Interest Rate Futures
Content
MONEY MARKET FUTURES
1. 2. 3. 4. 5. 6.
Conventions and Contract Specifications.............................................. 3 Main Markets of Money Market Futures.................................................. 7 Exchange and Clearing House ................................................................ 8 The Margin System ................................................................................... 9 Comparison: Money Market Futures vs. FRA ...................................... 14 Function of Futures for Pricing and Hedging FRAs............................ 15 6.1 6.2 6.3 6.4 6.5 6.6 Calculation of 3-months IMM FRAs ................................................ 15 Calculation of IMM FRAs with longer Periods (Futures Strips)... 15 Calculation of non-IMM FRAs ......................................................... 16 Stack Hedging .................................................................................. 17 Significance of Convexity Effects on FRA/Futures Hegdes ........ 18 Calculating the Hedge Ratio for FRA/Futures Hedge Positions.. 19
7.
Spread Strategies ................................................................................... 21
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MONEY MARKET FUTURES
Money market futures are exchange-traded interest rate contracts. Contrary to their counterpart in the OTC market – the FRA – the specifications of futures are strongly standardised. Usually, the underlying is a 3-month deposit, in some currencies also a 1month deposit, that represents the interest rate of a future time period.
Money market futures can be used like FRAs. That is, to eliminate a future interest rate risk (hedging) speculate on interest rate trends (trading) to arbitrage between different markets (arbitrage)
Money market futures are standardised products, because they are traded in the exchange market. Thus, some specifications are already fixed by the particular exchange:
contract volume maturity dates marginal price changes (tick size) value of a price change by one tick based on one contract (tick value)
For money market futures the most important exchanges are Euronext.Liffe (London), CME (Chicago) and SGX (Singapore) resp. Tiffe (Tokio). Mostly, futures contracts can only be closed at the same exchange where the position has been opened. Some contracts can be sold or bought (and consequently closed), at different exchanges [e.g. a USD 3-months contract purchased in Chicago (CME) and sold in Singapore (Simex)]. Thus the contract can be traded 24 hours and not only during the trading hours at the particular exchange.
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1.
Conventions and Contract Specifications
Trade dates Trade dates of money market futures are set by the futures exchange. For the core markets these are always the third Wednesday of the last month of the quarter (March, June, September, December). These trade dates are called IMM-dates (International money market dates).
The delivery months have the following abbreviations: March June September December H M U Z
(Note: the abbreviations do not follow any logic)
In addition, at most futures exchanges so-called serial months are traded. These are the maturities between the IMM dates. At the LIFFE for example, in addition to the IMM dates, 4 serial months are traded. Consequently, there are maturities for all following 6 months.
Trade date: Maturities: May June July August September October
4th April
(serial month) (IMM) (serial month) (serial month) (IMM) (serial Month)
(after settlement of the May contract the next new serial month will be November)
Front month is the contract with the next maturity. Contracts with a later maturity are called Back months. For the front month liquidity is usually the highest.
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Last trading day Last trading days of futures are determined by the exchanges and are usually two days before delivery date (an exception is GBP, where the theoretical delivery date is the last trading date, i.e. same-day fixing).
Quotation The quotation for futures prices is: 100.00 minus interest rate Therefore a forward interest rate of 4.50 % p.a. (i.e. an interest rate for a future period) equals a futures price of 95.50 (= 100 – 4.50). The consequences of this quoting convention are illustrated below:
interest rates interest rates
prices prices
If the interest rate rises from 4.50 % to 5 %, the future price will fall from 95.50 to 95.00. If the interest rate falls from 4.50 % to 4 %, the future price will rise from 95.50 to 96.00.
With the quotation of an interest rate on the basis of 100, the buying/selling of a money market future has just the opposite effect to an FRA purchase/sale:
FRA purchase = FRA sale =
future short future long
A future's quote of JUNE (M) 96.64 / 96.65 corresponds to an interest rate of 3.35 % / 3.36 % p.a. for the term from the third Wednesday in June XY until the third Wednesday in September XY, in a specific currency.
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Underlying Usually, the underlying is a 3-months interbank deposit (e.g. Eurodollar, Euroyen, Euro Swiss Franc, EURIBOR). The fixing for these contracts is normally BBA LIBOR (resp. EURIBOR for EURIBOR futures). The term is always exactly 90 days for the 3-months futures period (resp. 30 days for a 1-month futures period). The fixed LIBOR resp. EURIBOR though is calculated on the exact number of days.
Volume of the contract Not only the underlying but also the volume (principal) of a future contract is exactly specified. (see table below)
Futures purchase as hedging operation: as speculation: protection against falling interest rates speculation on falling interest rates
Futures sale as hedging operation: as speculation: protection against rising interest rates speculation on rising interest rates
Tick A tick is the marginal movement of the futures price. For EUR, USD and JPY money market futures, a tick is usually half a basis point, i.e. a hundredth of 0.5 % (= 0.005 % or 0.00005), for GBP contracts it is 1 BP. (see table below)
Tick value The tick value is the profit or loss which occurs when the price changes by one tick. Also the tick value is specified by the exchange (e.g. USD 12.5 for the 3-months Eurodollar contract at LIFFE). The tick value can be determined in the following way:
volume of thecontract × quantity of the tick ×
term 360
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3-months Eurodollar 1,000,000 • 0.00005 • 90/360 =
USD 12.5
1-months LIBOR 3,000,000 • 0.000025 • 30/360 =
USD 6.25
3-months EURIBOR 1,000,000 • 0.00005 • 90/360 =
EUR 12.5
3-months short sterling 500,000 • 0.0001 • 90/360=
GBP 12.5
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2.
Main Markets of Money Market Futures
Futures exchange Contract volume 1,000,000 1,000,000 500,000 3-mo EURIBOR 3-mo EURIBOR 3-mo LIBOR (Short Sterling) 0.5 BP 0.5 BP 1 BP 12.5 EUR 12.5 EUR 12.5 GBP Underlying Tick size Tick value
Currency
EUR EUR GBP
EUREX LIFFE LIFFE
JPY
LIFFE
100,000,000
3-mo TIBOR (Euroyen)
0.5 BP
1,250 JPY
CHF
LIFFE
1,000,000
3-mo LIBOR (Euroswiss)
1. BP
25 CHF
USD
CME
1,000,000
3-mo LIBOR (Eurodollar)
0.5 BP*)
12.50 USD*)
USD USD
CME CME
3,000,000 1,000,000
1-mo LIBOR 13-weeks T-Bill
0.25 BP 0.5 BP
6.25 USD 12.5 USD
*) At the CME the tick size for the 3-mo Eurodollar future can vary from 0.25 BP to 0.5 BP or 1 BP, depending on the delivery month.
