Chemical Futures &Options Inc Speaker MIDDLE EAST SEMINAR BAHRAIN 1995 Stephen Hulme VP 1January 18/19

Chemical Futures &Options Inc The construction of Synthetic Swaps using 3 Month futures strips In developed financial markets with a liquid futures markets the LIBOR cash curve is driven by short term futures contracts. For most major currencies (US$, Yen, Sterling, Deutschemarks etc.) contracts exist that are based on LIBOR. Using the LIBOR cash curve Forward Rate Agreements (FRA’s) are priced. Introduction 2

Chemical Futures &Options Inc Since Interest Rate Swaps define a set of cash exchanges in the future they can be decomposed into a series of FRA’s: an FRA corresponding to each cash exchange in the future. Given that FRA pricing is driven by exchange traded futures, Swap pricing will also be derived from the futures market. All swaps that fall within the time horizon of liquid futures contracts will be priced and valued based on those futures contracts. 3

Chemical Futures &Options Inc FRAs and interest rate swaps are both interest derivative products that lock in a fixed rate for a specific period of time. A FRA can be thought of as a single period forward swap and a swap can be thought of as a series of FRAs strung together Given a calculated fixed rate of a string of FRAs the same as the OTC fixed rate swap the trader can be indifferent between the two alternatives Because FRAs are determined by exchange traded futures contracts, an interest rate swap can also be constructed out of a series of exchange traded futures contracts 4

Chemical Futures &Options Inc 2 Yr $ 100 Million loan paying interest every six months at a rate equivalent to the six month Libor rate 13-Oct Apr Oct Apr Oct-96 0 x 66 x 1212 x 1818 x 24 Months

Chemical Futures &Options Inc To hedge the exposure completely, we need to fix the future six month LIBOR rate for periods 6x12, 12x18 and 18x24. There is no interest rate exposure for period 0x6 because the rate for this period is the six month cash rate To hedge the exposure we can buy three FRAs: 6x12, 12x18 and 18x24. The all in rate achieved by buying the series of FRAs and the cash instrument is derived by compounding the rates for each of the four periods. Since FRAs are determined by futures contracts the interest rate swap can be constucted as follows 6

Chemical Futures &Options Inc IMM FRA Calculations Future 1 Future 2 Future 3 Future 4 Future 5 Future 6 Future 7 Future Dec-94 Mar-95 Jun-95 Sep-95 Dec-95 Mar-96 Jun-96 Sep-96 IMM FRA's 2 X % 5 X % 8 X % 11 X % 14 X % 17 X % 20 X % 23 X % IMM Discount Days Factors note 1note 2note 3 note 1 = ( future price) / note 2 = 1 +((Fut days / 360)*IMM FRA Rate ) note 3 = Days in Future Month 7

Chemical Futures &Options Inc 3 Mth FRA Days Calculation Spot:13-Oct Spot Runs 3 Mth 6 x 9 9 x x x x x Apr Jul Oct Jul Oct Jan Jan Apr Apr Jul Jul Oct

Chemical Futures &Options Inc 6 Mth FRA Days Calculation Spot:13-Oct Spot Runs 6 Mth 0 x 6 6 x x x Oct Apr Oct Apr Oct Apr Apr Oct-96 Total : 732 9

Chemical Futures &Options Inc IMM & SPOT FRA DAY COUNT CALENDAR 13-Oct Apr-95 - Future 2 22-Mar Jul-9513-Oct-9515-Jan Apr-9615-Jul Oct Jun-95 Future 3 20-Sep-95 Future 4 20-Dec-95 Future 5 20-Mar-96 Future 6 19-Jun-96 Future 7 18-Sep-96 Future x 9 0 x 6 9 x 12 6 x x x x 1818 x 2121 x x 24 10

Chemical Futures &Options Inc SPOT FRA DISCOUNT FACTORS Future 1 Future 2 Future 3 Future 4 Future 5 Future 6 Future 7 Future 8 6x x x x x x note 1 note 1: IMM discount factor future 2 ^ (62/84) = IMM discount factor future 3 ^ (29/98) =

Chemical Futures &Options Inc % = (( * ) -1)*360/ % = (( * ) -1)*360/92 Days Spot:13-Oct Spot Runs 3 Mth 6 x 9 9 x x x x x 24 Rate % = (( * ) -1)*360/ % = (( * ) -1)*360/ % = (( * ) -1)*360/ % = (( * ) -1)*360/91 3 Mth. FRA Calculation 12

Chemical Futures &Options Inc % = spot rate Days Spot:13-Oct 6 Mth. FRA Calculation Spot Runs 6 Mth 0 x 6 6 x x x 24 Rate % = ((1+(91/360*6.432%))*(1+(92/360*6.785%))) - 1 / ((91+92)/360) % = ((1+(94/360*7.108%))*(1+(91/360*7.350%))) - 1 / ((94+91)/360) % = ((1+(91/360*7.437%))*(1+(91/360*7.561%))) - 1 / ((91+91)/360) 13

