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A Complete Guide to the Futures mArket
It should be emphasized that the futures price need not necessarily reach the strike price in order
for the out-of-the-money put to be profitable. If the market declines quickly, the put will increase in
value, and hence can be resold at aprofit. (However, this behavior will not necessarily hold for slow
price declines, since the depressant effect of the passage of time on the option premium could well
more than offset the supportive effect of the decreased price level of futures.)
For small price changes, the out-of-the-money put will change by less than afactor of one-half for
each dollar change in the futures price. Thus, for small price changes, each short futures position will
be equivalent to several short out-of-the-money puts in terms of risk.
Strategy 5c: Long put (In-the-Money)
example. Buy August $1,300 gold futures put at apremium of $108.70/oz ($10,870), with August
gold futures trading at $1,200/oz. (See Table 35.5c and Figure 35.5c.)
Comment. In many respects, along in-the-money put option is very similar to ashort futures posi-
tion. The three main differences between these two trading strategies are:
 1. The short futures position will gain slightly more in the event of aprice decline—an amount
equal to the time value portion of the premium paid for the option ($870 in this example).
 2. For moderate price advances, the short futures position will lose slightly less. (Once again, the
difference will be equal to the time value portion of the premium paid for the option.)
 3. In the event of alarge price advance, the loss on the in-the-money long put position would be
limited to the total option premium paid, while the loss on the short futures position would be
unlimited.
tabLe 35.5c profit/Loss Calculations: Long put (In-the-Money)
(1) (2) (3) (4) (5)
Futures price at
expiration ($/oz)
premium of august $1,300
put at Initiation ($/oz)
Dollar amount
of premium paid
Value of put
at expiration
profit/Loss on
position [(3) – (4)]
1,000 108.7 $10,870 $30,000 $19,130
1,050 108.7 $10,870 $25,000 $14,130
1,100 108.7 $10,870 $20,000 $9,130
1,150 108.7 $10,870 $15,000 $4,130
1,200 108.7 $10,870 $10,000 –$870
1,250 108.7 $10,870 $5,000 –$5,870
1,300 108.7 $10,870 $0 –$10,870
1,350 108.7 $10,870 $0 –$10,870
1,400 108.7 $10,870 $0 –$10,870

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OPTION TrAdINg STrATegIeS
 In asense, the long in-the-money put position can be thought of as ashort futures position with
abuilt-in stop. This characteristic is an especially important consideration for speculators who
typically employ protective stop loss orders on their positions—aprudent trading approach. Atrader using aprotective buy stop on ashort position faces the frustrating possibility of the market
advancing suffi ciently to activate his stop and subsequently breaking. The long in-the-money put
position off ers the speculator an alternative method of limiting risk that does not present this
danger. Of course, this benefi tdoes not come without acost: as mentioned earlier, the buyer of an
in-the-money put will gain slightly less than the outright short futures trader if the market declines
and lose slightly more if the market advances moderately. However, if the trader is anticipating
volatile market conditions, he might very well prefer along in-the-money put position to ashort
futures position combined with aprotective buy stop order. In any case, the key point is that the
trader who routinely compares the strategies of buying an in-the-money put versus going short
futures with aprotective buy stop should enjoy an advantage over those traders who never consider
the option-based alternative.
 Table 35.5 dsummarizes the profi t/loss implications of various long put positions for arange of
price assumptions. Note that as puts move deeper in-the-money, their profi tand loss characteristics
increasingly resemble ashort futures position.
 FIGURE  35.5c Profi t/loss Profi le: long Put (In-the-Money)
Price of August gold futures at option expiration ($/oz)
Futures
price at time
of position
initiation
Strike price
Breakeven price
= $1,191.30
Profit/loss at expiration ($)
1,000
10,000
−10,000
−15,000
5,000
−5,000
0
15,000
20,000
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400

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A Complete Guide to the Futures mArket
tabLe 35.5d profit/Loss Matrix for Long puts with Different Strike prices
Dollar amount of premium paid
$1,350
put
$1,300
put
$1,250
put
$1,200
put
$1,150
put
$1,100
put
$1,050
put
$15,410 $10,870 $6,870 $3,870 $1,990 $1,010 $510
position profit/Loss at expiration
Futures price at
expiration ($/oz)
Short Futures
at $1,200
In-the-Money at-the-Money Out-of-the-Money
$1,350
put
$1,300
puta
$1,250
put
$1,200
puta
$1,150
put
$1,100
puta
$1,050
put
1,000 $20,000 $19,590 $19,130 $18,130 $16,130 $13,010 $8,990 $4,490
1,050 $15,000 $14,590 $14,130 $13,130 $11,130 $8,010 $3,990 –$510
1,100 $10,000 $9,590 $9,130 $8,130 $6,130 $3,010 –$1,010 –$510
1,150 $5,000 $4,590 $4,130 $3,130 $1,130 –$1,990 –$1,010 –$510
1,200 $0 –$410 –$870 –$1,870 –$3,870 –$1,990 –$1,010 –$510
1,250 –$5,000 –$5,410 –$5,870 –$6,870 –$3,870 –$1,990 –$1,010 –$510
1,300 –$10,000 –$10,410 –$10,870 –$6,870 –$3,870 –$1,990 –$1,010 –$510
1,350 –$15,000 –$15,410 –$10,870 –$6,870 –$3,870 –$1,990 –$1,010 –$510
1,400 –$20,000 –$15,410 –$10,870 –$6,870 –$3,870 –$1,990 –$1,010 –$510
aThese puts are compared in Figure 35.5d.
Figure 35.5d compares the three types of long put positions to ashort futures position. It should
be noted that in terms of absolute price changes, the short futures position represents the largest
position size, while the out-of-the-money put represents the smallest position size. Figure 35.5d sug-
gests the following important observations:
 1. As previously mentioned, the in-the-money put is very similar to an outright short futures
position.
 2. The out-of-the-money put will lose the least in arising market, but will also gain the least in adeclining market.
 3. The at-the-money put will lose the most in asteady market and will be the middle-of-
the-road performer (relative to the other two types of puts) in declining and advancing
markets.
Again, it should be emphasized that these comparisons are based on single-unit positions that
may differ substantially in terms of their implied position size (as suggested by their respective delta
values). Acomparison that involved equivalent position size levels for each strategy (i.e., equal delta
values for each position) would yield different observations.

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509
OPTION TrAdINg STrATegIeS
example . Sell August $1,200 gold futures put at apremium of $38.70/oz ($3,870), with August gold
futures trading at $1,200/oz. (See Table 35.6 aand Figure 35.6 a.)
Price of August gold futures at option expiration ($/oz)
Futures price at time
of position initiation
Short futures
At-the-money put
(strike price = $1,200)
Out-of-the-money put
(strike price = $1,100)
In-the-money
put (strike price = $1,300)
Price/loss at expiration ($)
1,000
10,000
−10,000
−15,000
5,000
−5,000
0
15,000
20,000
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
 FIGURE  35.5d Profi t/loss Profi le: Short Futures and long Put Comparisons (In-the-Money,
At-the-Money, and Out-of-the-Money)
 tabLe 35.6a profit/Loss Calculations: Short put (at-the-Money)
(1) (2) (3) (4) (5)
 Futures price at
expiration ($/oz)
 premium of august $1,200
put at Initiation ($/oz)
 $ amount of
premium received
 put Value at
expiration
 profit/Loss on
position [(3) – (4)]
1,000 38.7 $3,870 $20,000 –$16,130
1,050 38.7 $3,870 $15,000 –$11,130
1,100 38.7 $3,870 $10,000 –$6,130
1,150 38.7 $3,870 $5,000 –$1,130
1,200 38.7 $3,870 $0 $3,870
1,250 38.7 $3,870 $0 $3,870
1,300 38.7 $3,870 $0 $3,870
1,350 38.7 $3,870 $0 $3,870
1,400 38.7 $3,870 $0 $3,870

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510A COMPleTe gUIde TO THe FUTUreS MArKeT
Comment. The short put is abullish position with amaximum potential gain equal to the premium
received for selling the put and unlimited risk. However, in return for assuming this unattractive
maximum reward/maximum risk relationship, the seller of aput enjoys agreater probability of real-
izing aprofi tthan aloss. Note that the short at-the-money put position will result in again as long as
the futures price at the time of the option expiration is not below the futures price at the time of the
option initiation by an amount greater than the premium level ($38.70/oz in our example). However,
the maximum possible profi t (i.e., the premium received on the option) will only be realized if the
futures price at the time of the option expiration is above the prevailing market price at the time the
option was sold (i.e., the strike price). The short put position is appropriate if the trader is modestly
bullish and views the probability of alarge price decline as being very low . If, however, the trader
anticipated alarge price advance, he would probably be better off buying acall or going long futures.
 Strategy 6b: Short put (Out-of-the-Money)
example . Sell August $1,100 gold futures put at apremium of $10.10 /oz ($1,010), with August gold
futures trading at $1,200/oz. (See Table 35.6 band Figure 35.6 b .)
Comment. The seller of an out-of-the-money put is willing to accept asmaller maximum gain (i.e.,
premium) in exchange for increasing the probability of gain on the trade. The seller of an out-of-the-
money put will retain the full premium received as long as the futures price does not decline by an
 FIGURE  35.6a Profi t/loss Profi le: Short Put (At-the-Money)
Price of August gold futures at option expiration ($/oz)
Futures price at time
of position initiation
and strike price
Breakeven price
= $1,161.30
Profit/loss at expiration ($)
1,000
−10,000
−12,500
5,000
2,500
−2,500
−5,000
−7,500
0
−15,000
−17,500
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400

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511
OPTION TrAdINg STrATegIeS
amount greater than the diff erence between the futures price at the time of the option sale and the
strike price. The trade will be profi table as long as the futures price at the time of the option expira-
tion is not below the strike price by more than the option premium ($10.10/oz in this example).
The short out-of-the-money put represents aless bullish posture than the short at-the-money put
 tabLe 35.6b profit/Loss Calculations: Short put (Out-of-the-Money)
(1) (2) (3) (4) (5)
 Futures price at
expiration ($/oz)
 premium of august $1,100
put at Initiation ($/oz)
 Dollar amount of
premium received
 Value of put
at expiration
 profit/Loss on
position [(3) – (4)]
1,000 10.1 $1,010 $10,000 –$8,990
1,050 10.1 $1,010 $5,000 –$3,990
1,100 10.1 $1,010 $0 $1,010
1,150 10.1 $1,010 $0 $1,010
1,200 10.1 $1,010 $0 $1,010
1,250 10.1 $1,010 $0 $1,010
1,300 10.1 $1,010 $0 $1,010
1,350 10.1 $1,010 $0 $1,010
1,400 10.1 $1,010 $0 $1,010
Price of August gold futures at option expiration ($/oz)
Futures price at time
of position initiation
Breakeven price
= $1,089.90
Profit/loss at expiration ($)
1,000
−10,000
2,500
−2,500
−5,000
−7,500
0
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
Strike price
 FIGURE  35.6b Profi t/loss Profi le: Short Put (Out-of-the-Money)