Some contracts are traded at several exchanges, e.g.: 3-months Eurodollar: CME, Euronext.LIFFE and SGX 3-months Euroyen: CME, Euronext.LIFFE and SGX
Links: Eurex: Euronext.Liffe: CME: SGX: www.eurexchange.com www.liffe.com www.cme.com www.sgx.com
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3.
Exchange and Clearing House
The exchange specifies the conditions for the trading. It defines – among other things – which contracts are traded and their specifications.
The settlement of the deals is carried out by the clearing house of the exchange. The clearing house has the following main functions:
It is counterparty for both the buyer and the seller in all traded contracts. Placing the clearing house between buyer and seller reduces the credit risk. To reduce this risk to a minimum, the clearing house deals solely with registered clearing members who for their part offer their services as brokers or clearers. In order to protect against default risk of exchange members, so-called initial margins and variation margins are calculated.
Daily revaluation and accounting of variation margins for all open deals
Fixing of the initial margin; the initial margin depends on the market’s volatility. Therefore it is adjusted regularly to the actual market conditions.
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4.
The Margin System
As mentioned above, margins are required when dealing with futures. They reduce the credit risk for the exchange to a minimum. They are demanded either “one-shot” and up-front in relation to the number of contracts (initial margin) or daily for the accrued profits and losses (variation margin).
The initial margin is a fixed amount; differing by contract and currency, e.g. USD 350 for each 3-month eurodollar contract. The amount is fixed by the clearing house and changes in relation to the volatility of the markets. The initial margin serves as an additional protection against default risk in order to cover the potential loss of a market participant that could result from the daily price fluctuations. The initial margin is usually not paid in cash but securities. The returns of these securities belong to the market participant. The initial margin is returned to the market participant at expiry of the position or if the position is closed earlier.
A spread margin is a reduced initial margin due to simultaneous long and short positions (in different periods), e.g. Eurodollar March long, 100 contracts and June short, 100 contracts. Instead of paying a margin of USD 350 for 200 contracts (total amount of contracts), i.e. USD 70,000, a reduced spread margin is applied, e.g. USD 250. New calculation 200 (total amount of contracts) x 250 = USD 50,000.
Some clearing houses calculate the initial margin by means of a risk-based system with certain parameters. This method is called span margin (Standardized Portfolio Analysis of Risk). Here the total risk of a position is calculated based on a series of risk factors. The result is converted by a specific ratio into a margin that is eventually charged.
Variation margin (Margin Calls) The variation margin is the daily accounting of all accrued profits or losses. Here the difference between closing price and purchase price (or the closing price of the day before) is determined daily, and thus, the real profits or losses are charged.
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5th of May 10:00 a.m., buy 100 June Eurodollar futures, price 96.60 (without initial margin)
closing price 5th of May 96.65: variation margin: 10 ticks x 12.5 tick value x 100 = USD 12,500 (credit)
closing price 6th of May 96.57: variation margin: 16 ticks x 12.5 tick value x 100 = USD 20,000 (charge)
Realised loss since the purchase = 6 x 12.5 x 100 = USD 7,500 (this equals the total sum of all margin calls)
Note: as the variation margin is paid cash, for the exact calculation of the total result of a futures position also the refinancing costs (resp. investment returns) have to be taken into account.
Settlement on the last Trading Date (EDSP) While bond futures (e.g. US T-bonds, UK gilt, Euro-Bund) need to be settled by physical delivery of the underlying, the money market futures are settled cash on the last trading date. The "cash settlement" is based on the EDSP (Exchange Delivery Settlement Price) which is determined on the last trading day. Thus, the EDSP is 100 – fixing rate (e.g. 3-months USD LIBOR). The settlement amount is calculated as the difference between the EDSP and the closing price of the day before. The result of a futures position is the sum of the daily variation margins plus the settlement amount of the last trading day.
You are long 100 contracts 3-months June Eurodollar futures. Purchase price: Yesterday closing price: 3-months BBA LIBOR today: What is the settlement amount? 96.50 96.75 3.30% ( = last trading date)
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The EDSP is 96.70 (100 – 3.30). Settlement amount: (96.70 – 96.75) x 2 x 12.5 x 100 = USD -12,500 You have to pay USD 12,500.
(Note: Of course the total result of this position is a profit. The remaining result has been taken into account for the daily variation margins.)
Closing a Futures Position Each futures position can be closed by an appropriate, opposite futures position before or at the last trading date. The closing leads to the elimination of the position and the related initial margin. The profits and losses result from the daily variation margin payments (plus possible interest returns resp. payments).
Open interest and traded volume These figures define the liquidity of contracts and periods. Generally the contract with the shortest period (front month) has the highest traded volume. The sum of all open contracts is the open interest. A contract has both a buyer and a seller, so the two market players combine to make one contract. The open interest position that is reported each day represents the increase or decrease in the number of contracts for that day, and it is shown as a positive or negative number.
The higher the traded volume and the open interest, the more liquid the market. This has the advantage for the market participants that they can trade big volumes at close spreads anytime. An increase in open interest along with an increase in price is said to confirm an upward trend. Similarly, an increase in open interest along with a decrease in price confirms a downward trend. An increase or decrease in prices while open interest remains flat or declining may indicate a possible trend reversal.
