (lowers default risk). Margin is a small commitment of funds for performance bond purposes. Marked-to-market at the end of each day. Example: A trader buys on Oct. 2, 2000 one Dec. 2000 T-bill futures contact at $94.83 (or discount yield of 5.17%). The contract value is $1 million and maturity is 13 weeks. If the discount rate on T-bills rose 2 basis points (i.e., $25 per basis point or $100 per year/4 quarters), the buyer would lose $50 in the margin account. The settlement price is: $986,880.63 = $1,000,000 - 91[(.0519 x $1,000,000)/360]

3. Using interest rate futures to hedge a dollar gap position Long (or buy) and short (or sell) hedges. –If the bank has a positive dollar gap, and interest rates fall, buy a futures contract. When interest rates fall in the future, losses in the gap position are offset by gains in the futures position. –Suppose that the bank has a negative dollar gap, and interest rates are expected to rise in the future. Now go short in futures contracts. –Number of contracts to purchase in a hedge: [(V/F) x (M C / M F )] b V = value of cash flow to be hedged F = face value of futures contract M C = maturity of cash assets M F = maturity of futures contacts b = variability of cash market to futures market. Example: A bank wishes to use 3-month futures to hedge a $48 million positive dollar gap over the next 6 months. Assume the correlation coefficient of cash and futures positions as interest rates change is 1.0. N = [(48/1) x (6/3)] 1 = 96 contracts.

4. Payoffs for futures contracts Payoff 00 -F 1 F 1 F F Buy futures Sell futures Gain if interest rates fall and prices rise of debt securities. Gain if interest rates rise and prices fall of debt securities. F 0 F 0 = Contract price at time 0 F 1 = Future price at time 1

5. Balance sheet hedging example Consider the problem of a bank with a negative dollar gap facing an expected increase interest rates in the near future. Assume that bank has assets comprised of only one-year loans earning 10% and liabilities comprised of only 90-day CDs paying 6%. If interest rates do not change: Day090180270360 Loans: Inflows $1,000.00 Outflows $909.09 CDs: Inflow $909.09 $922.43 $935.98 $949.71 Outflows $922.43 $935.98 $949.71 $963.65 Net cash flows 0 0 0 0 $ 36.35 Notice that for loans $1,000/(1.10) = $909.09. Also notice that CDs are rolled over every 90 days at the constant interest rate of 6% [e.g., $909.09 (1.06) 0.25, where 0.25 = 90 days/360 days].

6. Balance sheet hedging example As a hedge against this possibility, the bank may sell 90-day financial futures with a par of $1,000. To simplify matters, we will assume only one T-bill futures contract is needed. In this situation the following entries on its balance sheet would occur over time. Day090180270360 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 interest rates will not change (i.e., $1,000/(1.06) 0.25 = $985.54).

7. Balance sheet hedging example If interest rates increase by 2% in the next year (after the initial issue of CDs), the bank’s net cash flows will be affected as follows: Day 090180270360 Loans: Inflows $1,000.00 Outflows $909.09 CDs: Inflow $909.09 $922.43 $940.35 $958.62 Outflows $922.43 $940.35 $958.62 $977.24 Net cash flows 0 0 0 0 $ 22.76 Thus, the net cash flows would decline by $13.59. In terms of present value, this loss equals $13.59/1.10 = $12.35.

8. Balance sheet hedging example We next show the effect of this interest rate increase on net cash flows from the short T-bill futures position: Day090180270360 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 The total gain in net cash flows is $13.80. In present value terms, this equals 4.60/(1.10).25 + 4.60/(1.10).50 + 4.60/(1.10).75 = $13.16. Thus, the gain on T-bill futures exceeds the loss on spot bank loans and CDs.

9. Using interest rate futures to hedge a duration gap Assume that a bank has a positive duration gap as follows: Days to maturityAssetsLiabilities 90$ 500$3,299.18 180 600 270 1,000 360 1,400 Also assume that single-payment loans at 12% are rolled over during one year only (i.e., all loans mature at the end of the year). Liabilities pay 10%. Present value of loans: $3,221.50 [= $500/(1.12) 1/4 + $600/(1.12) 1/2 + $1,000/(1.12) 3/4 +$1,400/(1.12)] Present value of liabilities: $3,221.50 = $3,299.18/(1.10) 1/4 Duration of assets = 0.73 years Duration of liabilities = 0.25 years.