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A Complete Guide to the Futures mArket
position. Whereas the short at-the-money put position reflects an expectation that prices will either
rise or decline only slightly, the short out-of-the-money put merely reflects an expectation that prices
will not decline sharply.
Strategy 6c: Short put (In-the-Money)
example. Sell August $1,300 gold futures put at apremium of $108.70/oz ($10,870), with August
gold futures trading at $1,200/oz. (See Table 35.6c and Figure 35.6c.)
Comment. For most of the probable price range, the profit/loss characteristics of the short in-the-
money put are fairly similar to those of the outright long futures position. There are three basic dif-
ferences between these two positions:
 1. The short in-the-money put will lose modestly less than the long futures position in adeclining market because the loss will be partially offset by the premium received for
the put.
 2. The short in-the-money put will gain modestly more than the long futures position in amoder-
ately advancing market.
 3. In avery sharply advancing market, the profit potential on along futures position is open-ended,
whereas the maximum gain in the short in-the-money put position is limited to the total pre-
mium received for the put.
In effect, the seller of an in-the-money put chooses to lock in modestly better results for the
probable price range in exchange for surrendering the opportunity for windfall profits in the
event of aprice explosion.
generally speaking, atrader should only choose ashort in-the-money
put over along futures position if he believes that the probability of asharp price advance is
extremely small.
tabLe 35.6c profit/Loss Calculations: Short put (In-the-Money)
(1) (2) (3) (4) (5)
Futures price at
expiration ($/oz)
premium of august $1,300
put at Initiation ($/oz)
Dollar amount of
premium received
put Value at
expiration
profit/Loss on
position [(3) – (4)]
1,000 108.7 $10,870 $30,000 –$19,130
1,050 108.7 $10,870 $25,000 –$14,130
1,100 108.7 $10,870 $20,000 –$9,130
1,150 108.7 $10,870 $15,000 –$4,130
1,200 108.7 $10,870 $10,000 $870
1,250 108.7 $10,870 $5,000 $5,870
1,300 108.7 $10,870 $0 $10,870
1,350 108.7 $10,870 $0 $10,870
1,400 108.7 $10,870 $0 $10,870

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513
OPTION TrAdINg STrATegIeS
 Table 35.6 dsummarizes the profi t/loss results for various short put positions for arange of price
assumptions. As can be seen, as puts move more deeply in the money, they begin to more closely
resemble along futures position. (As previously explained in the case of calls, sellers of deep in-the-
money options should be cognizant of the real possibility of early exercise.) Short positions in deep
out-of-the-money puts will prove profi table for the vast range of prices, but the maximum gain is
small and the theoretical maximum loss is unlimited.
 Figure 35.6 dcompares each type of short put to along futures position. The short at-the-money
put position will be the most profi table strategy under stable market conditions and the middle-of-
the-road strategy (relative to the other two types of puts) in declining and rising markets. The short
out-of-the-money put will lose the least in adeclining market, but it will also be the least profi table
strategy if prices advance. The short in-the-money put is the type of put that has the greatest potential
and risk and, as mentioned above, there is astrong resemblance between this strategy and an outright
long position in futures.
 It should be emphasized that the comparisons in Figure 35.6 dare based upon single-unit positions.
However, as previously explained, these alternative strategies do not represent equivalent position
sizes. Comparisons based on positions weighted equally in terms of some risk measure (e.g., equal
delta values) would yield diff erent empirical conclusions.
 FIGURE  35.6c Profi t/loss Profi le: Short Put (In-the-Money)
Price of August gold futures at option expiration ($/oz)
Futures price
at time of
position initiation
Breakeven price
=$1,191.30
Profit/loss at expiration ($)
1,000
10,000
15,000
−10,000
5,000
−5,000
−15,000
−20,000
0
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
Strike price

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514A COMPleTe gUIde TO THe FUTUreS MArKeT
 tabLe 35.6d profit/Loss Matrix for Short puts with Different Strike prices
Dollar amount of premium received
$1,350
put
$1,300
put
$1,250
put
$1,200
put
$1,150
put
$1,100
put
$1,050
put
$15,410 $10,870 $6,870 $3,870 $1,990 $1,010 $510
position profit/Loss at expiration
Futures price at
expiration ($/oz)
Long
Futures
at $1,200
In-the-
Money
at-the-
Money
Out-of-
the-Money
$1,350
put
$1,300
put a
$1,250
put
$1,200
put a
$1,150
put
$1,100
put a
$1,050
put
1,000 –$20,000 –$19,590 –$19,130 –$18,130 –$16,130 –$13,010 –$8,990 –$4,490
1,050 –$15,000 –$14,590 –$14,130 –$13,130 –$11,130 –$8,010 –$3,990 $510
1,100 –$10,000 –$9,590 –$9,130 –$8,130 –$6,130 –$3,010 $1,010 $510
1,150 –$5,000 –$4,590 –$4,130 –$3,130 –$1,130 $1,990 $1,010 $510
1,200 $0 $410 $870 $1,870 $3,870 $1,990 $1,010 $510
1,250 $5,000 $5,410 $5,870 $6,870 $3,870 $1,990 $1,010 $510
1,300 $10,000 $10,410 $10,870 $6,870 $3,870 $1,990 $1,010 $510
1,350 $15,000 $15,410 $10,870 $6,870 $3,870 $1,990 $1,010 $510
1,400 $20,000 $15,410 $10,870 $6,870 $3,870 $1,990 $1,010 $510
 a These puts are compared in Figure 35.6 d.
Price of August gold futures at option expiration ($/oz)
Futures price at time
of position initiation
Long futures
At-the-money put
(strike price = $1,200)
Out-of-the money
put (strike price
= $1,100)
In-the-money put
(strike price = $1,300)
Profit/loss at expiration ($)
1,000
10,000
15,000
−10,000
5,000
−5,000
0
−15,000
−20,000
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
 FIGURE  35.6d Profi t/loss Profi le: long Futures and Short Put Comparisons (In-the-Money,
At-the-Money, and Out-of-the-Money)

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OPTION TrAdINg STrATegIeS
Strategy 7: Long Straddle (Long Call + Long put)
example. Buy August $1,200 gold futures call at apremium of $38.80/oz ($3,880) and simultane-
ously buy an August $1,200 gold futures put at apremium of $38.70/oz ($3,870). (See Table 35.7
and Figure 35.7.)
Comment. The long straddle position is avolatility bet. The buyer of astraddle does not have
any opinion regarding the probable price direction; he merely believes that option premiums
are underpriced relative to the potential market volatility. Andrew Tobias once offered asome -
what more cynical perspective of this type of trade
1: “Indeed, if you haven’tany idea of which
way the [market] is headed but feel it is headed someplace, you can buy both aput and acall
on it. That’scalled astraddle and involves enough commissions to keep your broker smiling
all week.”
As can be seen in Figure 35.7, the long straddle position will be unprofitable for awide price
range centered at the current price. Since this region represents the range of the most probable price
outcomes, the long straddle position has alarge probability of loss. In return for accepting alarge
probability of loss, the buyer of astraddle enjoys unlimited profit potential in the event of either alarge price rise or alarge price decline. The maximum loss on along straddle position is equal to the
total premium paid for both the long call and long put and will only be experienced if the expiration
price is equal to the futures price at the time the options were purchased. (Implicit assumption: both
the call and put are at-the-money options.)
tabLe 35.7 profit/Loss Calculations: Long Straddle (Long Call + Long put)
(1) (2) (3) (4) (5) (6) (7)
Futures price
at expiration
($/oz)
premium of august
$1,200 Call at
Initiation ($/oz)
premium of august
$1,200 put at
Initiation ($/oz)
$ amount of
total premium
paid
Call Value at
expiration
put Value at
expiration
profit/Loss on
position
[(5) + (6) – (4)]
1,000 38.8 38.7 $7,750 $0 $20,000 $12,250
1,050 38.8 38.7 $7,750 $0 $15,000 $7,250
1,100 38.8 38.7 $7,750 $0 $10,000 $2,250
1,150 38.8 38.7 $7,750 $0 $5,000 –$2,750
1,200 38.8 38.7 $7,750 $0 $0 –$7,750
1,250 38.8 38.7 $7,750 $5,000 $0 –$2,750
1,300 38.8 38.7 $7,750 $10,000 $0 $2,250
1,350 38.8 38.7 $7,750 $15,000 $0 $7,250
1,400 38.8 38.7 $7,750 $20,000 $0 $12,250
1 Andrew Tobias, Getting By on $100,000 a Year (and Other Sad Tales) (New York, NY: Simon & Schuster, 1980).

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516A COMPleTe gUIde TO THe FUTUreS MArKeT
 Strategy 8: Short Straddle (Short Call + Short put)
example . Sell August $1,200 gold futures call at apremium of $38.80/oz ($3,880 ) and simultane-
ously sell an August $1,200 put at apremium of $38.70/oz ($3,870). (See Table 35.8 and Figure 35.8 .)
Price of August gold futures at option expiration ($/oz)
Futures price at time
of position initiation
and call and put
strike prices
Breakeven price
= $1,122.50
Breakeven price
= 1,277.50
Profit/loss at expiration ($)
1,000
5,000
10,000
15,000
–10,000
–5,000
0
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
 FIGURE  35.7 Profi t/loss Profi le: long Straddle (long Call + long Put)
 tabLe 35.8 profit/Loss Calculations: Short Straddle (Short Call + Short put)
(1) (2) (3) (4) (5) (6) (7)
Futures price
at expiration
($/oz)
premium of august
$1,200 Call at
Initiation ($/oz)
premium of august
$1,200 put at
Initiation ($/oz)
$ amount of
total premium
received
Call Value at
expiration
put Value at
expiration
profit/Loss on
position
[(4) – (5) – (6)]
1,000 38.8 38.7 $7,750 $0 $20,000 –$12,250
1,050 38.8 38.7 $7,750 $0 $15,000 –$7,250
1,100 38.8 38.7 $7,750 $0 $10,000 –$2,250
1,150 38.8 38.7 $7,750 $0 $5,000 $2,750
1,200 38.8 38.7 $7,750 $0 $0 $7,750
1,250 38.8 38.7 $7,750 $5,000 $0 $2,750
1,300 38.8 38.7 $7,750 $10,000 $0 –$2,250
1,350 38.8 38.7 $7,750 $15,000 $0 –$7,250
1,400 38.8 38.7 $7,750 $20,000 $0 –$12,250