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Computing the open interest The open interest is not, despite common opinion, the volume of the traded options or futures. See the following example:
Day
Trading Activity
Open Interest
Volume per day 1 5 1 5
1st May 2nd May 3rd May 4th May
A buys 1 option and B sells 1 option C buys 5 options and D sells 5 options A sells his one option and D buys 1 option E buys 5 options from C, who sells his 5 options
1 6 5 5
Open interest = (all open long positions + all open short positions) / 2
1st May: A buys an option which leaves an open interest and creates trading volume of 1. 2nd May: C and D create trading volume of 5 and there are also 5 more options left open. 3rd May: A takes an offsetting position, therefore open interest is reduced by 1, volume 1. 4th May: E simply replaces C and therefore open interest does not change, trading volume increases by 5
Specifications for the 3-months Eurodollar futures at Euronext.Liffe (from: www.liffe.com )
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Three Month Eurodollar Interest Rate Futures Contract Unit of Trading Interest rate on three month deposit of $1,000,000
Delivery Months
March, June, September, December and four serial months, such that 24 delivery months are available for trading, with the nearest six delivery months being consecutive calendar months
Quotation Minimum Price Movement (Tick Size & Value) Last Trading Day
100.000 minus rate of interest 0.005 ($12.50) for all delivery months
11:00 London time – Two London business days prior to the third Wednesday of the delivery month
Delivery Day Trading Hours Daily Settlement
First business day following the Last Trading Day 07:00 to 21:00 London time Positions settled to nearest 0.005 20:00 London time
Exchange Delivery Settlement Price (EDSP): Based on the British Bankers’ Association offered rate (BBA US$ LIBOR) for three month US $ deposits at 11:00 London time on the Last Trading Day. The settlement price will be 100.000 minus the BBA US$ LIBOR. Where the EDSP Rate is not an exact multiple of 0.001, it will be rounded to the nearest 0.001 or, where the EDSP Rate is an exact uneven multiple of 0.0005, to the nearest lower 0.001 (e.g. BBA US$ LIBOR of 1.53750 becomes 1.537).
Contract Standard: Cash settlement based on the Exchange Delivery Settlement Price.
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5.
Comparison: Money Market Futures vs. FRA
Since money market futures and forward rate agreements have very similar effects, we compare these two instruments:
FRA quotation = interest rate (e.g. 4.50 %) OTC product non-standard contracts volume: unlimited (depending on dealer)
Money Market Futures quotation = 100 – interest rate (e.g. 95.50) product of exchange market standard contracts volume (e.g. EUR, USD 1 m ) fixed, depending on currency terms: unlimited (also broken dates) terms: 1 or 3 months (often only specific months, as March, June, etc.) spread: 1 – 4 points (main currencies) small credit risk small charge of capital reversal (doubled charge of the line, twice charge of capital, two FRAs in the books) low back office requirements a lot of back office work : margins must be booked daily calculation of interest: real number of days difference between interest rates is discounted calculation of interest: always 30 or 90 days if paid "flat”, no discounting "front fee” by margins spread: mostly 1 bp, sometimes ½ bp no credit risk no charge of capital buying / selling possible: in the future's book only balanced, open positions
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6.
Function of Futures for Pricing and Hedging FRAs
In practice, FRAs are priced via futures. Thus the market depth and the close quotes in the futures market can be utilized. For pricing FRAs via futures the contracts close to the FRA maturity are converted into an FRA rate, either by compound interest calculation (futures strip) or by interpolation.
6.1
Calculation of 3-months IMM FRAs
Easiest case: if the maturity and the period of the FRA match with the maturity of the future (like for a 3-months IMM FRA), the FRA rate can be derived directly from the future price.
Trade date: Fri 8th April 2005
3-mo EURIBOR-Future JUN 05 (M) 96.75 – 76 SEP 05 (U) 96.65 – 66 DEC 05 (Z) 96.50 – 51
IMM FRA 2x5 5x8 8 x 11
FRA Price 3.24 – 25 3.34 – 35 3.49 – 50
Period FRA 15.06. – 15.09.05 14.09. – 14.12.05 14.12. – 14.03.06
FRA days 91 91 90
Note: For hedges futures vs. FRAs you should have to take into account the difference in days – for futures it is always 90 days, for the FRAs in this example 91 days.
6.2
Calculation of IMM FRAs with longer Periods (Futures Strips)
Longer periods can be produced out of a series of futures - so-called futures strip. The FRA rate is the effective rate of the 3-months periods, i.e. compound interest is taken into account.
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Trade date: Fri 8th April 2005. What is the bid rate of a 2/11 IMM FRA? The bid rate can be calculated through the purchase of the futures strip JUN, SEP and DEC. Thus in the first step you have to derive the single FRA rates from the 3-months periods:
3-mo EURIBOR-Future JUN 05 (M) 96.75 – 76 SEP 05 (U) 96.65 – 66 DEC 05 (Z) 96.50 – 51
IMM FRA 2x5 5x8 8 x 11
FRA Price 3.24 – 25 3.34 – 35 3.49 – 50
Period FRA 15.06. – 15.09.05 14.09. – 14.12.05 14.12. – 14.03.06
FRA days 91 91 90
In the second step you calculate the price of the 2/11 IMM FRA with the effective rate formula:
⎡⎛ 91 ⎞ ⎛ 91 ⎞ ⎛ 90 ⎞ ⎤ 360 2 x 11FRA = ⎢⎜1 + 0.0324 × = 3.385% ⎟ − 1⎥ × ⎟ × ⎜1 + 0.0349 × ⎟ × ⎜1 + 0.0334 × 360 ⎠ ⎝ 360 ⎠ ⎝ 360 ⎠ ⎦ 272 ⎣⎝
6.3
Calculation of non-IMM FRAs
If the period of the FRA does not start on an IMM date, the FRA rate is calculated approximately through an effective rate which is weighted with the period.
Trade date: Fri 8th April 2005 Spot value: Tue 12th April 2005 What is the bid rate of a 3 x 9 spot FRA (184 days)?
3-mo EURIBOR-Future JUN 05 (M) SEP 05 (U) DEC 05 (Z) 96.75 – 76 96.65 – 66 96.50 – 51
IMM FRA 2x5 5x8 8 x 11
FRA Price 3.24 – 25 3.34 – 35 3.49 – 50
Period FRA 15.06. – 15.09.05 14.09. – 14.12.05 14.12. – 14.03.06
FRA days 91 91 90
For the calculation the FRA period is devided into the pro rate futures periods. The FRA rate is then produced by the effective rate of the individual periods:
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IMM JUN 12.4. 15.6. 64 days 12.7.
IMM SEP 14.9. 91 days
IMM DEC 14.12. 29 days 12.1. 184 days
Note: If you hedge an FRA with a futures strip you have remaining risks. This is due to the different conventions regarding time to settlement, maturity and settlement. In addition you have the risk of a turn in the yield curve (yield curve risk) as the futures have to be rolledover at maturity.
