Copyright © 2001 by Harcourt, Inc. All rights reserved.1 Chapter 11: Advanced Futures Strategies...

Copyright © 2001 by Harcourt, Inc. All rights reserved.

1

Chapter 11: Advanced Futures Strategies

Fund managers who aren’t using futures and options are Fund managers who aren’t using futures and options are dealing with an incomplete set of resources.dealing with an incomplete set of resources.

Paul DaleyPaul Daley

Portfolio Managers Talk Futures and Risk ManagementPortfolio Managers Talk Futures and Risk Management

Chicago Mercantile Exchange videotape, 1995Chicago Mercantile Exchange videotape, 1995


2

Important Concepts in Chapter 11

Futures spread and arbitrage strategiesFutures spread and arbitrage strategies Short-term interest rate futures strategiesShort-term interest rate futures strategies Intermediate-term interest rate futures strategiesIntermediate-term interest rate futures strategies Long-term interest rate futures strategiesLong-term interest rate futures strategies Stock index futures strategiesStock index futures strategies


3

Short-Term Interest Rate Futures Strategies

Treasury Bill Cash and Carry/Implied RepoTreasury Bill Cash and Carry/Implied Repo Cash and carry transaction means to buy asset and sell Cash and carry transaction means to buy asset and sell

futuresfutures Repurchase agreement/repo to obtain fundingRepurchase agreement/repo to obtain funding Overnight vs. term repoOvernight vs. term repo Cost of carry pricing model: fCost of carry pricing model: f00(T)(T) = S0 + Implied repo rate:

1S

(T)fr̂

1/t

0

0


4

Short-Term Interest Rate Futures Strategies (continued)

Treasury Bill Cash and Carry/Implied Repo RateTreasury Bill Cash and Carry/Implied Repo Rate Also equivalent to buying longer term bill and Also equivalent to buying longer term bill and

converting it to shorter term bill.converting it to shorter term bill. Example. See Example. See Table 11.1, p. 458Table 11.1, p. 458..

Eurodollar ArbitrageEurodollar Arbitrage See See Table 11.2, p. 460Table 11.2, p. 460..


5

Intermediate and Long-Term Interest Rate Futures Strategies

Recall the option to deliver any T-bond with at least 15 Recall the option to deliver any T-bond with at least 15 years to maturity or first call.years to maturity or first call.

Adjustment to futures price using conversion factor, Adjustment to futures price using conversion factor, which is the price per $1.00 par of a 6% bond delivered which is the price per $1.00 par of a 6% bond delivered on a particular expiration.on a particular expiration.

Invoice price = (Settlement price on position Invoice price = (Settlement price on position day)/(Conversion factor) + Accrued interestday)/(Conversion factor) + Accrued interest

Example: Delivery on March 2000 contract. Example: Delivery on March 2000 contract. Settlement price is 112-16 ($112,500) on position day.Settlement price is 112-16 ($112,500) on position day.


6


You plan to deliver the 7 7/8s of 2021 on March 3. CF You plan to deliver the 7 7/8s of 2021 on March 3. CF = 1.2207. Coupon dates of February 15 and August 15. = 1.2207. Coupon dates of February 15 and August 15. Last coupon on February 15, 2000. Days from 2/15 to Last coupon on February 15, 2000. Days from 2/15 to 3/3 is 17. Days from 2/15 to 8/15 is 182. Accrued 3/3 is 17. Days from 2/15 to 8/15 is 182. Accrued interestinterest $100,000(.07875/2)(17/182) = $368$100,000(.07875/2)(17/182) = $368

Invoice price:Invoice price: $112,500(1.2207) + $368 = $137,697$112,500(1.2207) + $368 = $137,697


7


Next day, Notice of Intention Day, Thursday, March 2, Next day, Notice of Intention Day, Thursday, March 2, the short invoices the long $137,.697. The long pays the short invoices the long $137,.697. The long pays for and receives the bond on Friday, March 3.for and receives the bond on Friday, March 3.

Table 11.3, p. 463Table 11.3, p. 463 shows CFs and invoice prices for shows CFs and invoice prices for other deliverable bonds on the March 2000 contract.other deliverable bonds on the March 2000 contract.


