Chemical Futures
&Options Inc
MIDDLE EAST SEMINAR
BAHRAIN 1995
Speaker
Stephen Hulme VP
January 18/19
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Chemical Futures
&Options Inc
The construction of Synthetic
Swaps using 3 Month futures
strips
Introduction
• 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.
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Chemical Futures
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• 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.
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Chemical Futures
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• 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
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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-94
13-Apr-95
15-Apr-96
13-Oct-95
14-Oct-96
Months
6
0x6
12
6 x 12
18
12 x 18
24
18 x 24
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Chemical Futures
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• 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
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Chemical Futures
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IMM FRA Calculations
IMM FRA's
Future 1
9407
Dec-94
2X5
Future 2
9370
Future 3
IMM Discount Days
Factors
Mar-95
5X8
5.930%
6.300%
1.0150
1.0147
9329
Jun-95
8 X 11 6.710%
1.0183
Future 4
9298
Sep-95
11 X 14 7.020%
1.0177
Future 5
9267
Dec-95
14 X 17 7.330%
1.0185
Future 6
9260
Mar-96
17 X 20 7.400%
1.0187
Future 7
9247
Jun-96 20 X 23 7.530%
1.0190
Future 8
9236
Sep-96 23 X 26 7.640%
1.0193
note 1
note 2
91
84
98
91
91
91
91
91
note 3
note 1 = (10000 - future price) / 10000
note 2 = 1 +((Fut days / 360)*IMM FRA Rate )
note 3 = Days in Future Month
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Chemical Futures
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3 Mth FRA Days Calculation
Spot: 13-Oct
Spot Runs
3 Mth
6x9
9 x 12
12 x 15
15 x 18
18 x 21
21 x 24
13-Apr-95 - 13-Jul-95
13-Jul-95 - 13-Oct-95
13-Oct-95 - 15-Jan-96
15-Jan-96 - 15-Apr-96
15-Apr-96 - 15-Jul-96
15-Jul-96 - 14-Oct-96
91
92
94
91
91
91
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Chemical Futures
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6 Mth FRA Days Calculation
Spot: 13-Oct
Spot Runs
6 Mth
0x6
13-Oct-94 - 13-Apr-95
6 x 12 13-Apr-95 - 13-Oct-95
12 x 18 13-Oct-95 - 15-Apr-96
18 x 24 15-Apr-96 - 14-Oct-96
182
183
185
182
Total : 732
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Chemical Futures
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IMM & SPOT FRA DAY COUNT
CALENDAR
84
98
13-Apr-95
62
13-Oct-94
Future 4
20-Sep-95
Future 3
14-Jun-95
Future 2
22-Mar-95
13-Jul-95
29
6x9
0x6
91
69
9 x 12
6 x 12
91
13-Oct-95
23
91
26
12 x 15
65
15 x 18
12 x 18
26
Future 8
18-Sep-96
91
15-Apr-96
15-Jan-96
68
Future 7
19-Jun-96
Future 6
20-Mar-96
Future 5
20-Dec-95
65
91
15-Jul-96
26
18 x 21
14-Oct-96
65
26
21 x 24
18 x 24
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Chemical Futures
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SPOT FRA DISCOUNT
FACTORS
note 1
Future 1
Future 2
Future 3
Future 4
Future 5
Future 6
Future 7
Future 8
6x9
1.000000
1.010829
1.005371
1.000000
1.000000
9x12
1.000000
1.000000
1.012826
1.004456
1.000000
1.000000
12x15
1.000000
1.000000
1.000000
1.013230
1.005259
1.000000
1.000000
15x18
18x21
1.000000
1.013200
1.005309
1.000000
1.000000
1.000000
1.000000
1.013326
1.005402
1.000000
1.000000
21x24
1.000000
1.000000
1.013559
1.005480
1.000000
1.000000
note 1: IMM discount factor future 2 ^ (62/84) = 1.010829
IMM discount factor future 3 ^ (29/98) = 1.005371
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Chemical Futures
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3 Mth. FRA Calculation
Days
91
92
94
91
91
91
Spot: 13-Oct
Spot Runs
3 Mth
6x9
9 x 12
12 x 15
15 x 18
18 x 21
21 x 24
Rate
6.432 % = ((1.010829*1.005371) -1)*360/91
6.785 % = ((1.012826*1.004456) -1)*360/92
7.108 % = ((1.013230*1.005259) -1)*360/94
7.350 % = ((1.013200*1.005309) -1)*360/91
7.437 % = ((1.013326*1.005402) -1)*360/91
7.561 % = ((1.013559*1.005480) -1)*360/91