6.4
Stack Hedging
In contrary to a strip hedge, where you trade a series of consecutive futures, for a stack hedge you only trade the future with the closest delivery month. Stack hedging is used when the futures which are needed for the hedge are not liquid enough (or are not traded at all). These futures are then replaced by futures with shorter periods and rolled-over at maturity. You are assuming that the price of the shorter future develops the same way as the price of the longer future. Especially when the yield curve turns this assumption is not correct; therefore this method is no perfect hedge.
In June, you want to hedge a short 3/12 FRA position over EUR 100 m with futures. As the March contract is not liquid enough, you trade a stack hedge.
futures hedge: You replace the illiquid MAR contract by the liquid DEC contract which results in the following transactions: sell 100 contracts 3-months EURIBOR SEP sell 200 contracts 3-months EURIBOR DEC
roll-over: Should the liquidity of the MAR contract increase, you roll-over the DEC future in parts:
Buy back 100 contracts 3-months EURIBOR DEC sell 100 contracts 3-months EURIBOR MAR
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6.5
Significance of Convexity Effects on FRA/Futures Hegdes
When trading FRAs you have convexity effects. This means that the present value (mark-tomarket) of an FRA position does not correspond completely to the interest rate movements.
Assuming you have a short FRA position. If the rates rise, the revaluation of this position will show a loss. The present value of this loss, however, will be less than expected as the (future) loss is now discounted at a higher interest rate. On the contrary, the profit for falling interest rates will be higher than expected as now it has to be discounted at a lower interest rate. A short FRA position therefore has a positive convexity, i.e. when rates change the result will always be better than expected. Analogically a long FRA position has a negative convexity as the profit for rising interest rates has to be discounted at a higher rate resp. the loss for falling rates has to be discounted at a lower rate.
When hedging (resp. for arbitrage activities with) cash positions or FRAs with FRAs these convexity effects are irrelevant as the cash position has the same convexity effects and therefore the effects are compensated.
In contrast, money market futures do not have any convexity effects as the value of one BP is always the same, independent from the level of interest rates (mostly 25 EUR, USD, etc.). As price changes are adjusted daily through variation margins the BP value is also always the present value (no matter if the interest rate level is at 10% or 1%).
If you hedge an FRA with futures (for arbitrage futures vs. FRA) you have to take into account the convexity. The following example shows the effects:
FRA/futures hedge: You are long USD 100 DEC IMM 3/6 FRA (90 days) at 5.00% and hedge this position with the purchase of 100 DEC Eurodollar Futures at 95.00. The volume and the period for both are the same. You therefore expect a perfect hedge (no profit, no loss).
On the same day interest rates rise to 8%. What is your result now?
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Fair price FRA at 8%:
Fair price future at 8%:
180 ⎤ ⎡ ⎥ 360 ⎢1 + 0.08 × 360 3x6 = ⎢ = 7.843% − 1⎥ × ⎥ 90 ⎢1 + 0.08 × 90 ⎥ ⎢ 360 ⎦ ⎣
Future = 100 – 7.843 = 92.157
Mark to Market FRA:
MTM future (= margin call)
(0.07843 − 0.05) × 100,000,000 × 180 1 + 0.08 × 360
90 360 = 683,413.46
284.3 BP x 25 x100= 710,750
Thus the revaluation shows a loss of USD 27,336.54 (683,413.46 – 710,750.00). The loss for the future position was bigger than the profit for the FRA position. This is due to the fact that the profit of the FRA is a future value and has therefore to be discounted, but the variation margin has to be paid today. I.e. the total position has a negative convexity.
6.6
Calculating the Hedge Ratio for FRA/Futures Hedge Positions
As the profit/loss of a future is always due today, i.e. with present value, one futures contract has more weight than an equivalent FRA. Therefore, when hedging, the futures volume has to be less than the FRA volume. For calculating the hedge ratio you have to discount the FRA volume for the FRA period (i.e. maturity date until spot).
Hedge Ratio =
Volume FRA period FRA 1+ i × basis
Hedge ratio for FRA/Futures Hedge: You are long USD 100 DEC IMM 3/6 FRA (90 days) at 5.00% and want to hedge this position with the purchase of 100 DEC Eurodollar Futures. How many futures do you have to buy? (interest rate 180 days: 5%)
HR =
100 180 1 + 0.05 × 360
= 97.56
The hedge ratio is 97.56, i.e. You have to buy 98 contracts.
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As the hedge ratio depends on the period and the level of interest rates it has to be adjusted dynamically. Should rates rise, the hedge ratio falls (and vice versa). Depending on the particular position, the hedge adjustment leads to profits or losses:
short FRA + short future:
rates rise rates fall
future falls future rises
HR falls HR rises
futures has to be bought back further futures has to be sold
profit profit
long FRA + long future:
rates rise rates fall
future falls future rises
HR falls HR rises
futures have to be sold again
loss loss
further futures have to be bought
Thus following rules can be defined for the convexity of futures/FRA (resp. cash) hedges:
FRA short + future short
profit on position when rates change (positive convexity)
FRA long + future long
loss on position when rates change (negative convexity)
Note: If the FRA period (mostly 91 or 92 days) differs from the futures period (always 90
days) this difference has to be taken into account for the hedge ratio as it has an impact on the weight of the FRA position.
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7.
Spread Strategies
Generally, the simultaneous purchase and sale of futures contracts with different times to maturity and the same underlying (or different underlyings) is called a spread.
Intra-Contract Spread
An Intra-Contract spread is the simultaneous purchase and sale of futures contracts with different times to maturity and the same underlying. The spread is calculated as follows:
Spread =
+ Price of short contract - Price of long contract
If the Spread is positive or negative depends on the prices of the of the contracts. Since the price of MM futures is mainly determined by the yield curve structure, a steep yield curve entails lower futures prices compared to the spot price. Thus the following rules hold:
Steep yield curve
Spread negative
Inverse yield curve
Spread positive
Like in options trading, spreads on futures are also traded separately. The terminology used is:
Buy Spread = Buy short contract, sell long contract
Sell Spread = Sell short contract, buy long contract
Intra-Contract spreads carry considerably less risk than ”pure” futures positions, since they depend on the relation between two contracts and not on the development of absolute values. Accordingly, stock exchanges demand usually lower margins for Spread deals.
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Inter-Contract Spread
An Inter-Contract Spread is the simultaneous purchase and sale of futures contracts on different underlyings. Different times to maturity are not required.
Generally, Inter-Spreading pays attention to a proven correlation between two contracts and that the strategy is backed by a market opinion towards the price developments of the two futures. In contrast to Intra-Spreading, there is no convention concerning terminology.