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517
OPTION TrAdINg STrATegIeSComment. The short straddle position will be profi table over awide range of prices. The best outcome
for aseller of astraddle is atotally unchanged market. In this circumstance, the seller will realize his
maximum profi t, which is equal to the total premium received for the sale of the call and put. The short
straddle position will remain profi table as long as prices do not rise or decline by more than the combined
total premium of the two options. The seller of the straddle enjoys alarge probability of aprofi table trade,
in exchange for accepting unlimited risk in the event of either avery sharp price advance or decline.
 This strategy is appropriate if the speculator expects prices to trade within amoderate range, but
has no opinion regarding the probable market direction. Atrader anticipating nonvolatile market con-
ditions, but also having aprice-directional bias, would be better off selling either calls or puts rather
than astraddle. For example, atrader expecting low volatility and modestly declining prices should
sell 2 calls instead of selling astraddle.
 Strategy 9: bullish “texas Option hedge” (Long Futures + Long Call) 2
example . Buy August gold futures at $1,200 and simultaneously buy an August $1,200 gold futures
call at apremium of $38.80 /oz ($3,880). (See Table 35.9 and Figure 35.9 .)
 FIGURE  35.8 Profi t/loss Profi le: Short Straddle (Short Call + Short Put)
 Profi t/loss Profi le: Short Straddle (Short Call + Short Put)
Price of August gold futures at option expiration ($/oz)
Breakeven price
= $1,122.50
Breakeven price
= 1,277.50
Profit/loss at expiration ($)
1,000
5,000
10,000
–10,000
–15,000
–5,000
0
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
Futures price at time
of position initiation
and call and put
strike prices
 2 By defi nition, ahedge implies afutures position opposite to an existing or anticipated actual position. In com-
modity trading, Texas hedge is afacetious reference to so-called “hedgers” who implement afutures position in the
same direction as their cash position. The classic example of a Texas hedge would be acattle feeder who goes long
cattle futures. Whereas normal hedging reduces risk, the Texas hedge increases risk. There are many option strate-
gies that combine off setting positions in options and futures. This strategy is unusual in that it combines reinforcing
positions in futures and options. Consequently, the term Texas option hedge seems to provide an appropriate label.

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518A COMPleTe gUIde TO THe FUTUreS MArKeT
 tabLe 35.9 profit/Loss Calculations: bullish “texas Option hedge” (Long Futures + Long Call)
(1) (2) (3) (4) (5) (6)
Futures price at
expiration ($/oz)
premium of august
$1,200 Call at
Initiation ($/oz)
$ amount of
premium paid
profit/Loss on Long
Futures position
Call Value at
expiration
profit/Loss on
position [(4)+(5)–(3)]
1,000 38.8 $3,880 –$20,000 $0 –$23,880
1,050 38.8 $3,880 –$15,000 $0 –$18,880
1,100 38.8 $3,880 –$10,000 $0 –$13,880
1,150 38.8 $3,880 –$5,000 $0 –$8,880
1,200 38.8 $3,880 $0 $0 –$3,880
1,250 38.8 $3,880 $5,000 $5,000 $6,120
1,300 38.8 $3,880 $10,000 $10,000 $16,120
1,350 38.8 $3,880 $15,000 $15,000 $26,120
1,400 38.8 $3,880 $20,000 $20,000 $36,120
 FIGURE  35.9 Profi t/loss Profi le: Bullish “Texas Option Hedge” (long Futures + long Call)
Price of August gold futures at option expiration ($/oz)
Futures price at time of position
initiation and strike price
Breakeven price = $1,219.40
Profit/loss at expiration ($)
1,000
37,500
50,000
25,000
−25,000
−37,500
12,500
−12,500
0
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
Long 2 futures
Long futures + long call

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519
OPTION TrAdINg STrATegIeS
Comment. This strategy provides an interesting alternative method of pyramiding—that is, increas-
ing the size of awinning position. For example, atrader who is already long afutures contract at aprofit and believes the market is heading higher may wish to increase his position without doubling
his risk in the event of aprice reaction—as would be the case if he bought asecond futures contract.
Such aspeculator could choose instead to supplement his long position with the purchase of acall,
thereby limiting the magnitude of his loss in the event of aprice retracement, in exchange for real-
izing amoderately lower profit if prices continued to rise.
Figure 35.9 compares the alternative strategies of buying two futures versus buying afutures con-
tract and acall. (For simplicity of exposition, the diagram assumes that both the futures contract and
the call are purchased at the same time.) As can be seen, the long two futures position will always do
moderately better in arising market (by an amount equal to the premium paid for the call), but will
lose more in the event of asignificant price decline. The difference in losses between the two strate-
gies will widen as larger price declines are considered.
Strategy 10: bearish “texas Option hedge” (Short Futures +
Long put)
example. Sell August gold futures at $1,200 and simultaneously buy an August $1,200 gold put at apremium of $38.70/oz ($3,870). (See Table 35.10 and Figure 35.10.)
Comment. This strategy is perhaps most useful as an alternative means of increasing ashort position.
As illustrated in Figure 35.10, the combination of ashort futures contract and along put will gain
moderately less than 2 short futures contracts in adeclining market, but will lose amore limited
amount in arising market.
tabLe 35.10 profit/Loss Calculations: bearish “texas Option hedge” (Short Futures + Long put)
(1) (2) (3) (4) (5) (6)
Futures price at
expiration ($/oz)
premium of august $1200
put at Initiation ($/oz)
$ amount of
premium paid
profit/Loss on Short
Futures position
put Value at
expiration
profit/Loss on position
[(4) + (5) – (3)]
1,000 38.7 $3,870 $20,000 $20,000 $36,130
1,050 38.7 $3,870 $15,000 $15,000 $26,130
1,100 38.7 $3,870 $10,000 $10,000 $16,130
1,150 38.7 $3,870 $5,000 $5,000 $6,130
1,200 38.7 $3,870 $0 $0 –$3,870
1,250 38.7 $3,870 –$5,000 $0 –$8,870
1,300 38.7 $3,870 –$10,000 $0 –$13,870
1,350 38.7 $3,870 –$15,000 $0 –$18,870
1,400 38.7 $3,870 –$20,000 $0 –$23,870

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520A COMPleTe gUIde TO THe FUTUreS MArKeT
 Strategy 11a: Option-protected Long Futures (Long Futures + Long
at-the-Money put)
example . Buy August gold futures at $1,200/oz and simultaneously buy an August $1200 gold put at
apremium of $38.70/oz ($3,870). (See Table 35.11 aand Figure 35.11 a.)
Comment. Afrequently recommended strategy is that the trader implementing (or holding) along
futures position can consider buying aput to protect his downside risk. The basic idea is that if the
market declines, the losses in the long futures position will be off set dollar for dollar by the long put
position. Although this premise is true, it should be stressed that such acombined position represents
nothing more than aproxy for along call. The reader can verify the virtually identical nature of these
two alternative strategies by comparing Figure 35.11 ato Figure 35.3 a. If prices increase, the long
futures position will gain, while the option will expire worthless. On the other hand, if prices decline,
the loss in the combined position will equal the premium paid for the put. In fact, if the call and put
premiums are equal, along futures plus long put position will be precisely equivalent to along call.
 In most cases, the trader who fi nds the profi t/loss profi le of this strategy attractive would be better
off buying acall, because the transaction costs are likely to be lower. However, if the trader already
holds along futures position, buying aput may be areasonable alternative to liquidating this position
and buying acall.
Price of August gold futures at option expiration ($/oz)
Futures price at
time of position
initiation and
strike price
Breakeven price = $1,180.65
Profit/loss at expiration ($)
1,000
37,500
50,000
25,000
−25,000
−37,500
12,500
−12,500
0
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
Short 2 futures
Short futures + long put
 FIGURE  35.10 Profi t/loss Profi le: Bearish “Texas Option Hedge” (Short Futures + long Put)

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521
OPTION TrAdINg STrATegIeS
 tabLe 35.11a profit/Loss Calculations: Option-protected Long Futures—Long Futures + Long at-the-
Money put (Similar to Long at-the-Money Call)
(1) (2) (3) (4) (5) (6)
Futures price at
expiration ($/oz)
premium of august $1,200
put at Initiation ($/oz)
$ amount of
premium paid
profit/Loss on Long
Futures position
put Value at
expiration
profit/Loss on position
[(4) + (5) – (3)]
1,000 38.7 $3,870 –$20,000 $20,000 –$3,870
1,050 38.7 $3,870 –$15,000 $15,000 –$3,870
1,100 38.7 $3,870 –$10,000 $10,000 –$3,870
1,150 38.7 $3,870 –$5,000 $5,000 –$3,870
1,200 38.7 $3,870 $0 $0 –$3,870
1,250 38.7 $3,870 $5,000 $0 $1,130
1,300 38.7 $3,870 $10,000 $0 $6,130
1,350 38.7 $3,870 $15,000 $0 $11,130
1,400 38.7 $3,870 $20,000 $0 $16,130
 FIGURE  35.11a Profi t/loss Profi le: Option-Protected long Futures—long Futures + long
at-the-Money Put (Similar to long At-the-Money Call)
Price of August gold futures at option expiration ($/oz)
Futures at time of
position initiation
and strike price
Breakeven price = $1,238.70
Profit/loss at expiration ($)
1,000
10,000
7,500
12,500
15,000
17,500
5,000
−5,000
−2,500
2,500
0
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400

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522A COMPleTe gUIde TO THe FUTUreS MArKeT
 Strategy 11b: Option-protected Long Futures (Long Futures + Long
Out-of-the-Money put)
example . Buy August gold futures at $1,200/oz and simultaneously buy an August $1,100 gold
futures put at apremium of $10.10/oz ($1,010). (See Table 35.11 band Figure 35.11 b.)
 tabLe 35.11b profit/Loss Calculations: Option-protected Long Futures—Long Futures + Long Out-of-
the-Money put (Similar to Long In-the-Money Call)
(1) (2) (3) (4) (5) (6)
Futures price at
expiration ($/oz)
premium of august $1,100
put at Initiation ($/oz)
$ amount of
premium paid
profit/Loss on Long
Futures position
put Value at
expiration
profit/Loss on position
[(4) + (5) – (3)]
1,000 10.1 $1,010 –$20,000 $10,000 –$11,010
1,050 10.1 $1,010 –$15,000 $5,000 –$11,010
1,100 10.1 $1,010 –$10,000 $0 –$11,010
1,150 10.1 $1,010 –$5,000 $0 –$6,010
1,200 10.1 $1,010 $0 $0 –$1,010
1,250 10.1 $1,010 $5,000 $0 $3,990
1,300 10.1 $1,010 $10,000 $0 $8,990
1,350 10.1 $1,010 $15,000 $0 $13,990
1,400 10.1 $1,010 $20,000 $0 $18,990
 FIGURE  35.11b Profi t/loss Profi le: Option-Protected long Futures—long Futures + long
Out-of-the-Money Put (Similar to long In-the-Money Call)
Price of August gold futures at option expiration ($/oz)
Futures price at time
of position initiation
Breakeven price = $1,210.10
Profit/loss at expiration ($)
1,000
10,000
15,000
20,000
5,000
−5,000
−10,000
−15,000
0
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
Strike price