8


Determining the Cheapest to Deliver Bond on the Treasury Determining the Cheapest to Deliver Bond on the Treasury Bond Futures ContractBond Futures Contract Recall the option to deliver any T-bond with at least 15 Recall the option to deliver any T-bond with at least 15

years to maturity or first call.years to maturity or first call. Example: Delivery on March 2000 contract of 7 7/8s Example: Delivery on March 2000 contract of 7 7/8s

of February 15, 2021.of February 15, 2021. Cost of delivering bondCost of delivering bond

f(CF) + AIf(CF) + AITT - [(B + AI - [(B + AItt)(1+r))(1+r)(T-t)(T-t) - FV of coupons at - FV of coupons at

T]T]


9

Intermediate and Long-Term Interest Rate Futures Strategies (continued)

Determining the Cheapest to Deliver Bond on the Treasury Determining the Cheapest to Deliver Bond on the Treasury Bond Futures Contract (continued)Bond Futures Contract (continued) Example: Deliver the 8 7/8s of 8/15/17 on the March Example: Deliver the 8 7/8s of 8/15/17 on the March

2000 contract on March 3. f = 94 1/32 = 94.03125, CF 2000 contract on March 3. f = 94 1/32 = 94.03125, CF = 1.3062, AI= 1.3062, AItt = 0.92, AI = 0.92, AITT = 0.41 (deliver on March 3), = 0.41 (deliver on March 3),

B = 124 21/32. 163 days between September 22 and B = 124 21/32. 163 days between September 22 and March 3. Repo rate = .058. March 3. Repo rate = .058.

Invoice priceInvoice price 94.03125(1.3062) + 0.41 = 123.2494.03125(1.3062) + 0.41 = 123.24


10


Determining the Cheapest to Deliver Bond on the Treasury Determining the Cheapest to Deliver Bond on the Treasury Bond Futures Contract (continued)Bond Futures Contract (continued) Coupon of 4.4375 received on February 15 is Coupon of 4.4375 received on February 15 is

reinvested at 5.8% for 17 days to grow to reinvested at 5.8% for 17 days to grow to 4.4375(1.058)4.4375(1.058)17/36517/365 = 4.45 = 4.45

Forward price of deliverable bondForward price of deliverable bond (124.65625 + 0.92)(1.058)(124.65625 + 0.92)(1.058)163/365163/365 - 4.45 = 124.33 - 4.45 = 124.33

So the bond would cost 1.09 more than it would return.So the bond would cost 1.09 more than it would return.


11


Determining the Cheapest to Deliver Bond on the Treasury Determining the Cheapest to Deliver Bond on the Treasury Bond Futures Contract (continued)Bond Futures Contract (continued) All we can do, however, is compare this result with that All we can do, however, is compare this result with that

for another bond. For the 9 1/8s of May 15, 2018 with for another bond. For the 9 1/8s of May 15, 2018 with CF = 1.3411 and price of 127 27/32, we have accrued CF = 1.3411 and price of 127 27/32, we have accrued interest of 3.22 on September 22 and 2.73 on March 3. interest of 3.22 on September 22 and 2.73 on March 3. Coupon of 4.5625 on November 15 is reinvested at Coupon of 4.5625 on November 15 is reinvested at 5.8% for 109 days and grows to 4.5625(1.058)5.8% for 109 days and grows to 4.5625(1.058)109/365109/365 = = 4.64.4.64.


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Intermediate and Long-Term Interest Rate Futures Strategies (continued) Determining the Cheapest to Deliver Bond on the Treasury Determining the Cheapest to Deliver Bond on the Treasury

Bond Futures Contract (continued)Bond Futures Contract (continued) Forward price is, therefore,Forward price is, therefore,

(127.84375 + 3.22)(1.058)(127.84375 + 3.22)(1.058)163/365163/365 - 4.64 = 129.77 - 4.64 = 129.77 Invoice price isInvoice price is

94.03125(1.3411) + 2.73 = 128.84.94.03125(1.3411) + 2.73 = 128.84. Thus, this bond would cost 0.93 more than it would return. Thus, this bond would cost 0.93 more than it would return.

So the 9 1/8 bond is better than the 8 7/8 bond.So the 9 1/8 bond is better than the 8 7/8 bond. Table 11.4, p. 406Table 11.4, p. 406 shows these calculations for all shows these calculations for all

deliverable bonds. deliverable bonds. Software Demonstration 11.1, p. 468Software Demonstration 11.1, p. 468 shows how to use ctd2.xls to do these calculations.shows how to use ctd2.xls to do these calculations.