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1. 2. 3. 4. 5. 6.
Conventions and Contract Specifications.............................................. 3 Main Markets of Money Market Futures.................................................. 7 Exchange and Clearing House ................................................................ 8 The Margin System ................................................................................... 9 Comparison: Money Market Futures vs. FRA ...................................... 14 Function of Futures for Pricing and Hedging FRAs............................ 15 6.1 6.2 6.3 6.4 6.5 6.6 Calculation of 3-months IMM FRAs ................................................ 15 Calculation of IMM FRAs with longer Periods (Futures Strips)... 15 Calculation of non-IMM FRAs ......................................................... 16 Stack Hedging .................................................................................. 17 Significance of Convexity Effects on FRA/Futures Hegdes ........ 18 Calculating the Hedge Ratio for FRA/Futures Hedge Positions.. 19
7.
Spread Strategies ................................................................................... 21
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MONEY MARKET FUTURES
Money market futures are exchange-traded interest rate contracts. Contrary to their counterpart in the OTC market – the FRA – the specifications of futures are strongly standardised. Usually, the underlying is a 3-month deposit, in some currencies also a 1month deposit, that represents the interest rate of a future time period.
Money market futures can be used like FRAs. That is, to eliminate a future interest rate risk (hedging) speculate on interest rate trends (trading) to arbitrage between different markets (arbitrage)
Money market futures are standardised products, because they are traded in the exchange market. Thus, some specifications are already fixed by the particular exchange:
contract volume maturity dates marginal price changes (tick size) value of a price change by one tick based on one contract (tick value)
For money market futures the most important exchanges are Euronext.Liffe (London), CME (Chicago) and SGX (Singapore) resp. Tiffe (Tokio). Mostly, futures contracts can only be closed at the same exchange where the position has been opened. Some contracts can be sold or bought (and consequently closed), at different exchanges [e.g. a USD 3-months contract purchased in Chicago (CME) and sold in Singapore (Simex)]. Thus the contract can be traded 24 hours and not only during the trading hours at the particular exchange.
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1.
Conventions and Contract Specifications
Trade dates Trade dates of money market futures are set by the futures exchange. For the core markets these are always the third Wednesday of the last month of the quarter (March, June, September, December). These trade dates are called IMM-dates (International money market dates).
The delivery months have the following abbreviations: March June September December H M U Z
(Note: the abbreviations do not follow any logic)
In addition, at most futures exchanges so-called serial months are traded. These are the maturities between the IMM dates. At the LIFFE for example, in addition to the IMM dates, 4 serial months are traded. Consequently, there are maturities for all following 6 months.
Trade date: Maturities: May June July August September October
4th April
(serial month) (IMM) (serial month) (serial month) (IMM) (serial Month)
(after settlement of the May contract the next new serial month will be November)
Front month is the contract with the next maturity. Contracts with a later maturity are called Back months. For the front month liquidity is usually the highest.
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Last trading day Last trading days of futures are determined by the exchanges and are usually two days before delivery date (an exception is GBP, where the theoretical delivery date is the last trading date, i.e. same-day fixing).
Quotation The quotation for futures prices is: 100.00 minus interest rate Therefore a forward interest rate of 4.50 % p.a. (i.e. an interest rate for a future period) equals a futures price of 95.50 (= 100 – 4.50). The consequences of this quoting convention are illustrated below:
interest rates interest rates
prices prices
If the interest rate rises from 4.50 % to 5 %, the future price will fall from 95.50 to 95.00. If the interest rate falls from 4.50 % to 4 %, the future price will rise from 95.50 to 96.00.
With the quotation of an interest rate on the basis of 100, the buying/selling of a money market future has just the opposite effect to an FRA purchase/sale:
FRA purchase = FRA sale =
future short future long
A future's quote of JUNE (M) 96.64 / 96.65 corresponds to an interest rate of 3.35 % / 3.36 % p.a. for the term from the third Wednesday in June XY until the third Wednesday in September XY, in a specific currency.
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Underlying Usually, the underlying is a 3-months interbank deposit (e.g. Eurodollar, Euroyen, Euro Swiss Franc, EURIBOR). The fixing for these contracts is normally BBA LIBOR (resp. EURIBOR for EURIBOR futures). The term is always exactly 90 days for the 3-months futures period (resp. 30 days for a 1-month futures period). The fixed LIBOR resp. EURIBOR though is calculated on the exact number of days.
Volume of the contract Not only the underlying but also the volume (principal) of a future contract is exactly specified. (see table below)
Futures purchase as hedging operation: as speculation: protection against falling interest rates speculation on falling interest rates
Futures sale as hedging operation: as speculation: protection against rising interest rates speculation on rising interest rates
Tick A tick is the marginal movement of the futures price. For EUR, USD and JPY money market futures, a tick is usually half a basis point, i.e. a hundredth of 0.5 % (= 0.005 % or 0.00005), for GBP contracts it is 1 BP. (see table below)
Tick value The tick value is the profit or loss which occurs when the price changes by one tick. Also the tick value is specified by the exchange (e.g. USD 12.5 for the 3-months Eurodollar contract at LIFFE). The tick value can be determined in the following way:
volume of thecontract × quantity of the tick ×
term 360
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3-months Eurodollar 1,000,000 • 0.00005 • 90/360 =
USD 12.5
1-months LIBOR 3,000,000 • 0.000025 • 30/360 =
USD 6.25
3-months EURIBOR 1,000,000 • 0.00005 • 90/360 =
EUR 12.5
3-months short sterling 500,000 • 0.0001 • 90/360=
GBP 12.5
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2.
Main Markets of Money Market Futures
Futures exchange Contract volume 1,000,000 1,000,000 500,000 3-mo EURIBOR 3-mo EURIBOR 3-mo LIBOR (Short Sterling) 0.5 BP 0.5 BP 1 BP 12.5 EUR 12.5 EUR 12.5 GBP Underlying Tick size Tick value
Currency
EUR EUR GBP
EUREX LIFFE LIFFE
JPY
LIFFE
100,000,000
3-mo TIBOR (Euroyen)
0.5 BP
1,250 JPY
CHF
LIFFE
1,000,000
3-mo LIBOR (Euroswiss)
1. BP
25 CHF
USD
CME
1,000,000
3-mo LIBOR (Eurodollar)
0.5 BP*)
12.50 USD*)
USD USD
CME CME
3,000,000 1,000,000
1-mo LIBOR 13-weeks T-Bill
0.25 BP 0.5 BP
6.25 USD 12.5 USD
*) At the CME the tick size for the 3-mo Eurodollar future can vary from 0.25 BP to 0.5 BP or 1 BP, depending on the delivery month.