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523
OPTION TrAdINg STrATegIeS
Comment. As can be verified by comparing Figure 35.11b to Figure 35.3c, this strategy is virtually
equivalent to buying an in-the-money call. Supplementing along futures position with the purchase
of an out-of-the-money put will result in slightly poorer results if the market advances, or declines
moderately, but will limit the magnitude of losses in the event of asharp price decline. Thus, much
like the long in-the-money call position, this strategy can be viewed as along position with abuilt-
in stop.
In most cases, it will make more sense for the trader to simply buy an in-the-money call since
the transaction cost will be lower. However, if aspeculator is already long futures, the purchase of
an out-of-the-money put might present aviable alternative to liquidating this position and buying an
in-the-money call.
Strategy 12a: Option-protected Short Futures (Short Futures + Long
at-the-Money Call)
example. Sell August gold futures at $1,200/oz and simultaneously buy an August $1,200 gold call
at apremium of $38.80/oz ($3,880). (See Table 35.12a and Figure 35.12a.)
Comment. Afrequently recommended strategy is that the trader implementing (or holding) ashort
futures position can consider buying acall to protect his upside risk. The basic idea is that if the mar-
ket advances, the losses in the short futures position will be offset dollar for dollar by the long call
position. Although this premise is true, it should be stressed that such acombined position represents
nothing more than aproxy for along put. The reader can verify the virtually identical nature of these
two alternative strategies by comparing Figure 35.12a to Figure 35.5a. If prices decline, the short
futures position will gain, while the option will expire worthless. And if prices advance, the loss in the
combined position will equal the premium paid for the call. In fact, if the put and call premiums are
equal, ashort futures plus long call position will be precisely equivalent to along put.
tabLe 35.12a profit/Loss Calculations: Option-protected Short Futures—Short Futures + Long at-the-
Money Call (Similar to Long at-the-Money put)
(1) (2) (3) (4) (5) (6)
Futures price at
expiration ($/oz)
premium of august $1,200
Call at Initiation ($/oz)
$ amount of
premium paid
profit/Loss on Short
Futures position
Call Value at
expiration
profit/Loss on position
[(4)+ (5) – (3)]
1,000 38.8 $3,880 $20,000 $0 $16,120
1,050 38.8 $3,880 $15,000 $0 $11,120
1,100 38.8 $3,880 $10,000 $0 $6,120
1,150 38.8 $3,880 $5,000 $0 $1,120
1,200 38.8 $3,880 $0 $0 –$3,880
1,250 38.8 $3,880 –$5,000 $5,000 –$3,880
1,300 38.8 $3,880 –$10,000 $10,000 –$3,880
1,350 38.8 $3,880 –$15,000 $15,000 –$3,880
1,400 38.8 $3,880 –$20,000 $20,000 –$3,880

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524A COMPleTe gUIde TO THe FUTUreS MArKeT
 In most cases, the trader who fi nds the profi t/loss profi le of this strategy attractive would be better
off buying aput, because the transaction costs are likely to be lower. However, if the trader already
holds ashort futures position, buying acall may be areasonable alternative to liquidating this position
and buying aput.
 Strategy 12b: Option-protected Short Futures (Short Futures + Long
Out-of-the-Money Call)
example . Sell August gold futures at $1,200/oz and simultaneously buy an August $1,300 gold
futures call at apremium of $9.10/oz ($910). (See Table 35.12 band Figure 35.12 b.)
Comment. As can be verifi ed by comparing Figure 35.12 bto Figure 35.5 c, this strategy is virtually
equivalent to buying an in-the-money put. Supplementing ashort futures position with the purchase
of an out-of-the-money call will result in slightly poorer results if the market declines or advances
moderately, but will limit the magnitude of losses in the event of asharp price advance. Thus, much
as with the long in-the-money put position, this strategy can be viewed as ashort position with abuilt-in stop.
Price of August gold futures at option expiration ($/oz)
Futures price at time
of position initiation
and strike priceBreakeven price = $1,161.20
Profit/loss at expiration ($)
1,000
10,000
17,500
15,000
12,500
7,500
5,000
2,500
−5,000
−2,500
0
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
 FIGURE  35.12a Profi t/loss Profi le: Option-Protected Short Futures—Short Futures + long
At-the-Money Call (Similar to long At-the-Money Put)

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525
OPTION TrAdINg STrATegIeS
 In most cases, it will make more sense for the trader simply to buy an in-the-money put since the
transaction costs will be lower. However, if aspeculator is already short futures, the purchase of an
out-of-the-money call might present aviable alternative to liquidating this position and buying an
in-the-money put.
 tabLe 35.12b profit/Loss Calculations: Option-protected Short Futures—Short Futures + Long Out-
of-the-Money Call (Similar to Long In-the-Money put)
(1) (2) (3) (4) (5) (6)
Futures price at
expiration ($/oz)
premium of august $1,300
Call at Initiation ($/oz)
$ amount of
premium paid
profit/Loss on Short
Futures position
Call Value at
expiration
profit/Loss on position
[(4) + (5) – (3)]
1,000 9.1 $910 $20,000 $0 $19,090
1,050 9.1 $910 $15,000 $0 $14,090
1,100 9.1 $910 $10,000 $0 $9,090
1,150 9.1 $910 $5,000 $0 $4,090
1,200 9.1 $910 $0 $0 –$910
1,250 9.1 $910 –$5,000 $0 –$5,910
1,300 9.1 $910 –$10,000 $0 –$10,910
1,350 9.1 $910 –$15,000 $5,000 –$10,910
1,400 9.1 $910 –$20,000 $10,000 –$10,910
 FIGURE  35.12b Profi t/loss Profi le: Option-Protected Short Futures—Short Futures + long
Out-of-the-Money Call (Similar to long In-the-Money Put)
Price of August gold futures at option expiration ($/oz)
Futures price at time
of position initiation
Breakeven price = $1,190.90
Profit/loss at expiration ($)
1,000
10,000
15,000
20,000
5,000
−5,000
−10,000
−15,000
0
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
Strike price

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526
A Complete Guide to the Futures mArket
Strategy 13: Covered Call Write (Long Futures + Short Call)
example. Buy August gold futures at $1,200/oz and simultaneously sell an August $1,200 gold
futures call at apremium of $38.80/oz ($3,880). (See Table 35.13 and Figure 35.13.)
Comment. There has been alot of nonsense written about covered call writing. In fact, even
the term is misleading. The implication is that covered call writing—the sale of calls against long
positions—is somehow amore conservative strategy than naked call writing—the sale of calls without
any offsetting long futures position. This assumption is absolutely false. Although naked call writing
implies unlimited risk, the same statement applies to covered call writing. As can be seen in Figure
35.13, the covered call writer merely exchanges unlimited risk in the event of amarket advance (as is
the case for the naked call writer) for unlimited risk in the event of amarket decline. In fact, the reader
can verify that this strategy is virtually equivalent to a “naked” short put position (see Strategy 35.6a).
One frequently mentioned motivation for covered call writing is that it allows the holder of along
position to realize abetter sales price. For example, if the market is trading at $1,200 and the holder
of along futures contract sells an at-the-money call at apremium of $38.80/oz instead of liquidating
his position, he can realize an effective sales price of $1,238.80 if prices move higher (the $1,200
strike price plus the premium received for the sale of the call). And, if prices move down by no more
than $38.80/oz by option expiration, he will realize an effective sales price of at least $1,200. Pre-
sented in this light, this strategy appears to be a “heads you win, tails you win” proposition. However,
there is no free lunch. The catch is that if prices decline by more than $38.80, the trader will realize alower sales price than if he had simply liquidated the futures position. And, if prices rise substantially
higher, the trader will fail to participate fully in the move as he would have if he had maintained his
long position.
The essential point is that although many motivations are suggested for covered call writing, the
trader should keep in mind that this strategy is entirely equivalent to selling puts.
tabLe 35.13 profit/Loss Calculations: Covered Call Write—Long Futures + Short Call (Similar to
Short put)
(1) (2) (3) (4) (5) (6)
Futures price
at expiration
($/oz)
premium of
august $1,200 Call
at Initiation ($/oz)
$ amount of
premium received
profit/Loss on Long
Futures position
Call Value at
expiration
profit/Loss on position
[(3) + (4) – (5)]
1,000 38.8 $3,880 –$20,000 $0 –$16,120
1,050 38.8 $3,880 –$15,000 $0 –$11,120
1,100 38.8 $3,880 –$10,000 $0 –$6,120
1,150 38.8 $3,880 –$5,000 $0 –$1,120
1,200 38.8 $3,880 $0 $0 $3,880
1,250 38.8 $3,880 $5,000 $5,000 $3,880
1,300 38.8 $3,880 $10,000 $10,000 $3,880
1,350 38.8 $3,880 $15,000 $15,000 $3,880
1,400 38.8 $3,880 $20,000 $20,000 $3,880

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527
OPTION TrAdINg STrATegIeS
 Strategy 14: Covered put Write (Short Futures + Short put)
example . Sell August futures at $1,200 and simultaneously sell an August $1,200 gold futures put at
apremium of $38.70/oz ($3,870). (See Table 35.14 and Figure 35.14 .)
 FIGURE  35.13 Profi t/loss Profi le: Covered Call Write—long Futures + Short Call (Similar to
Short Put)
 Profi t/loss Profi le: Covered Call Write—long Futures + Short Call (Similar to
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
5,000
2,500
0
−2,500
−7 ,500
−10,000
−12,500
−15,000
−5,000
1,050 1,100 1,150 1,200 1,250
Futures price at time
of position initiation
and strike price
 Breakeven price
= $1,161 .20
1,300 1,350 1,400
−17 ,500
 tabLe 35.14 profit/Loss Calculations: Covered put Write—Short Futures + Short put (Similar to
Short Call)
(1) (2) (3) (4) (5) (6)
Futures price
at expiration
($/oz)
premium of
august $1,200 put
at Initiation ($/oz)
$ amount of
premium received
profit/Loss on Short
Futures position
put Value at
expiration
profit/Loss on position
[(3) + (4) – (5)]
1,000 38.7 $3,870 $20,000 $20,000 $3,870
1,050 38.7 $3,870 $15,000 $15,000 $3,870
1,100 38.7 $3,870 $10,000 $10,000 $3,870
1,150 38.7 $3,870 $5,000 $5,000 $3,870
1,200 38.7 $3,870 $0 $0 $3,870
1,250 38.7 $3,870 –$5,000 $0 –$1,130
1,300 38.7 $3,870 –$10,000 $0 –$6,130
1,350 38.7 $3,870 –$15,000 $0 –$11,130
1,400 38.7 $3,870 –$20,000 $0 –$16,130