13

Intermediate and Long-Term Interest Rate Futures Strategies (continued) Determining the Cheapest to Deliver Bond on the Treasury Determining the Cheapest to Deliver Bond on the Treasury

Bond Futures Contract (continued)Bond Futures Contract (continued) Why identifying the cheapest-to-deliver bond is Why identifying the cheapest-to-deliver bond is

important:important: Identifying the true spot priceIdentifying the true spot price Calculating the correct hedge ratioCalculating the correct hedge ratio


14


Delivery OptionsDelivery Options The Wild Card OptionThe Wild Card Option

Futures market closes at 3:00 pm while spot market Futures market closes at 3:00 pm while spot market stays open until at least 5:00 pm.stays open until at least 5:00 pm.

This allows the holder of a short futures contract This allows the holder of a short futures contract during the delivery month to potentially profit from during the delivery month to potentially profit from a decline in the price of a deliverable bond during a decline in the price of a deliverable bond during that two hour period in the expiration month.that two hour period in the expiration month.

Illustration: fIllustration: f33 = futures price at 3:00 pm, S = futures price at 3:00 pm, S33 = spot = spot

price at 3:00 pm. CF = conversion factorprice at 3:00 pm. CF = conversion factor


15


Delivery Options (continued)Delivery Options (continued) The Wild Card Option (continued)The Wild Card Option (continued)

Let the short own 1/CF bonds (CF must be > 1.0, so Let the short own 1/CF bonds (CF must be > 1.0, so coupon must be > 8 percent). This is less than one coupon must be > 8 percent). This is less than one bond per contract so additional bonds, called “the tail,” bond per contract so additional bonds, called “the tail,” will have to be purchased in order to make delivery.will have to be purchased in order to make delivery.

At 5:00 pm, the spot price is SAt 5:00 pm, the spot price is S55. It is profitable to . It is profitable to

purchase these bonds at 5:00 pm if Spurchase these bonds at 5:00 pm if S55 < f < f33(CF).(CF). This holds because the invoice price is locked in but This holds because the invoice price is locked in but

the spot price of the bonds can potentially fall.the spot price of the bonds can potentially fall.


16


Delivery Options (continued)Delivery Options (continued) The Wild Card Option (continued)The Wild Card Option (continued)

If the spot price does not fall sufficiently, then the If the spot price does not fall sufficiently, then the short simply waits until the next day. By the last short simply waits until the next day. By the last eligible delivery day, the short would have to make eligible delivery day, the short would have to make delivery.delivery.

This is a potentially valuable option granted by the This is a potentially valuable option granted by the long to the short and its value would have to be long to the short and its value would have to be reflected in a lower futures price at 3:00 pm.reflected in a lower futures price at 3:00 pm.


17


Delivery Options (continued)Delivery Options (continued) The Quality OptionThe Quality Option

Also called the switching option, it gives the short Also called the switching option, it gives the short the right to change deliverable bonds if another the right to change deliverable bonds if another becomes more attractive. This right also exists in becomes more attractive. This right also exists in various other futures markets.various other futures markets.

Similar to this is the location option, which is the Similar to this is the location option, which is the right to choose from among several eligible delivery right to choose from among several eligible delivery locations. This can be valuable when the underlying locations. This can be valuable when the underlying is a storable commodity.is a storable commodity.


18


Delivery Options (continued)Delivery Options (continued) The End-of-the-Month OptionThe End-of-the-Month Option

The right to make delivery any one of the business The right to make delivery any one of the business days at the end of the month after the futures days at the end of the month after the futures contract has stopped trading, around the third week contract has stopped trading, around the third week of the month.of the month.

Similar to the wild card option because the invoice Similar to the wild card option because the invoice price is locked in when the futures stops trading.price is locked in when the futures stops trading.


19


Delivery Options (continued)Delivery Options (continued) The Timing OptionThe Timing Option

The right to deliver on any eligible day of the The right to deliver on any eligible day of the delivery month.delivery month.

Delivery will be made early in the month if the bond Delivery will be made early in the month if the bond earns a coupon that is less than the cost of financing earns a coupon that is less than the cost of financing it.it.