Some contracts are traded at several exchanges, e.g.: 3-months Eurodollar: CME, Euronext.LIFFE and SGX 3-months Euroyen: CME, Euronext.LIFFE and SGX
Links: Eurex: Euronext.Liffe: CME: SGX: www.eurexchange.com www.liffe.com www.cme.com www.sgx.com
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3.
Exchange and Clearing House
The exchange specifies the conditions for the trading. It defines – among other things – which contracts are traded and their specifications.
The settlement of the deals is carried out by the clearing house of the exchange. The clearing house has the following main functions:
It is counterparty for both the buyer and the seller in all traded contracts. Placing the clearing house between buyer and seller reduces the credit risk. To reduce this risk to a minimum, the clearing house deals solely with registered clearing members who for their part offer their services as brokers or clearers. In order to protect against default risk of exchange members, so-called initial margins and variation margins are calculated.
Daily revaluation and accounting of variation margins for all open deals
Fixing of the initial margin; the initial margin depends on the market’s volatility. Therefore it is adjusted regularly to the actual market conditions.
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4.
The Margin System
As mentioned above, margins are required when dealing with futures. They reduce the credit risk for the exchange to a minimum. They are demanded either “one-shot” and up-front in relation to the number of contracts (initial margin) or daily for the accrued profits and losses (variation margin).
The initial margin is a fixed amount; differing by contract and currency, e.g. USD 350 for each 3-month eurodollar contract. The amount is fixed by the clearing house and changes in relation to the volatility of the markets. The initial margin serves as an additional protection against default risk in order to cover the potential loss of a market participant that could result from the daily price fluctuations. The initial margin is usually not paid in cash but securities. The returns of these securities belong to the market participant. The initial margin is returned to the market participant at expiry of the position or if the position is closed earlier.
A spread margin is a reduced initial margin due to simultaneous long and short positions (in different periods), e.g. Eurodollar March long, 100 contracts and June short, 100 contracts. Instead of paying a margin of USD 350 for 200 contracts (total amount of contracts), i.e. USD 70,000, a reduced spread margin is applied, e.g. USD 250. New calculation 200 (total amount of contracts) x 250 = USD 50,000.
Some clearing houses calculate the initial margin by means of a risk-based system with certain parameters. This method is called span margin (Standardized Portfolio Analysis of Risk). Here the total risk of a position is calculated based on a series of risk factors. The result is converted by a specific ratio into a margin that is eventually charged.
Variation margin (Margin Calls) The variation margin is the daily accounting of all accrued profits or losses. Here the difference between closing price and purchase price (or the closing price of the day before) is determined daily, and thus, the real profits or losses are charged.
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5th of May 10:00 a.m., buy 100 June Eurodollar futures, price 96.60 (without initial margin)
closing price 5th of May 96.65: variation margin: 10 ticks x 12.5 tick value x 100 = USD 12,500 (credit)
closing price 6th of May 96.57: variation margin: 16 ticks x 12.5 tick value x 100 = USD 20,000 (charge)
Realised loss since the purchase = 6 x 12.5 x 100 = USD 7,500 (this equals the total sum of all margin calls)
Note: as the variation margin is paid cash, for the exact calculation of the total result of a futures position also the refinancing costs (resp. investment returns) have to be taken into account.
Settlement on the last Trading Date (EDSP) While bond futures (e.g. US T-bonds, UK gilt, Euro-Bund) need to be settled by physical delivery of the underlying, the money market futures are settled cash on the last trading date. The "cash settlement" is based on the EDSP (Exchange Delivery Settlement Price) which is determined on the last trading day. Thus, the EDSP is 100 – fixing rate (e.g. 3-months USD LIBOR). The settlement amount is calculated as the difference between the EDSP and the closing price of the day before. The result of a futures position is the sum of the daily variation margins plus the settlement amount of the last trading day.
You are long 100 contracts 3-months June Eurodollar futures. Purchase price: Yesterday closing price: 3-months BBA LIBOR today: What is the settlement amount? 96.50 96.75 3.30% ( = last trading date)
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The EDSP is 96.70 (100 – 3.30). Settlement amount: (96.70 – 96.75) x 2 x 12.5 x 100 = USD -12,500 You have to pay USD 12,500.
(Note: Of course the total result of this position is a profit. The remaining result has been taken into account for the daily variation margins.)
Closing a Futures Position Each futures position can be closed by an appropriate, opposite futures position before or at the last trading date. The closing leads to the elimination of the position and the related initial margin. The profits and losses result from the daily variation margin payments (plus possible interest returns resp. payments).
Open interest and traded volume These figures define the liquidity of contracts and periods. Generally the contract with the shortest period (front month) has the highest traded volume. The sum of all open contracts is the open interest. A contract has both a buyer and a seller, so the two market players combine to make one contract. The open interest position that is reported each day represents the increase or decrease in the number of contracts for that day, and it is shown as a positive or negative number.
The higher the traded volume and the open interest, the more liquid the market. This has the advantage for the market participants that they can trade big volumes at close spreads anytime. An increase in open interest along with an increase in price is said to confirm an upward trend. Similarly, an increase in open interest along with a decrease in price confirms a downward trend. An increase or decrease in prices while open interest remains flat or declining may indicate a possible trend reversal.