10. Using interest rate futures to hedge a duration gap Solution: Sell (short) 3-month T-bill futures until the duration of assets falls to 0.25. D p = D rsa + D f N f FP/ V rsa D p = duration of cash and futures assets portfolio D rsa = duration of rate sensitive assets V rsa = market value of rate sensitive assets D f = duration of futures contract N f = number of futures contracts FP = futures price Assuming that 3-month T-bills are yielding 12% (price = $100/1.12 1/4 = $97.21): 0.25 = 0.73 + 0.25 (N f ) $97.21/$3,221.50 N f = 64

11. A perfect futures short hedge MonthCash Market Futures Market JuneSecurities firm makes a Sells 10 December munis bond commitment to purchaseindex futures at 96-8/32 for $1 million of munis bonds $962,500. yielding 8.59% (based on current munis’ cash price at 98-28/32) for $988,750. OctoberSecurities firm purchases Buys 10 December munis bond and then sells $1 million of index futures at 93, or $930,000, munis bonds to investorsto yield 8.95%. at a price of 95-20/32 for $956,250. Loss: (32,500)Gain: $32,500

12. An imperfect futures short hedge Date Cash Market Futures Market October/YrX Purchase $5million corporate bonds Sell $5 million T-bonds maturing Aug. 20005, 8% coupon futures contracts at at 87-10/32: 86-21/32: Principal = $4,365,625 Contract value = $4,332,813 March/YrX+1 Sell $5 million corporate bonds Buy $5 million T-bond futures at 79.0: at 79-21/32: : Principal = $3,950,00 Contract value = $3,951,563 Loss: ($415,625) Gain: $381,250

13. Complications in using financial futures Accounting and regulatory guidelines. Macro hedge of the bank’s entire portfolio -- cannot defer gains and losses on futures, so earnings are less stable with this hedge strategy. Micro hedge linked to a specific asset -- can defer gains and losses on futures until contracts mature. Basis risk is the difference between the cash and futures prices. These two prices are not normally perfectly correlated (e.g., corporate bond rates in a cash position versus T-bill futures rates). Bank gaps are dynamic and change over time. Futures options allow the execution of the futures position only to hedge losses in the cash position. Gains in the cash position are not offset by losses in the futures position.

14. Options Definition: Right but not obligation to buy or sell at a specified price (“striking price”) on or before a specified date (“expiration date”). –Call option: Right to buy -- pay “premium” to seller for this right. –Put Option: Right to sell -- pay “premium” to seller for this right. –Note: Seller of option must buy or sell as arranged in the option, so the seller gets a premium for this risk. The premium is the price of the option. The Black-Scholes option pricing model can be used to figure out the premium (or price) of an option. –Long position: The buyer of the option, who gains if the price of the option increases. –Short position: The seller of the option, who earns the premium if the option is not exercised (because it is not valuable to the buyer of the option).

15. Option Payoffs to Buyers 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

16. Option Payoffs to Buyers Gross profit Net payoff Price of security Put Option Premium = $5 NOTE: Sellers earn premium if option not exercised by buyers. $40 $35 Buy put for $5 with exercise price of $40. Payoff “ In the money ” 0 -4

17. Interest rate swaps BEFORE Firm 1 Firm 2 Fixed rate assets Variable rate assets Variable rate liabilities Fixed rate liabilities AFTER Firm 1 Firm 2 Fixed rate assetsVariable rate assets Fixed rate liabilities Variable rate liabilities Started in 1981 in Eurobond market Long-term hedge Private negotiation of terms Difficult to find opposite party Costly to close out early Default by opposite party causes loss of swap Difficult to hedge interest risk due to problem of finding exact opposite mismatch in assets or liabilities

18. Firm AFirm B Bank 13.1%Libor Starting conditions: Firm A borrows floating rate bank loan at Libor + 1% (premium for risk) Starting conditions: Firm B borrows fixed rate 12% bonds (AAA bonds with no premium for risk) Results (A) Firm A has total or “all-in” fixed rate obligation of 12% + 0.1%(bank service fee + 1.0% (premium over Libor) = 13.1%. (B) Firm B has floating rate obligation to pay LIBOR rate Interest rate SWAP Libor + 1% 12% Bank makes debt payments

19. Hedging strategies Use swaps for long-term hedging. Use futures and options for short-term hedges. Use futures to “lock-in” the price of cash positions in securities: – For example, a corporate treasurer has a payroll due in 5 days and wants to fix the value of marketable securities being held to meet the payroll -- a short hedge gives downside price protection in this case. Use options to minimize downside losses on a cash position and take advantage of possible profitable price movements in your cash position: – For example, you have a cash position in bonds and believe that interest rates are more likely to rise than fall -- -- you could buy by a put option on bonds -- if rates do rise, you are “in the money” on the option and offset losses in the cash position in bonds -- however, if rates fall, you do not exercise the option and make price gains on the cash position in bonds. Use options on futures to protect against losses in a futures position and take advantage of price gains in a cash position. Use options to speculate on price movements in stocks and bonds and put a floor on losses.