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528A COMPleTe gUIde TO THe FUTUreS MArKeT
Comment. Comments analogous to those made for Strategy 13 would apply here. The sale of aput
against ashort futures position is equivalent to the sale of acall. The reader can verify this by compar-
ing Figure 35.14 to Figure 35.4 a. The two strategies would be precisely equivalent (ignoring transac-
tion cost diff erences) if the put and call premiums were equal.
 Strategy 15: Synthetic Long Futures (Long Call + Short put)
example . Buy an August $1,150 gold futures call at apremium of $70.10/oz ($7,010) and simultane-
ously sell an August $1,150 gold futures put at apremium of $19.90/oz ($1,990). (See Table 35.15
and Figure 35.15 .)
Comment. Asynthetic long futures position can be created by combining along call and ashort put
for the same expiration date and the same strike price. For example, as illustrated in Table 35.15 and Figure
 35.15 , the combined position of along August $1,150 call and ashort August $1,150 put is virtually
identical to along August futures position. The reason for this equivalence is tied to the fact that the
diff erence between the premium paid for the call and the premium received for the put is approxi-
mately equal to the intrinsic value of the call. each $1 increase in price will raise the intrinsic value of
the call by an equivalent amount and each $1 decrease in price will reduce the intrinsic value of the
 FIGURE  35.14 Profi t/loss Profi le: Covered Put Write—Short Futures + Short Put (Similar
to Short Call)
Price of August gold futures at option expiration ($/oz)
1,000 1,050 1,100 1,150 1,200 1,250
Futures price at time
of position initiation
and strike price Breakeven price
= $1,238.70
1,300 1,350 1,400
Profit/loss at expiration ($)
5,000
2,500
0
−2,500
−7 ,500
−10,000
−12,500
−17 ,500
−15,000
−5,000

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529
OPTION TrAdINg STrATegIeS
 tabLe 35.15 profit/Loss Calculations: Synthetic Long Futures (Long Call + Short put)
(1) (2) (3) (4) (5) (6) (7) (8)
Futures price
at expiration
($/oz)
premium of
august $1,150
Call at Initiation
($/oz)
$ amount
of premium
paid
premium of
august $1,150
put at Initiation
($/oz)
$ amount
of premium
received
Call Value
at
expiration
put Value
at
expiration
profit/Loss on
position
[(5) − (3) + (6) − (7)]
1,000 70.1 $7,010 19.9 $1,990 $0 $15,000 −$20,020
1,050 70.1 $7,010 19.9 $1,990 $0 $10,000 −$15,020
1,100 70.1 $7,010 19.9 $1,990 $0 $5,000 −$10,020
1,150 70.1 $7,010 19.9 $1,990 $0 $0 −$5,020
1,200 70.1 $7,010 19.9 $1,990 $5,000 $0 −$20
1,250 70.1 $7,010 19.9 $1,990 $10,000 $0 $4,980
1,300 70.1 $7,010 19.9 $1,990 $15,000 $0 $9,980
1,350 70.1 $7,010 19.9 $1,990 $20,000 $0 $14,980
1,400 70.1 $7,010 19.9 $1,990 $25,000 $0 $19,980
 FIGURE  35.15 Profi t/loss Profi le: Synthetic long Futures (long Call + Short Put)
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
20,000
15,000
10,000
5,000
−5,000
−10,000
−15,000
−20,000
0
1,050 1,100 1,150 1,200 1,250
Futures price at time
of position initiation
Breakeven price
= $1,200.20
1,300 1,350 1,400

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A Complete Guide to the Futures mArket
call (or if prices decline below $1,150, increase the value of the put) by an equivalent amount. Thus,
as long as the expiration date and strike price of the two options are identical, along call/short put
position acts just like along futures contract.
The futures equivalent price implied by asynthetic position is given by the following formula:
Synthetic futures pos itio nprices trike pricec all prem ium=+ − −put premi um
It should be noted there will be one synthetic futures position price corresponding to each strike
price for which options are traded for the given futures contract.
In this example, the synthetic long position is the same price as along futures contract. (Synthetic
futures position price = $1,150 + $70.10 − $19.90 = $1,200.20.) Thus, ignoring transaction costs
and interest income effects, buying the August $1,150 call and simultaneously selling the August
$1,150 put would be equivalent to buying an August futures contract. Of course, the trader consider-
ing this strategy as an alternative to an outright long futures position must incorporate transaction
costs and interest income effects into the calculation. In this example, the true cost of the synthetic
futures position would be raised vis-à-vis along futures contract as aresult of the following three
factors:
 1. Because the synthetic futures position involves two trades, in aless liquid market, it is reason-
able to assume the execution costs will also be greater. In other words, the option-based strategy
will require the trader to give up more points (relative to quoted levels) in order to execute the
trade.
 2. The synthetic futures position will involve greater commission costs.
 3. The dollar premium paid for the call ($7,010) exceeds the dollar premium received for the put
($1,990). Thus, the synthetic futures position will involve an interest income loss on the differ-
ence between these two premium payments ($5,020). This factor, however, would be offset by
the margin requirements on along futures position.
Once the above differences are accounted for, the apparent relative advantage asynthetic futures
position will sometimes seemingly offer will largely, if not totally, disappear. Nonetheless, insofar as
some market inefficiencies may exist, the synthetic long futures position will sometimes offer aslight
advantage over the direct purchase of afutures contract. In fact, the existence of such discrepancies
would raise the possibility of pure arbitrage trades.
3 For example, if the price implied by the synthetic
long futures position was less than the futures price, even after accounting for transaction costs and
interest income effects, the arbitrageur could lock in aprofit by buying the call, selling the put, and
selling futures. Such atrade is called areverse conversion. Alternately, if after adjusting for transaction
costs and interest income effects, the implied price of the synthetic long futures position were greater
than the futures price, the arbitrageur could lock in aprofit by buying futures, selling the call, and
buying the put. Such atrade is called aconversion.
3 Pure arbitrage implies arisk-free trade in which the arbitrageur is able to lock in asmall profit by exploiting
temporary price distortions between two related markets.

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531
OPTION TrAdINg STrATegIeS
It should be obvious that such risk-free profit opportunities will be limited in terms of
both duration and magnitude. generally speaking, conversion and reverse conversion arbitrage
will normally only be feasible for professional arbitrageurs who enjoy much lower transac-
tion costs (commissions plus execution costs) than the general public. The activity of these
arbitrageurs will tend to keep synthetic futures position prices about in line with actual futures
prices.
Strategy 16: Synthetic Short Futures (Long put + Short Call)
example. Buy an August $1,300 gold futures put at apremium of $108.70/oz ($10,870) and simul-
taneously sell an August $1,300 gold futures call at apremium of $9.10/oz ($910). (See Table 35.16
and Figure 35.16.)
Comment. As follows directly from the discussion of the previous strategy, asynthetic short futures
position can be created by combining along put and ashort call with the same expiration date and the same
strike price. In this example, the synthetic futures position based upon the $1,300 strike price options
is $0.40 higher priced than the underlying futures contract. (Synthetic futures position = $1,300
+ $9.10 − $108.70 = $1,200.40.) However, for reasons similar to those discussed in the previous
strategy, much of the advantage of an implied synthetic futures position price versus the actual futures
price typically disappears once transaction costs and interest income effects are incorporated into the
evaluation. An arbitrage employing the synthetic short futures position is called aconversion and was
detailed in the previous strategy.
tabLe 35.16 profit/Loss Calculations: Synthetic Short Futures (Long put + Short Call)
(1) (2) (3) (4) (5) (6) (7) (8)
Futures
price at
expiration
($/oz)
premium of
august $1,300
Call at Initiation
($/oz)
Dollar
amount of
premium
received
premium of
august $1,300
put at Initiation
($/oz)
Dollar
amount of
premium
paid
Value of
Call at
expiration
Value of
put at
expiration
profit/Loss on
position
[(3) − (5) + (7) − (6)]
1,000 9.1 $910 108.7 $10,870 $0 $30,000 $20,040
1,050 9.1 $910 108.7 $10,870 $0 $25,000 $15,040
1,100 9.1 $910 108.7 $10,870 $0 $20,000 $10,040
1,150 9.1 $910 108.7 $10,870 $0 $15,000 $5,040
1,200 9.1 $910 108.7 $10,870 $0 $10,000 $40
1,250 9.1 $910 108.7 $10,870 $0 $5,000 –$4,960
1,300 9.1 $910 108.7 $10,870 $0 $0 –$9,960
1,350 9.1 $910 108.7 $10,870 $5,000 $0 –$14,960
1,400 9.1 $910 108.7 $10,870 $10,000 $0 –$19,960

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532A COMPleTe gUIde TO THe FUTUreS MArKeT
 Strategy 17: the ratio Call Write (Long Futures + Short 2 Calls)
example . Buy August gold futures at $1,200 and simultaneously sell two August $1,200 gold futures
calls at apremium of $38.80/ oz. ($7,760). (See Table 35.17 and Figure 35.17 .)
 FIGURE  35.16 Profi t/loss Profi le: Synthetic Short Futures (long Put + Short Call).
Futures price at time
of position initiation
Breakeven price
= $1,210.40
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
20,000
15,000
10,000
5,000
−5,000
−10,000
−15,000
−20,000
0
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
 tabLe 35.17 profit/Loss Calculations: ratio Call Write—Long Futures + Short 2 Calls (Similar to
Short Straddle)
(1) (2) (3) (4) (5) (6)
Futures price
at expiration
($/oz)
premium of
august $1,200 Call
at Initiation ($/oz)
$ amount of
total premium
received
profit/Loss on
Long Futures
position
Value of 2 Calls
at expiration
profit/Loss on position
[(3) + (4) − (5)]
1,000 38.8 $7,760 –$20,000 $0 –$12,240
1,050 38.8 $7,760 –$15,000 $0 –$7,240
1,100 38.8 $7,760 –$10,000 $0 –$2,240
1,150 38.8 $7,760 –$5,000 $0 $2,760
1,200 38.8 $7,760 $0 $0 $7,760
1,250 38.8 $7,760 $5,000 $10,000 $2,760
1,300 38.8 $7,760 $10,000 $20,000 –$2,240
1,350 38.8 $7,760 $15,000 $30,000 –$7,240
1,400 38.8 $7,760 $20,000 $40,000 –$12,240

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533
OPTION TrAdINg STrATegIeS
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
10,000
5,000
−5,000
−10,000
0
1,050 1,100 1,150 1,200 1,250
Breakeven price
= $1,122.40
Breakeven price
= $1,277 .60
1,300 1,350 1,400
−15,000
Futures price at time
of position initiation
 FIGURE  35.17 Profi t/loss Profi le: ratio Call Write—long Futures + Short 2 Calls (Similar to
Short Straddle)
Comment. The combination of 1 long futures contract and 2 short at-the-money calls is abalanced
position in terms of delta values. In other words, at any given point in time, the gain or loss in the
long futures contract due to small price changes (i.e., price changes in the vicinity of the strike price)
will be approximately off set by an opposite change in the call position. (Over time, however, amar-
ket characterized by small price changes will result in the long futures position gaining on the short
call position due to the evaporation of the time value of the options.) The maximum profi tin this
strategy will be equal to the premium received for the 2 calls and will occur when prices are exactly
unchanged. This strategy will show anet profi tfor awide range of prices centered at the prevailing
price level at the time the position was initiated. However, the position will imply unlimited risk in
the event of very sharp price increases or declines.
 The profi t/loss profi le for this strategy should look familiar—it is virtually identical to the short
straddle position (see Strategy 35.8). The virtual equivalence of this strategy to the short straddle
position follows directly from the previously discussed structure of asynthetic futures position:
Ratio call wr itel ong futures short calls
=+ 2
 However, from the synthetic futures position relationship, we know that:
 Long futures long call short put ≈+