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Computing the open interest The open interest is not, despite common opinion, the volume of the traded options or futures. See the following example:
Day
Trading Activity
Open Interest
Volume per day 1 5 1 5
1st May 2nd May 3rd May 4th May
A buys 1 option and B sells 1 option C buys 5 options and D sells 5 options A sells his one option and D buys 1 option E buys 5 options from C, who sells his 5 options
1 6 5 5
Open interest = (all open long positions + all open short positions) / 2
1st May: A buys an option which leaves an open interest and creates trading volume of 1. 2nd May: C and D create trading volume of 5 and there are also 5 more options left open. 3rd May: A takes an offsetting position, therefore open interest is reduced by 1, volume 1. 4th May: E simply replaces C and therefore open interest does not change, trading volume increases by 5
Specifications for the 3-months Eurodollar futures at Euronext.Liffe (from: www.liffe.com )
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Three Month Eurodollar Interest Rate Futures Contract Unit of Trading Interest rate on three month deposit of $1,000,000
Delivery Months
March, June, September, December and four serial months, such that 24 delivery months are available for trading, with the nearest six delivery months being consecutive calendar months
Quotation Minimum Price Movement (Tick Size & Value) Last Trading Day
100.000 minus rate of interest 0.005 ($12.50) for all delivery months
11:00 London time – Two London business days prior to the third Wednesday of the delivery month
Delivery Day Trading Hours Daily Settlement
First business day following the Last Trading Day 07:00 to 21:00 London time Positions settled to nearest 0.005 20:00 London time
Exchange Delivery Settlement Price (EDSP): Based on the British Bankers’ Association offered rate (BBA US$ LIBOR) for three month US $ deposits at 11:00 London time on the Last Trading Day. The settlement price will be 100.000 minus the BBA US$ LIBOR. Where the EDSP Rate is not an exact multiple of 0.001, it will be rounded to the nearest 0.001 or, where the EDSP Rate is an exact uneven multiple of 0.0005, to the nearest lower 0.001 (e.g. BBA US$ LIBOR of 1.53750 becomes 1.537).
Contract Standard: Cash settlement based on the Exchange Delivery Settlement Price.
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5.
Comparison: Money Market Futures vs. FRA
Since money market futures and forward rate agreements have very similar effects, we compare these two instruments:
FRA quotation = interest rate (e.g. 4.50 %) OTC product non-standard contracts volume: unlimited (depending on dealer)
Money Market Futures quotation = 100 – interest rate (e.g. 95.50) product of exchange market standard contracts volume (e.g. EUR, USD 1 m ) fixed, depending on currency terms: unlimited (also broken dates) terms: 1 or 3 months (often only specific months, as March, June, etc.) spread: 1 – 4 points (main currencies) small credit risk small charge of capital reversal (doubled charge of the line, twice charge of capital, two FRAs in the books) low back office requirements a lot of back office work : margins must be booked daily calculation of interest: real number of days difference between interest rates is discounted calculation of interest: always 30 or 90 days if paid "flat”, no discounting "front fee” by margins spread: mostly 1 bp, sometimes ½ bp no credit risk no charge of capital buying / selling possible: in the future's book only balanced, open positions
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6.
Function of Futures for Pricing and Hedging FRAs
In practice, FRAs are priced via futures. Thus the market depth and the close quotes in the futures market can be utilized. For pricing FRAs via futures the contracts close to the FRA maturity are converted into an FRA rate, either by compound interest calculation (futures strip) or by interpolation.
6.1
Calculation of 3-months IMM FRAs
Easiest case: if the maturity and the period of the FRA match with the maturity of the future (like for a 3-months IMM FRA), the FRA rate can be derived directly from the future price.
Trade date: Fri 8th April 2005
3-mo EURIBOR-Future JUN 05 (M) 96.75 – 76 SEP 05 (U) 96.65 – 66 DEC 05 (Z) 96.50 – 51
IMM FRA 2x5 5x8 8 x 11
FRA Price 3.24 – 25 3.34 – 35 3.49 – 50
Period FRA 15.06. – 15.09.05 14.09. – 14.12.05 14.12. – 14.03.06
FRA days 91 91 90
Note: For hedges futures vs. FRAs you should have to take into account the difference in days – for futures it is always 90 days, for the FRAs in this example 91 days.
6.2
Calculation of IMM FRAs with longer Periods (Futures Strips)
Longer periods can be produced out of a series of futures - so-called futures strip. The FRA rate is the effective rate of the 3-months periods, i.e. compound interest is taken into account.
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Trade date: Fri 8th April 2005. What is the bid rate of a 2/11 IMM FRA? The bid rate can be calculated through the purchase of the futures strip JUN, SEP and DEC. Thus in the first step you have to derive the single FRA rates from the 3-months periods:
3-mo EURIBOR-Future JUN 05 (M) 96.75 – 76 SEP 05 (U) 96.65 – 66 DEC 05 (Z) 96.50 – 51
IMM FRA 2x5 5x8 8 x 11
FRA Price 3.24 – 25 3.34 – 35 3.49 – 50
Period FRA 15.06. – 15.09.05 14.09. – 14.12.05 14.12. – 14.03.06
FRA days 91 91 90
In the second step you calculate the price of the 2/11 IMM FRA with the effective rate formula:
⎡⎛ 91 ⎞ ⎛ 91 ⎞ ⎛ 90 ⎞ ⎤ 360 2 x 11FRA = ⎢⎜1 + 0.0324 × = 3.385% ⎟ − 1⎥ × ⎟ × ⎜1 + 0.0349 × ⎟ × ⎜1 + 0.0334 × 360 ⎠ ⎝ 360 ⎠ ⎝ 360 ⎠ ⎦ 272 ⎣⎝
6.3
Calculation of non-IMM FRAs
If the period of the FRA does not start on an IMM date, the FRA rate is calculated approximately through an effective rate which is weighted with the period.
Trade date: Fri 8th April 2005 Spot value: Tue 12th April 2005 What is the bid rate of a 3 x 9 spot FRA (184 days)?
3-mo EURIBOR-Future JUN 05 (M) SEP 05 (U) DEC 05 (Z) 96.75 – 76 96.65 – 66 96.50 – 51
IMM FRA 2x5 5x8 8 x 11
FRA Price 3.24 – 25 3.34 – 35 3.49 – 50
Period FRA 15.06. – 15.09.05 14.09. – 14.12.05 14.12. – 14.03.06
FRA days 91 91 90
For the calculation the FRA period is devided into the pro rate futures periods. The FRA rate is then produced by the effective rate of the individual periods:
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IMM JUN 12.4. 15.6. 64 days 12.7.
IMM SEP 14.9. 91 days
IMM DEC 14.12. 29 days 12.1. 184 days
Note: If you hedge an FRA with a futures strip you have remaining risks. This is due to the different conventions regarding time to settlement, maturity and settlement. In addition you have the risk of a turn in the yield curve (yield curve risk) as the futures have to be rolledover at maturity.
6.4
Stack Hedging
In contrary to a strip hedge, where you trade a series of consecutive futures, for a stack hedge you only trade the future with the closest delivery month. Stack hedging is used when the futures which are needed for the hedge are not liquid enough (or are not traded at all). These futures are then replaced by futures with shorter periods and rolled-over at maturity. You are assuming that the price of the shorter future develops the same way as the price of the longer future. Especially when the yield curve turns this assumption is not correct; therefore this method is no perfect hedge.