Delivery will be made late in the month if the bond Delivery will be made late in the month if the bond earns a coupon that exceeds the cost of financing it.earns a coupon that exceeds the cost of financing it.


20


Implied Repo/Cost of CarryImplied Repo/Cost of Carry Buy spot T-bond, sell futures.Buy spot T-bond, sell futures. This will produce a return (implied repo rate) ofThis will produce a return (implied repo rate) of

1AIS

AI(T))(CF)(fr̂

(1/T)

T0

T0


21


Implied Repo/Cost of Carry (continued)Implied Repo/Cost of Carry (continued) Example: On September 22, 1999, CTD bond on Example: On September 22, 1999, CTD bond on

March contract is 8 1/8s maturing in about 21 years. March contract is 8 1/8s maturing in about 21 years. Spot price is 118 21/32, accrued interest is 0.84, CF = Spot price is 118 21/32, accrued interest is 0.84, CF = 1.2532 and futures price is 94.03125. From September 1.2532 and futures price is 94.03125. From September 22 to March 1 is 161 days so T = 161/365 = 0.4411. 22 to March 1 is 161 days so T = 161/365 = 0.4411. Accrued interest reflects the reinvestment of a coupon Accrued interest reflects the reinvestment of a coupon on February 15 for 15 days and the accrual of 15 days on February 15 for 15 days and the accrual of 15 days toward the next coupon. So accrued interest istoward the next coupon. So accrued interest is 4.0625(1.058)4.0625(1.058)15/36515/365 + 4.0625(15/184) = 4.40. + 4.0625(15/184) = 4.40.


22


Implied Repo/Cost of Carry (continued)Implied Repo/Cost of Carry (continued) Implied repo rate is, therefore,Implied repo rate is, therefore,

If the bond can be financed in the repo market for less If the bond can be financed in the repo market for less than 5.28%, then the arbitrage would be profitable.than 5.28%, then the arbitrage would be profitable.

.052810.84118.65625

4.401.2532)94.031125(r̂

1/.4411


23


A Treasury Bond Futures SpreadA Treasury Bond Futures Spread See See Table 11.5, p. 475Table 11.5, p. 475..


24


Treasury Bond Spread/Implied Repo RateTreasury Bond Spread/Implied Repo Rate Let time t be expiration of nearby futures and T be Let time t be expiration of nearby futures and T be

expiration of deferred futures. expiration of deferred futures. Go long the nearby and short the deferred.Go long the nearby and short the deferred. When nearby expires, take delivery and hold until When nearby expires, take delivery and hold until

expiration of deferred. This creates a forward expiration of deferred. This creates a forward transaction beginning at t and ending at Ttransaction beginning at t and ending at T


25


Treasury Bond Spread/Implied Repo Rate (continued)Treasury Bond Spread/Implied Repo Rate (continued) Implied repo rateImplied repo rate

Example: On September 22, CTD was 8 1/8s maturing in Example: On September 22, CTD was 8 1/8s maturing in about 21years. Examine the March-June spread. March about 21years. Examine the March-June spread. March priced at fpriced at f00(t) = 94.03125 with CF(t) = 1.2532. June priced at (t) = 94.03125 with CF(t) = 1.2532. June priced at

ff00(T) = 93.625 with CF(T) = 1.2518. AI(T) = 93.625 with CF(T) = 1.2518. AItt (March 3) = 0.38 (March 3) = 0.38

and AIand AITT (June 2) = 2.41. From March 3 to June 2 is 91 days. (June 2) = 2.41. From March 3 to June 2 is 91 days.

1AI(t)(CF(t))f

AI(T)(CF(T))fr̂

t)1/(T

t0

T0


26


Treasury Bond Spread/Implied Repo Rate (continued)Treasury Bond Spread/Implied Repo Rate (continued) Implied repo rateImplied repo rate

Compare to actual repo rate and note that this is a Compare to actual repo rate and note that this is a forward rate.forward rate.