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534
A Complete Guide to the Futures mArket
Thus:
Ratio call writ el ong call short put short calls or
Rati
 ≈+ + 2,
oo call wr ite short put short call≈+
The right-hand term of this last equation is, in fact, the definition of ashort straddle. In similar
fashion, it can be demonstrated that ashort put write (short futures + short 2 puts) would also yield
aprofit/loss profile nearly identical to the short straddle position.
Strategy 18: bull Call Money Spread (Long Call with Lower Strike
price/Short Call with higher Strike price)
example. Buy an August $1,250 gold futures call at apremium of $19.20/oz ($1,920) and
simultaneously sell an August $1,300 call at apremium of $9.10 ($910). (See Table 35.18 and
Figure 35.18.)
Comment. This type of spread position is also called adebit spread because the amount of premium
paid for the long call is greater than the amount of the premium received for the short call. The maxi-
mum risk in this type of trade is equal to the difference between these two premiums. The maximum
possible gain in this spread will be equal to the difference between the two strike prices minus the
net difference between the two premiums. The maximum loss will occur if prices fail to rise at least
beyond the lowest strike price. The maximum gain will be realized if prices rise above the higher
strike price. Note that although the maximum profit exceeds the maximum risk by afactor of nearly
4 to 1, the probability of aloss is significantly greater than the probability of again. This condition is
true since prices must rise $60.10/oz before the strategy proves profitable.
tabLe 35.18 profit/Loss Calculations: bull Call Money Spread (Long Call with Lower Strike price/
Short Call with higher Strike price)
(1) (2) (3) (4) (5) (6) (7) (8)
Futures price
at expiration
($/oz)
premium of
august $1,250
Call ($/oz)
$ amount
of premium
paid
premium of
august $1,300
Call ($/oz)
Dollar amount
of premium
received
$1,250 Call
Value at
expiration
$1,300 Call
Value at
expiration
profit/Loss on
position
[(5) − (3) + (6) − (7)]
1,000 19.2 $1,920 9.1 $910 $0 $0 -$1,010
1,050 19.2 $1,920 9.1 $910 $0 $0 -$1,010
1,100 19.2 $1,920 9.1 $910 $0 $0 -$1,010
1,150 19.2 $1,920 9.1 $910 $0 $0 -$1,010
1,200 19.2 $1,920 9.1 $910 $0 $0 -$1,010
1,250 19.2 $1,920 9.1 $910 $0 $0 -$1,010
1,300 19.2 $1,920 9.1 $910 $5,000 $0 $3,990
1,350 19.2 $1,920 9.1 $910 $10,000 $5,000 $3,990
1,400 19.2 $1,920 9.1 $910 $15,000 $10,000 $3,990

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535
OPTION TrAdINg STrATegIeS
 This strategy can perhaps be best understood by comparing it to the long call position (e.g., long
August $1,250 gold futures call). In eff ect, the spread trader reduces the premium cost for the long
call position by the amount of premium received for the sale of the more deeply out-of-the-money
call. This reduction in the net premium cost of the trade comes at the expense of sacrifi cing the pos-
sibility of unlimited gain in the event of alarge price rise. As can be seen in Figure 35.18 , in contrast
to the outright long call position, price gains beyond the higher strike price will cease to aff ect the
profi tability of the trade.
 Strategy 19a: bear Call Money Spread (Short Call with Lower Strike
price/Long Call with higher Strike price)—Case 1
example . Buy August $1,150 gold futures call at apremium of $70.10/oz ($7,010) and simultane-
ously sell an August $1,100 gold futures call at apremium of $110.10/oz ($11,010), with August
gold futures trading at $1,200/oz. (See Table 35.19 aand Figure 35.19 a.)
Comment. This type of spread is called acredit spread, since the amount of premium received for
the short call position exceeds the premium paid for the long call position. The maximum possible
gain on the trade is equal to the net diff erence between the two premiums. The maximum possible
loss is equal to the diff erence between the two strike prices minus the diff erence between the two
premiums. The maximum gain would be realized if prices declined to the lower strike price. The
maximum loss would occur if prices failed to decline to at least the higher strike price. Although
 FIGURE  35.18 Profi t/loss Profi le: Bull Call Money Spread (long Call with lower Strike Price/
Short Call with Higher Strike Price)
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
3,750
5,000
2,500
0
−1,250
1,250
1,050 1,100 1,150 1,200 1,250
Breakeven price
= $1,260.10
1,300 1,350 1,400
−2,500
Futures price at time
of position initiation

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536A COMPleTe gUIde TO THe FUTUreS MArKeT
 tabLe 35.19a profit/Loss Calculations: bear Call Money Spread (Short Call with Lower Strike price/
Long Call with higher Strike price); Case 1—both Calls In-the-Money
(1) (2) (3) (4) (5) (6) (7) (8)
Futures price
at expiration
($/oz)
premium of
august $1,150
Call ($/oz)
$ amount
of premium
paid
premium of
august $1,100
Call ($/oz)
$ amount
of premium
received
$1,150 Call
Value at
expiration
$1,100 Call
Value at
expiration
 profit/Loss on
position
 [(5) − (3) + (6) − (7)]
1,000 70.1 $7,010 110.1 $11,010 $0 $0 $4,000
1,050 70.1 $7,010 110.1 $11,010 $0 $0 $4,000
1,100 70.1 $7,010 110.1 $11,010 $0 $0 $4,000
1,150 70.1 $7,010 110.1 $11,010 $0 $5,000 –$1,000
1,200 70.1 $7,010 110.1 $11,010 $5,000 $10,000 –$1,000
1,250 70.1 $7,010 110.1 $11,010 $10,000 $15,000 –$1,000
1,300 70.1 $7,010 110.1 $11,010 $15,000 $20,000 –$1,000
1,350 70.1 $7,010 110.1 $11,010 $20,000 $25,000 –$1,000
1,400 70.1 $7,010 110.1 $11,010 $25,000 $30,000 –$1,000
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
3,750
5,000
2,500
0
−1,250
1,250
1,050 1,100 1,150 1,200 1,250
Breakeven price = $1,140
1,300 1,350 1,400
Futures price at time
of position initiation
 FIGURE  35.19a Profi t/loss Profi le: Bear Call Money Spread (Short Call with lower Strike
Price/long Call with Higher Strike Price); Case 1—Both Calls In-the-Money

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537
OPTION TrAdINg STrATegIeS
in the above example the maximum gain exceeds the maximum risk by afactor of 4 to 1, there is
agreater probability of anet loss on the trade, since prices must decline by $60/oz before aprofit
is realized.
In this type of spread, the trader achieves abearish position at afairly low premium cost at the
expense of sacrificing the potential for unlimited gains in the event of avery sharp price decline. This
strategy might be appropriate for the trader expecting aprice decline but viewing the possibility of avery large price slide as being very low .
Strategy 19b: bear Call Money Spread (Short Call with Lower Strike
price/Long Call with higher Strike price)—Case 2
example. Buy an August $1,300 gold futures call at apremium of $9.10/oz ($9.10) and simultane-
ously sell an August $1,200 gold futures call at apremium of $38.80/oz ($3,880), with August gold
futures trading at $1,200/oz. (See Table 35.19b and Figure 35.19b.)
Comment. In contrast to the previous strategy, which involved two in-the-money calls, this illustra-
tion is based on aspread consisting of ashort at-the-money call and along out-of-the-money call.
In asense, this type of trade can be thought of as ashort at-the-money call position with built-in
stop-loss protection. (The long out-of-the-money call will serve to limit the risk in the short at-the-
money call position.) This risk limitation is achieved at the expense of areduction in the net premium
received by the seller of the at-the-money call (by an amount equal to the premium paid for the out-
of-the-money call). This trade-off between risk exposure and the amount of net premium received
is illustrated in Figure 35.19b, which compares the outright short at-the-money call position to the
above spread strategy.
tabLe 35.19b profit/Loss Calculations: bear Call Money Spread (Short Call with Lower Strike price/Long
Call with higher Strike price); Case 2—Short at-the-Money Call/Long Out-of-the-Money
Call
(1) (2) (3) (4) (5) (6) (7) (8)
Futures price
at expiration
($/oz)
premium of
august $1,300
Call ($/oz)
$ amount
of premium
paid
premium of
august $1,200
Call ($/oz)
$ amount
of premium
received
Value of
$1,300 Call at
expiration
Value of
$1,200 Call at
expiration
profit/Loss on
position
[(5) − (3) + (6) − (7)]
1,000 9.1 $910 38.8 $3,880 $0 $0 $2,970
1,050 9.1 $910 38.8 $3,880 $0 $0 $2,970
1,100 9.1 $910 38.8 $3,880 $0 $0 $2,970
1,150 9.1 $910 38.8 $3,880 $0 $0 $2,970
1,200 9.1 $910 38.8 $3,880 $0 $0 $2,970
1,250 9.1 $910 38.8 $3,880 $0 $5,000 –$2,030
1,300 9.1 $910 38.8 $3,880 $0 $10,000 –$7,030
1,350 9.1 $910 38.8 $3,880 $5,000 $15,000 –$7,030
1,400 9.1 $910 38.8 $3,880 $10,000 $20,000 –$7,030

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538A COMPleTe gUIde TO THe FUTUreS MArKeT
 Strategy 20a: bull put Money Spread (Long put with Lower Strike
price/Short put with higher Strike price)—Case 1
example . Buy an August $1,250 gold futures put at apremium of $68.70/oz ($6,870) and simulta-
neously sell an August $1,300 put at apremium of $108.70/oz ($10,870), with August gold futures
trading at $1,200/oz. (See Table 35.20 aand Figure 35.20 a.)
Comment. This is anet credit bull spread that uses puts instead of calls. The maximum gain in this
strategy is equal to the diff erence between the premium received for the short put and the premium
paid for the long put. The maximum loss is equal to the diff erence between the strike prices minus
the diff erence between the premiums. The maximum gain will be achieved if prices rise to the higher
strike price, while the maximum loss will occur if prices fail to rise at least to the lower strike price.
The profi t/loss profi le of this trade is very similar to the profi le of the net debit bull call money
spread illustrated in Figure 35.18 .
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
5,000
2,500
0
−2,500
−5,000
−7 ,500
−10,000
−12,500
−17 ,500
1,050 1,100 1,150 1,200 1,250
Bear call money spread
Short at-the-money
call
Breakeven price on
spread = $1,229.70
Breakeven price on
short call = $1,238.80
1,300 1,350 1,400
−15,000
Futures price at time
of position initiation
 FIGURE  35.19b Profi t/loss Profi le: Bear Call Money Spread (Short Call with lower Strike
Price/long Call with Higher Strike Price); Case 2—Short At-the-Money Call/long Out-of-the-
Money Call with Comparison to Short At-the-Money Call