Chemical Futures &Options Inc Compounded 2 Yr. Fixed Rate 5.750% 6.665% 7.294% 7.570% Invest $ Invest $ Invest $ Oct Apr Oct Apr Oct-96 0 x 66 x 1212 x 1818 x 24 Invest $ Return $ Return $ Return $ Return $ yr. effective fixed rate (A/360) = (1+(6Mth Libor*182/360)) * (1+ (6x12 FRA*183/360)) * (1+ (12x18 FRA*185/360)) * (1+ (18x24 FRA*182/360)) - 1 = 14.61% 14

Chemical Futures &Options Inc Conversion of 2 Yr effective rate to semi annual bond equivalent yield (BEY) Decompound to days (semiannual) : Divide by total number of days /732 = Raise 2 Yr eff. rate to resulting exponent [y^x] ^0.249 Subtract 1 = Annualise this result : *365 = Divide by /182.5 = % BEY (Synthetic 2 Yr Swap Rate) 15

Chemical Futures &Options Inc Allocation of Contracts to hedge BEY Swap Rate Here we are going to look at an approach that hedges against changes in the cash flow rather than changes in the net present value of the swap. Consider our simple generic swap. The first net cash payment is fixed at the time the deal is struck. The next three net payments depend on realised values of six month Libor. In each case, the nominal value of a basis point change in six month Libor for a $100 million swap is $5000 if the actual number of days between payments is

Chemical Futures &Options Inc Hedging the Legs of a Swap The present value of these changes, however, depend on term Libor to each payment. The first uncertain payment is made in twelve months, the second in eighteen, and the third in twenty four. Given the futures derived zero coupon money market rates that we have used in our swap example, the values of twelve, eighteen and twenty four month Libor we would need to discount these nominal cash flows are: 17

Chemical Futures &Options Inc Implied Libor discount rates R12 = 100 * (( 1+( * 182/360)) * ( 1+( * 183/360)) - 1) * 360/365 = % R18 = 100 * (( 1+( * 365/360)) * ( 1+( * 185/360)) - 1) * 360/550 = % R24 = 100 * (( 1+( * 550/360)) * ( 1+( * 182/360)) - 1) * 360/732 = % Given these term Libor rates, the present value of a day count adjusted $5000 change in each of the uncertain cash flows is: 18

Chemical Futures &Options Inc Present value of a 1bp rate change for each future PV02 (F2) : (62/360*10000)/(1+( *365/360)) = PV03 (F3) : (98/360*10000)/(1+( *365/360)) = PV04 (F4) : (23/360*10000)/(1+( *365/360)) = x 18 6 x 12 PV04 (F4) : (68/360*10000)/(1+( *550/360)) = PV05 (F5) : (91/360*10000)/(1+( *550/360)) = PV06 (F6) : (26/360*10000)/(1+( *550/360)) = x 24 PV06 (F6) : (65/360*10000)/(1+( *732/360)) = PV07 (F7) : (91/360*10000)/(1+( *732/360)) = PV08 (F8) : (26/360*10000)/(1+( *732/360)) =

Chemical Futures &Options Inc Derived Futures Strip 2 Yr Swap Future 1 Future 2 Future 3 Future 4 Future 5 Future 6 Future 7 Future 8 Dec-94 Mar-95 Jun-95 Sep-95 Dec-95 Mar-96 Jun-96 Sep-96 = $ / $25 = contracts = $ / $25 = contracts = $ / $25 = contracts = $ / $25 = contracts = $ / $25 = contracts = $ / $25 = contracts = $ / $25 = contracts Total = contracts 20

Chemical Futures &Options Inc SUMMARY A synthetic swap with a fixed rate of % (BEY) has been constructed from a strip of exchange traded futures contracts. Given an efficient market the cost of this strip versus the OTC interest rate swap should be cheaper to hedge the original 6 Month LIBOR reset exposure over 2 years due to narrow bid and ask spreads. Because futures markets are extremely liquid and transaction costs are low barriers to opening and closing positions are low 21

Chemical Futures &Options Inc Futures Sales Contacts Chicago: Mark Psaltis VP, Ph London : Stephen Hulme VP, Ph Philadelphia : Bob Damerjian VP, Ph The information herein has been obtained from sources believed to be reliable, but Chemical Futures & Options, Inc (CF&O) does not warrant its completeness or accuracy nor shall it be liable for damages arising out of any person’s reliance thereon. Prices, opinions and estimates reflect CF&O’s judgement on the date hereof and are subject to change without notice. Nothing contained herein shall be construed as an offer to buy or sell any commodity, security, option or futures contract. CF&O is a separately incorporated, wholly owned subsidiary of Chemical Banking Corporation. Member NASD/NFA/SFA. All rights reserved c 1995.