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A Complete Guide to the Futures mArket
can be achieved by using acontract ratio that is inversely proportional to the contract value (CV) ratio.
This can be expressed as follows (see footnote 2 for symbol definitions):
N
N
CV
CV
UP
UP
tt
2
1
1
2
11 0
22 0
== =
=
,
,
or, NN CV
CV21
1
2
= 





For example, if New York coffee is trading at $1.41/lb and London coffee at $.80/lb, the equal-dollar-
value spread would indicate acontract ratio of 1 New York coffee/3 London coffee:
NN CV
CV N UP
UP
tt
21
1
2
1
11 0
22 0
= 




 =






=
=
,
,
If New York coffee contractN1 1= ,
N2 =× ×=37 5001 41/22 0430 80 3 London contracts,$ ., $.
Thus, in an equal-dollar-value spread position, 3 New York coffee contracts would be balanced by 9
(not 5) London contracts.
It may help clarify matters to compare the just-defined equal-dollar-value approach to the
equal-unit approach for the case of the New York coffee/London coffee spread. Although the equal-
unit spread is indifferent to equal absolute price changes, it will be affected by equal-percentage
price changes (unless, of course, the price levels in both markets are equal, in which case the two
approaches are equivalent). For example, given initiation price levels of New York coffee = $1.41/lb
and London coffee = $.80/lb, consider the effect of a 25 percent price decline on along 3 New York/
short 5 London coffee (equal unit) spread:
Profit/loss in long New York coffee positio n3 37 5000=× ×−,( $. .) $,3525 39 656=−
Profit/loss in short London coffee position 52 20 43 0=× ×−,( $. 220 +2 20 43)$ ,=
Profit/loss in sprea d1 7 613=− $,
The equal-dollar-value spread, however, would be approximately unchanged:
Profit/loss in long New York coffee positio n3 37 5000=× ×−,( $. .) $,3525 39 656=−
Profit/loss in short London coffee position 92 20 43 0=× ×+,( $. 220 +3 96 77)$ ,=
 Profit/loss in sprea d+ 21= $
Returning to our original example, if the trader anticipating price weakness in London coffee rela-
tive to New York coffee had used the equal-dollar-value approach (assuming a 3-contract position for
New York coffee), the results would have been as follows:
Profit/loss in long New York coffee positio n3 37 5000=× ×−,( $. .) $,10 11 250=−
Profit/loss in short London coffee position 92 20 43 +0=× ×,( $. 115 29 758) $,=+
Profit/loss in sprea d+ 18 508= $,

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INTERCOMMODITY SPREADS: DETERMINING CONTRACT RATIOS
 Thus, while the naive placement of an equal contract spread actually results in a $2,218 loss
despite the validity of the trade concept, the more appropriate equal-dollar-value approach results in
a $18,508 gain. This example emphasizes the critical importance of determining appropriate contract
ratios in intercommodity and intermarket spreads.
 An essential point to note is that if intercommodity and intermarket spreads are traded using an
equal-dollar-value approach—as they should be—the price diff erence between the markets is no
longer the relevant subject of analysis. Rather, such an approach is most closely related to the price
ratio between the two markets. This fact means that chart analysis and the defi nition of historical
ranges should be based on the price ratio, not the price diff erence. Figures 31.1 , 31.2 , and 31.3 illus-
trate this point. Figure 31.1 depicts the September 2013 wheat/September 2013 corn spread in the
standard form as aprice diff erence. Figure 31.2 illustrates the price ratio of September 2013 wheat
to September 2013 corn during the same period. Finally, Figure 31.3 plots the equity fl uctuations of
the approximate equal-dollar-value spread: 3 wheat versus 4 corn. Note how much more closely the
equal dollar position is paralleled by the ratio than by the price diff erence.
3
 3 The equal-dollar-value spread would be precisely related to the price ratio only if the contract ratios in the
spread were continuously adjusted to refl ect changes in the price ratio. (An analogous complication does not
exist in equal-unit spreads, since the contract weightings are determined independent of price levels.) However,
unless price levels change drastically during the holding period of the spread, the absence of theoretical readjust-
ments in contract ratios will make little practical diff erence. In other words, equity fl uctuations in the equal-
dollar-value spread will normally closely track the movements of the price ratio.
 FIGURE /uni00A031.1 September 2013 Wheat Minus September 2013 Corn
Chart created using TradeStation. ©TradeStation Technologies, Inc. All rights reserved.