In June, you want to hedge a short 3/12 FRA position over EUR 100 m with futures. As the March contract is not liquid enough, you trade a stack hedge.
futures hedge: You replace the illiquid MAR contract by the liquid DEC contract which results in the following transactions: sell 100 contracts 3-months EURIBOR SEP sell 200 contracts 3-months EURIBOR DEC
roll-over: Should the liquidity of the MAR contract increase, you roll-over the DEC future in parts:
Buy back 100 contracts 3-months EURIBOR DEC sell 100 contracts 3-months EURIBOR MAR
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6.5
Significance of Convexity Effects on FRA/Futures Hegdes
When trading FRAs you have convexity effects. This means that the present value (mark-tomarket) of an FRA position does not correspond completely to the interest rate movements.
Assuming you have a short FRA position. If the rates rise, the revaluation of this position will show a loss. The present value of this loss, however, will be less than expected as the (future) loss is now discounted at a higher interest rate. On the contrary, the profit for falling interest rates will be higher than expected as now it has to be discounted at a lower interest rate. A short FRA position therefore has a positive convexity, i.e. when rates change the result will always be better than expected. Analogically a long FRA position has a negative convexity as the profit for rising interest rates has to be discounted at a higher rate resp. the loss for falling rates has to be discounted at a lower rate.
When hedging (resp. for arbitrage activities with) cash positions or FRAs with FRAs these convexity effects are irrelevant as the cash position has the same convexity effects and therefore the effects are compensated.
In contrast, money market futures do not have any convexity effects as the value of one BP is always the same, independent from the level of interest rates (mostly 25 EUR, USD, etc.). As price changes are adjusted daily through variation margins the BP value is also always the present value (no matter if the interest rate level is at 10% or 1%).
If you hedge an FRA with futures (for arbitrage futures vs. FRA) you have to take into account the convexity. The following example shows the effects:
FRA/futures hedge: You are long USD 100 DEC IMM 3/6 FRA (90 days) at 5.00% and hedge this position with the purchase of 100 DEC Eurodollar Futures at 95.00. The volume and the period for both are the same. You therefore expect a perfect hedge (no profit, no loss).
On the same day interest rates rise to 8%. What is your result now?
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Fair price FRA at 8%:
Fair price future at 8%:
180 ⎤ ⎡ ⎥ 360 ⎢1 + 0.08 × 360 3x6 = ⎢ = 7.843% − 1⎥ × ⎥ 90 ⎢1 + 0.08 × 90 ⎥ ⎢ 360 ⎦ ⎣
Future = 100 – 7.843 = 92.157
Mark to Market FRA:
MTM future (= margin call)
(0.07843 − 0.05) × 100,000,000 × 180 1 + 0.08 × 360
90 360 = 683,413.46
284.3 BP x 25 x100= 710,750
Thus the revaluation shows a loss of USD 27,336.54 (683,413.46 – 710,750.00). The loss for the future position was bigger than the profit for the FRA position. This is due to the fact that the profit of the FRA is a future value and has therefore to be discounted, but the variation margin has to be paid today. I.e. the total position has a negative convexity.
6.6
Calculating the Hedge Ratio for FRA/Futures Hedge Positions
As the profit/loss of a future is always due today, i.e. with present value, one futures contract has more weight than an equivalent FRA. Therefore, when hedging, the futures volume has to be less than the FRA volume. For calculating the hedge ratio you have to discount the FRA volume for the FRA period (i.e. maturity date until spot).
Hedge Ratio =
Volume FRA period FRA 1+ i × basis
Hedge ratio for FRA/Futures Hedge: You are long USD 100 DEC IMM 3/6 FRA (90 days) at 5.00% and want to hedge this position with the purchase of 100 DEC Eurodollar Futures. How many futures do you have to buy? (interest rate 180 days: 5%)
HR =
100 180 1 + 0.05 × 360
= 97.56
The hedge ratio is 97.56, i.e. You have to buy 98 contracts.
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As the hedge ratio depends on the period and the level of interest rates it has to be adjusted dynamically. Should rates rise, the hedge ratio falls (and vice versa). Depending on the particular position, the hedge adjustment leads to profits or losses:
short FRA + short future:
rates rise rates fall
future falls future rises
HR falls HR rises
futures has to be bought back further futures has to be sold
profit profit
long FRA + long future:
rates rise rates fall
future falls future rises
HR falls HR rises
futures have to be sold again
loss loss
further futures have to be bought
Thus following rules can be defined for the convexity of futures/FRA (resp. cash) hedges:
FRA short + future short
profit on position when rates change (positive convexity)
FRA long + future long
loss on position when rates change (negative convexity)
Note: If the FRA period (mostly 91 or 92 days) differs from the futures period (always 90
days) this difference has to be taken into account for the hedge ratio as it has an impact on the weight of the FRA position.
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7.
Spread Strategies
Generally, the simultaneous purchase and sale of futures contracts with different times to maturity and the same underlying (or different underlyings) is called a spread.
Intra-Contract Spread
An Intra-Contract spread is the simultaneous purchase and sale of futures contracts with different times to maturity and the same underlying. The spread is calculated as follows:
Spread =
+ Price of short contract - Price of long contract
If the Spread is positive or negative depends on the prices of the of the contracts. Since the price of MM futures is mainly determined by the yield curve structure, a steep yield curve entails lower futures prices compared to the spot price. Thus the following rules hold:
Steep yield curve
Spread negative
Inverse yield curve
Spread positive
Like in options trading, spreads on futures are also traded separately. The terminology used is:
Buy Spread = Buy short contract, sell long contract
Sell Spread = Sell short contract, buy long contract
Intra-Contract spreads carry considerably less risk than ”pure” futures positions, since they depend on the relation between two contracts and not on the development of absolute values. Accordingly, stock exchanges demand usually lower margins for Spread deals.
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Inter-Contract Spread
An Inter-Contract Spread is the simultaneous purchase and sale of futures contracts on different underlyings. Different times to maturity are not required.
Generally, Inter-Spreading pays attention to a proven correlation between two contracts and that the strategy is backed by a market opinion towards the price developments of the two futures. In contrast to Intra-Spreading, there is no convention concerning terminology.
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