Note the turtle trade: Implied repo rate on T-bond Note the turtle trade: Implied repo rate on T-bond spread to T-bill futures ratespread to T-bill futures rate

.04810.38.2532)94.03125(1

2.41518)93.625(1.2r̂

365/91


27


Intermarket SpreadsIntermarket Spreads NOB and MOB spreadsNOB and MOB spreads

Bond Market Timing With FuturesBond Market Timing With Futures Adjusting a bond portfolio’s current duration to a target Adjusting a bond portfolio’s current duration to a target

durationduration

This is very similar to the hedging example in Chapter This is very similar to the hedging example in Chapter 10 where the target duration is zero.10 where the target duration is zero.

S

f

f

STf y1

y1

f

S

DUR

DURDURN


28


Bond Market Timing With Futures (continued)Bond Market Timing With Futures (continued) See See Table 11.6, p. 480Table 11.6, p. 480 Predicted price change of -2.72 %. Actual change was Predicted price change of -2.72 %. Actual change was

-2.26 %. Without hedge, price change would have -2.26 %. Without hedge, price change would have been -5.26 %, while predicted change without hedge been -5.26 %, while predicted change without hedge would have been -5.33 %.would have been -5.33 %.


29

Stock Index Futures Strategies

Stock Index ArbitrageStock Index Arbitrage Recall the stock index futures pricing modelRecall the stock index futures pricing model

Example: Let S&P 500 = 1305.00, risk-free rate is 5.2 %, dividend Example: Let S&P 500 = 1305.00, risk-free rate is 5.2 %, dividend yield is 3 % and time to expiration is 40 days so T = 40/365 yield is 3 % and time to expiration is 40 days so T = 40/365 = .1096. Futures should be at= .1096. Futures should be at 1305e1305e(.052 - .03)(.1096)(.052 - .03)(.1096) = 1308.15 = 1308.15

Now let the actual futures price be 1309.66. This is too high so sell Now let the actual futures price be 1309.66. This is too high so sell the futures and buy the index. Hold until expiration. Sell the the futures and buy the index. Hold until expiration. Sell the stocks and buy back the futures.stocks and buy back the futures.

)T(r00

ceS(T)f


30

Stock Index Futures Strategies (continued)

Stock Index Arbitrage (continued)Stock Index Arbitrage (continued) Now find the implied repo rate. Let fNow find the implied repo rate. Let f00(T) be the actual (T) be the actual

futures price. Thenfutures price. Then

In our example, this isIn our example, this is

So if you could get financing at less than this rate, the So if you could get financing at less than this rate, the arbitrage would be worth doing.arbitrage would be worth doing.

T

)(T)/Sln(fr 00^

.0625.03.1096

/1305)ln(1309.66r^


31


Stock Index Arbitrage (continued)Stock Index Arbitrage (continued) Some practical considerationsSome practical considerations

buying and selling all stocks simultaneouslybuying and selling all stocks simultaneously buying fractional contractsbuying fractional contracts transaction costs of about .005 % of spot value.transaction costs of about .005 % of spot value.

Program trading. See Program trading. See Figure 11.1, p. 484Figure 11.1, p. 484.. See See Table 11.7, p. 485Table 11.7, p. 485 for stock index arbitrage for stock index arbitrage

example.example.


32


Speculating on Unsystematic RiskSpeculating on Unsystematic Risk To eliminate systematic risk in order to capture To eliminate systematic risk in order to capture

unsystematic return of a stock believed to be unsystematic return of a stock believed to be underpriced.underpriced.

Use same hedge ratio previously obtained: NUse same hedge ratio previously obtained: Nff = = (S/f)

Example: See Table 11.8, p. 488


33


Stock Market Timing With FuturesStock Market Timing With Futures To change the beta on a portfolio of stocks to a target To change the beta on a portfolio of stocks to a target

beta use the hedge ratiobeta use the hedge ratio

See example in See example in Table 11.9, p. 490Table 11.9, p. 490

N )S

ff T S

(


34


Arbitraging Stock Index Futures With Stock Index OptionsArbitraging Stock Index Futures With Stock Index Options Can construct synthetic futures with options.Can construct synthetic futures with options. Recall put-call-forward/futures parityRecall put-call-forward/futures parity

PPee(S(S00,T,X) = C,T,X) = Cee(S(S00,T,X) + (X - f,T,X) + (X - f00(T))(1+r)(T))(1+r)-T-T

See See Table 11.10, p. 492Table 11.10, p. 492.. Example using S&P 500. On May 14, S&P 500 at Example using S&P 500. On May 14, S&P 500 at

1337.80 and June futures at 1339.30. June 1340 call at 1337.80 and June futures at 1339.30. June 1340 call at 40 and put at 39. Expiration of June 18 so T = 35/365 40 and put at 39. Expiration of June 18 so T = 35/365 = .0959. Risk-free rate at 4.56.= .0959. Risk-free rate at 4.56.