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INTERCOMMODITY SPREADS: DETERMINING CONTRACT RATIOS
 In the preceding example, because wheat is alarger contract than corn (in dollar-value terms),
along 1 wheat/short 1 corn spread would be biased in the direction of the general price trend of
grains. For example, during November 2012–August 2013, aperiod of declining grain prices (see
Figure 31.4 ), the equal contract spread seems to suggest that wheat prices weakened signifi cantly
relative to corn prices (see Figure 31.1 ). In reality, as indicated by Figures 31.2 and 31.3 , the
wheat/corn relationship during this period was best characterized by atrading range. Toillustrate
the trading implications of the spread ratio, consider along wheat/short corn spread initiated at the
late-November 2012 relative high and liquidated at the August 2013 peak. This trade would have
resulted in anear breakeven trade if the spread were implemented on an equal-dollar-value basis
(see Figure 31.2 or 31.3 ), but asignifi cant loss if an equal contract criterion were used instead (see
Figure 31.1 ).
 It should now be clear why the standard assumption of an equal contract position is usually valid
for intramarket spreads. In these spreads, contract sizes are identical, while price levels are normally
close. Thus, the equal-dollar-value approach suggests acontract ratio very close to 1:1.
 If, however, two contracts in an intramarket spread are trading at signifi cantly diff erent price
 levels, the argument for using the equal-dollar-value approach (as opposed to equal contract positions)
would be analogous to the intercommodity and intermarket case. Wide price diff erences between
contracts in an intramarket spread can occur in extreme bull markets that place alarge premium on
 FIGURE /uni00A031.4 September 2013 Wheat and September 2013 Corn

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461
The stock market is but amirror which . . . provides an image of the underlying or
fundamental economic situation.
—John Kenneth Galbraith
 ■ Intramarket Stock Index Spreads
Spreads in carrying charge markets, such as gold, provide agood starting point for developing atheo-
retical behavioral model for spreads in stock index futures. As is the case for gold, there can never
be any near-term shortage in stock indexes, which means spreads will be entirely determined by
carrying charges. As was explained in Chapter 30, gold spreads are largely determined by short-term
interest rates. For example, since atrader could accept delivery of gold on an expiring contract and
redeliver it against asubsequent contract, the price spread between the two months would primarily
reflect financing costs and, hence, short-term rates. If the premium of the forward contract were sig-
nificantly above the level implied by short-term rates, the arbitrageur could lock in arisk-free profit
by performing acash-and-carry operation. And if the premium were significantly lower, an arbitra-
geur could lock in arisk-free profit by implementing ashort nearby/long forward spread, borrowing
gold to deliver against the nearby contract and accepting delivery at the expiration of the forward
contract. These arbitrage forces will tend to keep the intramarket spreads within areasonably well-
defined band for any given combination of short-term interest rates and gold prices.
The same arguments could be duplicated substituting astock index for gold. In abroad sense this
is true, but there is one critical difference between stock index spreads and gold spreads: Stocks pay
Spread Trading in
Stock Index Futures
Chapter 32

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dividends. Thus, the interest rate cost of holding astock position is offset (partially, or more than
totally) by dividend income. The presence of dividends is easily incorporated into the framework of
calculating atheoretical spread level. The spread would be in equilibrium if, based on current prices,
interest rates, and dividends, there would be no difference between holding the actual equities in
the index for the interim between the two spread months versus buying the forward index futures
contract. Holding equities would incur an interest rate cost that does not exist in holding futures, but
would also accrue the dividend yield the holder of futures does not receive. The theoretical spread
level (P
2 − P1) at the expiration of P 1 at which these two alternative means of holding along equity
position—equity and stock index futures—would imply an equivalent outcome can be expressed
symbolically as follows:
PP Ptid21 1 360−= 
 