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OPTION TrAdINg STrATegIeS
 tabLe 35.20a profit/Loss Calculations: bull put Money Spread (Long put with Lower Strike price/
Short put with higher Strike price); Case 1—both puts In-the-Money
(1) (2) (3) (4) (5) (6) (7) (8)
Futures price
at expiration
($/oz)
premium of
august $1,250
put ($/oz)
$ amount
of premium
paid
premium of
august $1,300
put ($/oz)
$ amount
of premium
received
$1,250 put
Value at
expiration
$1,300 put
Value at
expiration
profit/Loss on
position
[(5) − (3) + (6) −(7)]
1,000 68.7 $6,870 108.7 $10,870 $25,000 $30,000 –$1,000
1,050 68.7 $6,870 108.7 $10,870 $20,000 $25,000 –$1,000
1,100 68.7 $6,870 108.7 $10,870 $15,000 $20,000 –$1,000
1,150 68.7 $6,870 108.7 $10,870 $10,000 $15,000 –$1,000
1,200 68.7 $6,870 108.7 $10,870 $5,000 $10,000 –$1,000
1,250 68.7 $6,870 108.7 $10,870 $0 $5,000 –$1,000
1,300 68.7 $6,870 108.7 $10,870 $0 $0 $4,000
1,350 68.7 $6,870 108.7 $10,870 $0 $0 $4,000
1,400 68.7 $6,870 108.7 $10,870 $0 $0 $4,000
 FIGURE  35.20a
 Profi t/loss Profi le: Bull Put Money Spread (long Put with lower Strike Price/
Short Put with Higher Strike Price); Case 1—Both Puts In-the-Money
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
3,750
5,000
2,500
0
1,250
1,050 1,100 1,150 1,200 1,250
Breakeven price
= $1,260
1,300 1,350 1,400
−1,250
Futures price at time
of position initiation

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A Complete Guide to the Futures mArket
Strategy 20b: bull put Money Spread (Long put with Lower Strike
price/Short put with higher Strike price)—Case 2
example. Buy an August $1,100 gold futures put at apremium of $10.10/oz ($1,010) and simul-
taneously sell an August $1,200 put at apremium of $38.70/oz ($3,870), with August gold futures
trading at $1,200/oz. (See Table 35.20b and Figure 35.20b.)
Comment. In contrast to Case 1, which involved two in-the-money puts, this strategy is based on
along out-of-the-money put versus ashort at-the-money put spread. In asense, this strategy can
be viewed as ashort at-the-money put position with abuilt-in stop. (The purchase of the out-of-
the-money put serves to limit the maximum possible loss in the event of alarge price decline.) This
risk limitation is achieved at the expense of areduction in the net premium received. This trade-off
between risk exposure and the amount of premium received is illustrated in Figure 35.20b, which
compares the outright short at-the-money put position to this spread strategy.
Strategy 21: bear put Money Spread (Short put with Lower Strike
price/Long put with higher Strike price)
example. Sell an August $1,100 gold futures put at apremium of $10.10/oz ($1,010) and simul-
taneously buy an August $1,150 put at apremium of $19.90/oz ($1,990), with August gold futures
trading at $1,200/oz. (See Table 35.21 and Figure 35.21.)
Comment. This is adebit bear spread using puts instead of calls. The maximum risk is equal to the
difference between the premium paid for the long put and the premium received for the short put. The
maximum gain equals the difference between the two strike prices minus the difference between
the premiums. The maximum loss will occur if prices fail to decline to at least the higher strike price.
The maximum gain will be achieved if prices decline to the lower strike price. The profit/loss profile of
this spread is approximately equivalent to the profile of the bear call money spread (see Figure 35.19a).
tabLe 35.20b profit/Loss Calculations: bull put Money Spread (Long put with Lower Strike price/Short put
with higher Strike price); Case 2—Long Out-of-the-Money put/Short at-the-Money put
(1) (2) (3) (4) (5) (6) (7) (8)
Futures price
at expiration
($/oz)
premium of
august $1,100
put ($/oz)
Dollar
amount of
premium paid
premium of
august $1,200
put ($/oz)
Dollar amount
of premium
received
Value of
$1,100 put at
expiration
Value of
$1,200 put at
expiration
profit/Loss on
position
[(5) − (3) + (6) − (7)]
1,000 10.1 $1,010 38.7 $3,870 $10,000 $20,000 –$7,140
1,050 10.1 $1,010 38.7 $3,870 $5,000 $15,000 –$7,140
1,100 10.1 $1,010 38.7 $3,870 $0 $10,000 –$7,140
1,150 10.1 $1,010 38.7 $3,870 $0 $5,000 –$2,140
1,200 10.1 $1,010 38.7 $3,870 $0 $0 $2,860
1,250 10.1 $1,010 38.7 $3,870 $0 $0 $2,860
1,300 10.1 $1,010 38.7 $3,870 $0 $0 $2,860
1,350 10.1 $1,010 38.7 $3,870 $0 $0 $2,860
1,400 10.1 $1,010 38.7 $3,870 $0 $0 $2,860

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541
OPTION TrAdINg STrATegIeS FIGURE  35.20b Profi t/loss Profi le: Bull Put Money Spread (long Put with lower Strike Price/
Short Put with Higher Strike Price); Case 2—long Out-of-the-Money Put/Short At-the-Money
Put with Comparison to Short At-the-Money Put
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
5,000
2,500
0
−2,500
−5,000
−7 ,500
−10,000
−12,500
−15,000
1,050 1,100 1,150 1,200 1,250
Bull put money spread
Short at-the-money
put
Breakeven price on spread = $1,171.40
Breakeven price on short put $1,161.30
1,300 1,350 1,400
−17 ,500
Futures price at time
of position initiation
 tabLe 35.21 profit/Loss Calculations: bear put Money Spread (Short put with Lower Strike price/Long
put with higher Strike price)
(1) (2) (3) (4) (5) (6) (7)
Futures price
at expiration
($/oz)
premium of
august $1,150
put ($/oz)
$ amount
of premium
paid
premium of
august $1,100
put ($/oz)
$ amount
of premium
received
Value of
$1,150
put
Value of
$1,100
put
profit/Loss on position
[(5) − (3) + (6) − (7)]
1,000 19.9 $1,990 10.1 $1,010 $15,000 $10,000 $4,020
1,050 19.9 $1,990 10.1 $1,010 $10,000 $5,000 $4,020
1,100 19.9 $1,990 10.1 $1,010 $5,000 $0 $4,020
1,150 19.9 $1,990 10.1 $1,010 $0 $0 –$980
1,200 19.9 $1,990 10.1 $1,010 $0 $0 –$980
1,250 19.9 $1,990 10.1 $1,010 $0 $0 –$980
1,300 19.9 $1,990 10.1 $1,010 $0 $0 –$980
1,350 19.9 $1,990 10.1 $1,010 $0 $0 –$980
1,400 19.9 $1,990 10.1 $1,010 $0 $0 –$980

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542A COMPleTe gUIde TO THe FUTUreS MArKeT
 Other Spread Strategies
 Money spreads represent only one class of option spreads. Acomplete discussion of option spread
strategies would require asubstantial extension of this section—adegree of detail beyond the scope
of this presentation. The following are examples of some other types of spreads.
time spread. Atime spread is aspread between two calls or two puts with the same strike price,
but adiff erent expiration date. An example of atime spread would be: long 1 August $1,300
gold futures call/short 1 december $1,300 gold futures call. Time spreads are more complex
than the other strategies discussed in this section, because the profi t/loss profi le at the time
of expiration cannot be precisely predetermined, but rather must be estimated on the basis of
theoretical valuation models.
Diagonal spread. This is aspread between two calls or two puts that diff er in terms of both the
strike price and the expiration date. An example of adiagonal spread would be: long 1 August
$1,200 gold futures call/short 1 december $1,250 gold futures call. In eff ect, this type of
spread combines the money spread and the time spread into one trade.
butterfl yspread. This is athree-legged spread in which the options have the same expiration
date but diff er in strike prices. Abutterfl yspread using calls consists of two short calls at agiven
strike price, one long call at ahigher strike price, and one long call at alower strike price.
 The list of types of option spreads can be significantly extended, but the above examples
should be sufficient to give the reader some idea of the potential range of complexity of spread
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
3,750
5,000
2,500
0
−1,250
−2,500
1,250
1,050 1,100 1,150 1,200 1,250
Breakeven price
= $1,140.20
1,300 1,350 1,400
Futures price at time
of position initiation
 FIGURE  35.21 Profi t/loss Profi le; Bear Put Money Spread (Short Put with lower Strike Price/
long Put with Higher Strike Price)

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543
OPTION TrAdINg STrATegIeS
strategies. One critical point that must be emphasized regarding option spreads is that these
strategies are normally subject to amajor disadvantage: the transaction costs (commissions plus
cumulative bid/asked spreads) for these trades are relatively large compared to the profit poten-
tial. This consideration means that the option spread trader must be right alarge percentage of
the time if he is to come out ahead of the game. The importance of this point cannot be overem -
phasized. In short, as ageneralization, other option strategies will usually offer better trading
opportunities.
Multiunit Strategies
The profit/loss profile can also be used to analyze multiple-unit option strategies. In fact, multiple-
unit option positions may often provide the more appropriate strategy for purposes of comparison.
For example, as previously detailed, along futures position is more volatile than along or short call
position. In fact, for small price changes, each $1 change in afutures price will only result in approxi-
mately a $0.50 change in the call price (the delta value for an at-the-money call is approximately
equal to 0.5). As aresult, in considering the alternatives of buying futures and buying calls, it probably
makes more sense to compare the long futures position to two long calls (see Table 35.22) as opposed
to one long call.
Figure 35.22 compares the strategies of long futures versus long two calls, which at the time of
initiation are approximately equivalent in terms of delta values. Note this comparison indicates that
the long futures position is preferable if prices change only moderately, but that the long two-call
position will gain more if prices rise sharply, and lose less if prices decline sharply. In contrast, the
comparison between long futures and along one-call position would indicate that futures provide
the better strategy in the event of aprice advance of any magnitude (see Figure 35.3d). For most
purposes, the comparison employing two long calls will be more meaningful because it comes much
closer to matching the risk level implicit in the long futures position.
tabLe 35.22 profit/Loss Calculations: Long two at-the-Money Calls
(1) (2) (3) (4) (5)
Futures price at
expiration ($/oz)
premium of august
$1,200 Call ($/oz)
$ amount of total
premium paid
Value of 2 Calls
at expiration
profit/Loss on
position [(4) − (3)]
1,000 38.8 $7,760 $0 –$7,760
1,050 38.8 $7,760 $0 –$7,760
1,100 38.8 $7,760 $0 –$7,760
1,150 38.8 $7,760 $0 –$7,760
1,200 38.8 $7,760 $0 –$7,760
1,250 38.8 $7,760 $10,000 $2,240
1,300 38.8 $7,760 $20,000 $12,240
1,350 38.8 $7,760 $30,000 $22,240
1,400 38.8 $7,760 $40,000 $32,240