35


Arbitraging Stock Index Futures With Stock Index Options Arbitraging Stock Index Futures With Stock Index Options (continued)(continued) So PSo Pee(S(S00,T,X) = 39,T,X) = 39

CCee(S(S00,T,X) + (X - f,T,X) + (X - f00(T))(1+r)(T))(1+r)-T-T

= 40 + (1340 - 1339.30)(1.0456)= 40 + (1340 - 1339.30)(1.0456)-.0959-.0959 = 40.70. = 40.70. Buy put and futures for 39, sell call and bond for 40.70 Buy put and futures for 39, sell call and bond for 40.70

and net 1.70 profit at no risk. Transaction costs would and net 1.70 profit at no risk. Transaction costs would have to be considered.have to be considered.


36

Summary

See Figure 11.2, p. 494 for linkages between puts, calls, See Figure 11.2, p. 494 for linkages between puts, calls, and forwards/futures.and forwards/futures.


37

Appendix 11A: Determining the CBOT Treasury Bond Conversion Factor

Determine maturity in years (YRS), months (MOS) and Determine maturity in years (YRS), months (MOS) and days as of first date of expiration month. Use first call days as of first date of expiration month. Use first call date if callable. Ignore days. Let c be coupon rate. Round date if callable. Ignore days. Let c be coupon rate. Round months down to 0, 3, 6, or 9. Call this MOS*.months down to 0, 3, 6, or 9. Call this MOS*. If MOSIf MOS** = 0, = 0,

YRS*2YRS*2

0 (1.03).03

(1.03)1

2

cCF


38

Appendix 11A: Determining the CBOT Treasury Bond Conversion Factor (continued)

If MOSIf MOS** = 3, = 3,



c/4c/2)(1.03)(CFCF .503

1)YRS*2(1)YRS*2(

6 (1.03).03

(1.03)1

2

cCF

c/4c/2)(1.03)(CFCF .569


39


Example: 7 7/8s of February 15, 2021 delivered on March Example: 7 7/8s of February 15, 2021 delivered on March 2000 contract. On March 1, 2000 remaining life is 20 2000 contract. On March 1, 2000 remaining life is 20 years, 11 months, 14 days. YRS = 20, MOS = 11. Round years, 11 months, 14 days. YRS = 20, MOS = 11. Round down so that MOSdown so that MOS** = 9. Find CF = 9. Find CF66::

Then CFThen CF99 is is

1.2195 (1.03).03

(1.03)1

2

.07875CF 1)*(20)2(

1)*(20)2(

6

1.2207.07875/41.03).07875/2)((1.2195CF .59


40


Excel spreadsheet cf1.xls described in Excel spreadsheet cf1.xls described in Software Software Demonstration 11.2, p. 500Demonstration 11.2, p. 500 will calculate conversion will calculate conversion factor.factor.


41

Appendix 11B: Derivation of the Hedge Ratio for Adjusting Duration With Treasury Bond Futures

The value of the position isThe value of the position is V = S + vV = S + vffNNff

Use the following results:Use the following results: vvff//r = r = f/f/rr ys/r = yf/r

All of this follows the procedure in Appendix 10A. All of this follows the procedure in Appendix 10A. Differentiate with respect to r, use the above results, Differentiate with respect to r, use the above results, apply the chain rule, set DURapply the chain rule, set DURvv to DUR to DURTT and solve for and solve for

NNff. The approximation is. The approximation is


42

Appendix 11A: Derivation of the Hedge Ratio for Adjusting Duration With Treasury Bond Futures (continued)

NDUR DUR

DUR

S

f

y

1+ yfS T

f

f

S

1

Copyright © 2001 by Harcourt, Inc. All rights reserved.1 Chapter 11: Advanced Futures Strategies...

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Transcript of Copyright © 2001 by Harcourt, Inc. All rights reserved.1 Chapter 11: Advanced Futures Strategies...