 −()
where P1 = price of nearby (expiring) futures contract
 P2 = price of forward futures contract
 t = number of days between expiration of nearby contract and expiration of forward contract
 i = short-term interest rate level at time of P1 expiration
 d = annualized dividend yield (%)
As is evident from this equation, if short-term interest rates exceed dividend yields, forward
futures will trade at apremium to nearby contracts. Conversely, if the dividend yield exceeds short-
term interest rates, forward futures will trade at adiscount.
Since the dividend yield is not subject to sharp changes in the short run, for any given index
(price) level, intramarket stock index spreads would primarily reflect expected future short-term
rates (similar to gold spreads). If short-term interest rates exhibit low volatility, as characterized by
the near-zero interest rate environment that prevailed in the years following the 2008 financial crisis,
stock index spreads will tend to trade in relatively narrow range—aconsequence of both major
drivers of stock index spreads (interest rates and dividend yield) being stable.
 ■ Intermarket Stock Index Spreads
As is the case with intercommodity and intermarket spreads trading at disparate price levels, stock
index spreads should be traded as ratios rather than differences—an approach that will make the
spread position indifferent to equal percentage price changes in both markets (indexes). As areminder,
to trade aratio, the trader should implement each leg of the spread in approximately equal contract
value positions, which, as was shown in Chapter 31, can be achieved by using acontract ratio that is
inversely proportional to the contract value ratio.
For example, if the E-mini Nasdaq 100 futures contract, which has acontract value of 20 times the
index, is trading at 4,300 (acontract value of $86,000), and the Russell 2000 Mini futures contract,

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SPREAd TRAdING IN SToCK INdEx FuTuRES
which has acontract value of 100 times the index, is trading at 1,150 (acontract value of $115,000),
the contract value ratio (CVR) of Nasdaq to Russell futures would be equal to:
CVR2 04 ,300 /1 00 1,150 07 478=× ×=() () .
Therefore, the contract ratio would be equal to the inverse of the contract value ratio:
1/0.7478 = 1.337. Thus, for example, aspread with 3 long (short) Russell contracts would be bal-
anced by 4 Nasdaq short (long) contracts: 3 × 1.337 = 4.01.
Because some stock indexes are inherently more volatile than other indexes—for example, smaller-
cap indexes tend to be more volatile than larger-cap indexes—some traders may wish to make an
additional adjustment to the contract ratio to neutralize volatility differences. If this were done, the
contract ratio defined by the inverse of the contract value ratio would be further adjusted by multiply-
ing by the inverse of some volatility measure ratio.
one good candidate for such avolatility measure is
the average true range (ATR), which was defined in Chapter 17. As an illustration, if in the aforemen-
tioned example of the Nasdaq 100/Russell 2000 ratio, the prevailing ATR of the Nasdaq 100 is 0.8
times the ATR of the Russell 2000, then the Nasdaq/Russell 2000 contract ratio of 1.337 would be
further adjusted by multiplying by the inverse of the ATR ratio (1 / 0.8 = 1.25), yielding acontract
ratio of 1.671 instead of 1.337. If this additional adjustment is made, then aspread with 3 long (short)
Russell contracts would be balanced by 5 short (long) Nasdaq contracts: 3 × 1.671= 5.01.
It is up traders to decide whether they wish to further adjust the contract ratio for volatility. For the
remainder of this chapter, we assume the more straightforward case of contract ratios being adjusted
only for contract value differences (i.e., without any additional adjustment for volatility differences).
The four most actively traded stock index futures contracts are the E-mini S&P 500, E-mini
Nasdaq 100, E-mini
dow , and the Russell 2000 Mini. There are six possible spread pairs for these
four markets:
 ■ E-mini S&P 500 / E-mini dow
 ■ E-mini S&P 500 / E-mini Nasdaq 100
 ■ E-mini S&P 500 / Russell 2000 Mini
 ■ E-mini Nasdaq 100 / E-mini dow
 ■ E-mini Nasdaq 100 / Russell 2000 Mini
 ■ E-mini dow / Russell 2000 Mini
Traders who believe acertain group of stocks will perform better or worse than another group
can express this view through stock index spreads. For example, atrader who expected large-cap
stocks to outperform small-cap stocks could initiate long E-mini S&P 500/short Russell 2000 Mini
spreads or long E-mini
dow/short Russell 2000 Mini spreads. Atrader expecting relative outperfor-
mance by small-cap spreads would place the reverse spreads. As another example, atrader expecting
relative outperformance by technology stocks might consider spreads that are long the tech-heavy
Nasdaq 100 index and short another index, such as long E-mini Nasdaq 100/short E-mini S&P 500