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544A COMPleTe gUIde TO THe FUTUreS MArKeT
 Choosing an Optimal Strategy
 It the previous sections we examined awide range of alternative trading strategies. Now what? How
does atrader decide which of these alternatives provides the best trading opportunity? This ques-
tion can be answered only if probability is incorporated into the analysis. The selection of an optimal
option strategy will depend entirely on the trader’sprice and volatility expectations. Insofar as these
expectations will diff er from trader to trader, the optimal option strategy will also vary, and the
success of the selected option strategy will depend on the accuracy of the trader’sexpectations. In
order to select an optimal option strategy, the trader needs to translate his price expectations into
probabilities.
 The basic approach requires the trader to assign estimated probability levels for the entire range
of feasible price intervals. Figure 35.23 illustrates six diff erent types of probability distributions for
August gold futures. These distributions can be thought of as representing six diff erent hypothetical
expectations. (The charts in Figure 35.23 implicitly assume that the current price of August gold
futures is $1,200.) Several important points should be made regarding these probability distributions:
 1. The indicated probability distributions only represent approximations of traders’ price expec-
tations. In reality, any reasonable probability distribution would be represented by asmooth
curve. The stair-step charts in Figure 35.23 are only intended as crude models that greatly sim-
plify calculations. (The use of smooth probability distributions would require integral calculus
in the evaluation process.)
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
25,000
12,500
−12,500
−25,000
0
1,050 1,100 1,150 1,200 1,250
Breakeven price on long
2 calls = $1,238.80
Long futures
Long 2 calls
1,300 1,350 1,400
37 ,500
+37 ,500
Futures price at time
of position initiation
 FIGURE  35.22 Profi t/loss Profi le: Two long Calls vs. long Futures

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546
A Complete Guide to the Futures mArket
 5. The probability distributions in Figure 35.23 represent sample hypothetical illustrations
of personal price expectations. The indicated optimal strategy in any given situation will
depend upon the specific shape of the expected price distribution, an input that will differ from
trader to trader.
The general nature of the price expectations implied by each of the distributions in Figure 35.23
can be summarized as follows:
Expected Probability Distribution 1. Higher prices and low volatility. This interpretation follows from
the fact that there is agreater probability of higher prices and that the probabilities are heavily
weighted toward intervals close to the current price level.
Expected Probability Distribution 2. Higher prices and high volatility. This distribution reflects the
same 60/40 probability bias toward higher prices as was the case for
distribution 1, but the
assumed probability of asubstantially higher or lower price is much greater.
Expected Probability Distribution 3. lower prices and low volatility. This distribution is the bearish
counterpart of distribution 1.
Expected Probability Distribution 4. lower prices and high volatility. This distribution is the bearish
counterpart of distribution 2.
Expected Probability Distribution 5. Neutral price assumptions and low volatility. This distribution is
symmetrical in terms of higher and lower prices, and probability levels are heavily weighted
toward prices near the current level.
Expected Probability Distribution 6. Neutral price assumptions and high volatility. This distribution is
also symmetrical in terms of high and low prices, but substantially higher and lower prices have
amuch greater probability of occurrence than in
distribution 5.
Figure 35.24 combines expected Probability distribution 1 with three alternative bullish strat-
egies. (Since it is assumed that there is agreater probability of higher prices, there is no need to
consider bearish or neutral trading strategies.) Insofar as the assumed probability distribution is
very heavily weighted toward prices near the current level, the short put position appears to offer
the best strategy. Figure 35.25 combines the same three alternative bullish strategies with the bull -
ish/volatile price scenario suggested by
expected Probability distribution 2. In this case, the long
call position appears to be the optimal strategy, since it is by far the best performer for large price
advances and declines—price outcomes that account for asignificant portion of the overall prob -
ability distribution.
In analogous fashion, Figure 35.26 suggests the preferability of the short call position given
the bearish/nonvolatile price scenario assumption, while Figure 35.27 suggests that the long put
position is the optimal strategy given the bearish/volatile price scenario. Finally, two alternative
neutral strategies are compared in Figures 35.28 and 35.29 for two neutral price distributions
that differ in terms of assumed volatility. The short straddle appears to offer the better strategy in
the low volatility distribution assumption, while the reverse conclusion is suggested in the volatile
price case.

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548A COMPleTe gUIde TO THe FUTUreS MArKeT
 FIGURE  35.26 “Bearish/Nonvolatile” expected Probability distribution and Profi t/loss
Profi les for Three Alternative Bearish Strategies
 “Bearish/Nonvolatile” expected Probability distribution and Profi t/loss
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
25,000
12,500
−12,500
−25,000
0
1,050 1,100 1,150 1,200 1,250
Short futures
Short 2 calls
Long 2 puts
.20
.18
.16
.14
.12
.10
Probability
.08
.06
.04
.02
1,300 1,350 1,400
 FIGURE  35.27 “Bearish/Volatile” expected Probability distribution and Profi t/loss Profi les
for Three Alternative Bearish Strategies
Price of August gold futures at option expiration ($/oz)
Profit/loss at expiration ($)
1,000
25,000
12,500
−12,500
−25,000
0
1,050 1,100 1,150 1,200 1,250
.20
.18
.16
.14
.12
.10
Probability
.08
.06
.04
.02
1,300 1,350 1,400
Short futures
Short 2 calls
Long 2 puts

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OPTION TrAdINg STrATegIeS
tabLe 35.26 probability-Weighted profit/Loss ratio Comparisons for “bearish/Volatile” expected
probability Distribution
Short Futures Short Call Long put
price range
($/oz)
average
price
($/oz)
assumed
probability
Gain/Loss
at average
price ($)
probability-
Weighted
Gain/Loss ($)
Gain/Loss
at average
price ($)
probability-
Weighted
Gain/Loss ($)
Gain/Loss
at
average
price ($)
probability-
Weighted
Gain/Loss ($)
950–999.9 975 0.06 22,500 1,350 3,880 233 18,630 1,117.8
1,000–1,049.9 1,025 0.1 17,500 1,750 3,880 388 13,630 1,363
1,050–1,099.9 1,075 0.12 12,500 1,500 3,880 466 8,630 1,035.6
1,100–1,149.9 1,125 0.14 7,500 1,050 3,880 543 3,630 508.2
1,150–1,199.9 1,175 0.18 2,500 450 3,880 698 –1,370 –246.6
1,200–1,249.9 1,225 0.12 –2,500 –300 1,380 166 –3,870 –464.4
1,250–1,299.9 1,275 0.1 –7,500 –750 –3,620 –362 –3,870 –387
1,300–1,349.9 1,325 0.08 –12,500 –1,000 –8,620 –690 –3,870 –309.6
1,350–1,399.9 1,375 0.06 –17,500 –1,050 –13,620 –817 –3,870 –232.2
1,400–1,449.9 1,425 0.04 –22,500 –900 –18,620 –745 –3,870 –154.8
Probability-weighted profit/loss ratio: 6,100/4,000 = 1.53 2,494/2,614 = 0.95 4,025/1,795 = 2.24
tabLe 35.27 probability-Weighted profit/Loss ratio Comparisons for “Neutral/Nonvolatile” expected
probability Distribution
Long Straddle Short Straddle
price range
($/oz)
average
price ($/oz)
assumed
probability
Gain/Loss at
average price ($)
probability-
Weighted
Gain/Loss ($)
Gain/Loss at
average price ($)
probability-
Weighted
Gain/Loss ($)
1,000–1,049.9 1,025 0.05 9750 488 –9,750 –488
1,050–1,099.9 1,075 0.1 4,750 475 –4,750 –475
1,100–1,149.9 1,125 0.15 –250 –38 250 38
1,150–1,199.9 1,175 0.2 –5,250 –1,050 5,250 1,050
1,200–1,249.9 1,225 0.2 –5,250 –1,050 5,250 1,050
1,250–1,299.9 1,275 0.15 –250 –38 250 38
1,300–1,349.9 1,325 0.1 4,750 475 –4,750 –475
1,350–1,399.9 1,375 0.05 9,750 488 –9,750 –488
Probability-weighted profit/loss ratio: 1,925/2,175 = 0.89 2,175/1,925 = 1.13

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A Complete Guide to the Futures mArket
hedging applications
The entire discussion in this chapter has been approached from the vantage point of the speculator.
However, option-based strategies can also be employed by the hedger. Toillustrate how options can be
used by the hedger, we compare five basic alternative strategies for the gold jeweler who anticipates arequirement for 100 ounces of gold in August. The assumed date in this illustration is April 13, 2015,
aday on which the relevant price quotes were as follows: spot gold = $1,198.90, August gold futures
= $1,200, August $1,200 gold call premium = $38.80, August $1,200 gold put premium = $38.70.
The five purchasing alternatives are:
5
 1. Wait until time of requirement. In this approach, the jeweler simply waits until August
before purchasing the gold. In effect, the jeweler gambles on the interim price movement of
gold. If gold prices decline, he will be better off. However, if gold prices rise, his purchase price
will increase. If the jeweler has forward-contracted for his products, he may need to lock in his
raw material purchase costs in order to guarantee asatisfactory profit margin. Consequently, the
price risk inherent in this approach may be unacceptable.
tabLe 35.28 probability-Weighted profit/Loss ratio Comparisons for “Neutral/Volatile” expected
probability Distribution
Long Straddle Short Straddle
price range
($/oz)
average
price ($/oz)
assumed
probability
Gain/Loss at
average price ($)
probability-
Weighted
Gain/Loss ($)
Gain/Loss at
average price ($)
probability-
Weighted
Gain/Loss ($)
950–999.9 975 0.05 14,750 738 –14,750 –738
1,000–1,049.9 1,025 0.08 9,750 780 –9,750 –780
1,050–1,099.9 1,075 0.1 4,750 475 –4,750 –475
1,100–1,149.9 1,125 0.12 –250 –30 250 30
1,150–1,199.9 1,175 0.15 –5,250 –788 5,250 788
1,200–1,249.9 1,225 0.15 –5,250 –788 5,250 788
1,250–1,299.9 1,275 0.12 –250 –30 250 30
1,300–1,349.9 1,325 0.1 4,750 475 –4,750 –475
1,350–1,399.9 1,375 0.08 9,750 780 –9,750 –780
1,400–1,449.9 1,425 0.05 14,750 738 –14,750 –738
Probability-weighted profit/loss ratio: 3,985/1,635 = 2.44 1,635/3,985 = 0.41
5 There is no intention to imply that the following list of alternative hedging strategies is all-inclusive. Many other
option-based strategies are also possible. For example, the jeweler could buy acall and sell aput at the same
strike price—astrategy similar to buying afutures contract (see Strategy 15).

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