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Chemical Futures
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6 Mth. FRA Calculation
Spot: 13-Oct
Spot Runs
Days 6 Mth
Rate
182 0 x 6
5.750 % = spot rate
183 6 x 12
6.665 % = ((1+(91/360*6.432%))*(1+(92/360*6.785%))) - 1 / ((91+92)/360)
185 12 x 18
7.294 % = ((1+(94/360*7.108%))*(1+(91/360*7.350%))) - 1 / ((94+91)/360)
182 18 x 24
7.570 % = ((1+(91/360*7.437%))*(1+(91/360*7.561%))) - 1 / ((91+91)/360)
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Chemical Futures
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Compounded 2 Yr. Fixed Rate
7.570%
Return $1.1460
Invest $1.1037
7.294%
Return $1.1038
Invest $1.0639
6.665%
Return $1.0639
Invest $1.0291
5.750%
Return $1.0291
Invest $1.0000
13-Oct-94
0x6
13-Apr-95 -
15-Apr-96
13-Oct-95
6 x 12
12 x 18
14-Oct-96
18 x 24
2 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))
14
- 1 = 14.61%
Chemical Futures
&Options Inc
Conversion of 2 Yr effective
rate to semi annual bond
equivalent yield (BEY)
Decompound to 182.5 days (semiannual) :
182.5
Divide by total number of days
/732
= 0.2493
Raise 2 Yr eff. rate to resulting exponent [y^x]
Subtract 1
1.1460^0.249
= 0.0346
Annualise this result :
0.0346*365
= 12.6122
Divide by 182.5
12.6122/182.5
= 6.9108% BEY (Synthetic 2 Yr Swap Rate)
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Chemical Futures
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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
is180.
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Chemical Futures
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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:
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Chemical Futures
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Implied Libor discount rates
R12 = 100 * (( 1+(0.057500 * 182/360)) * ( 1+(0.06650 * 183/360)) - 1) * 360/365 =
6.3025%
R18 = 100 * (( 1+(0.063025 * 365/360)) * ( 1+(0.07294 * 185/360)) - 1) * 360/550 =
6.7942%
R24 = 100 * (( 1+(0.067942 * 550/360)) * ( 1+(0.07570 * 182/360)) - 1) * 360/732 =
7.1852%
Given these term Libor rates, the present value of a day
count adjusted $5000 change in each of the uncertain cash
flows is:
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Chemical Futures
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Present value of a 1bp rate
change for each future
6 x 12
PV02 (F2) : (62/360*10000)/(1+(0.063025*365/360)) = 1618.78
PV03 (F3) : (98/360*10000)/(1+(0.063025*365/360)) = 2558.72
PV04 (F4) : (23/360*10000)/(1+(0.063025*365/360)) = 600.52
12 x 18
PV04 (F4) : (68/360*10000)/(1+(0.067942*550/360)) = 1711.26
PV05 (F5) : (91/360*10000)/(1+(0.067942*550/360)) = 2290.07
PV06 (F6) : (26/360*10000)/(1+(0.067942*550/360)) = 654.31
18 x 24
PV06 (F6) : (65/360*10000)/(1+(0.071852*732/360)) = 1575.39
PV07 (F7) : (91/360*10000)/(1+(0.071852*732/360)) = 2205.50
PV08 (F8) : (26/360*10000)/(1+(0.071852*732/360)) = 630.16
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Chemical Futures
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Derived Futures Strip 2 Yr Swap
Future 1 Dec-94
Future 2 Mar-95
= $1618.78 / $25 = 64.75 contracts
Future 3 Jun-95
Future 4
Sep-95
= $2558.72 / $25 = 102.35 contracts
= $2311.78 / $25 = 92.47 contracts
Future 5
Dec-95
= $2290.07 / $25 = 91.60 contracts
Future 6 Mar-96
= $2229.70 / $25 = 89.19 contracts
Future 7
Jun-96
Future 8
Sep-96
= $2205.50 / $25 = 88.22 contracts
= $ 630.16 / $25 = 25.21 contracts
Total = 553.79 contracts
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Chemical Futures
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SUMMARY
• A synthetic swap with a fixed rate of 6.9108%
(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
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Chemical Futures
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Futures Sales Contacts
• Chicago: Mark Psaltis VP, Ph. 312 726 9250
• London : Stephen Hulme VP, Ph. 071 777 4419
• Philadelphia : Bob Damerjian VP, Ph. 215 561 3030
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.
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