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464A CoMPLETE GuIdE To THE FuTuRES MARKET
spreads. Again, to trade these types of spreads as price ratios, the spreads would be implemented so
the contract values of each side are approximately equal, acondition that will be achieved when the
contract ratio between the indexes is equal to the inverse of the contract value ratio.
 Figures 32.1 through 32.6 illustrate the contract value ratios for these six spread pairs during
2002–2015. In some cases, such as the S&P 500/dow spread, the contract value ratio does not vary
much. As can be seen in Figure 32.1 , the contract value ratio for this pair ranged by afactor of only
about 1.2 from low to high over the entire period. For other index pairs, however, the contract value
ratio ranged widely. For example, Figure 32.4 shows that during the same period, the high Nasdaq/
dow contract value ratio was nearly 2.5 times the low ratio. Since the contract ratio required to keep
the trade neutral to equal percentage price changes in both markets is equal to the inverse of the
prevailing contract value ratio, the appropriate contract ratio for these spreads can range widely over
time. For example, for the aforementioned Nasdaq 100/dow ratio, athree-contract dow position
would have been balanced by aseven-contract Nasdaq position when the contract value ratio was at
its low versus only athree-contract position (rounding up) when the ratio was at its high.
 Figures 32.7 through 32.12 illustrate the price ratios for the six stock index pairs during the same
period, along with an overlay of one of the indexes to facilitate visually checking of the relationships
between the index price ratio and the overall stock market direction. Note that the price ratios
in Figures 32.7 through 32.12 are identical in pattern to the contract value ratios in Figures 32.1
through 32.6 , which is aconsequence of the contract value ratio being equal to the price ratio times
aconstant—the constant being equal to the ratio of the multipliers for the indexes.
 FIGURE  32.1 Contract Value Ratio: S&P 500/dow E-Mini Futures

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471
Spread Trading in
Currency Futures
Lenin was certainly right. There is no subtler, no surer means of overturning the existing basis of
society than to debauch the currency. The process engages all the hidden forces of economic law on
the side of destruction, and does it in amanner which not one man in amillion is able to diagnose.
—John Maynard Keynes
 ■ Intercurrency Spreads
Conceptually, intercurrency spreads are identical to outright currency trades. After all, anet long or short
currency futures position is also aspread in that it implies an opposite position in the dollar. For example,
anet long Japanese yen (JY) position means that one is long the JY versus the U.S. dollar (USD). If the JY
strengthens against the USD, the long JY position will gain. If the JY strengthens against the Swiss franc
(SF) and euro but remains unchanged against the USD, the long JY position will also remain unchanged.
In an intercurrency spread, the implied counterposing short in the USD is replaced by another
currency. For example, in along JY/short euro spread, the position will gain when the JY strengthens
relative to the euro, but will be unaffected by fluctuations of the JY relative to the dollar. The long
JY/short euro spread is merely the combination of along JY/short USD and along USD short euro
position, in which the opposite USD positions offset each other. (Tobe precise, the implied USD posi-
tions will only be completely offset if the dollar values of the JY and euro positions are exactly equal.)
There are two possible reasons for implementing an intercurrency spread:
 1. The trader believes currency 1 will gain against the USD, while currency 2 will lose against the USD. In
this case, along currency 1/short currency 2 spread is best thought of as two separate outright trades.
 2. The trader believes that one foreign currency will gain on another, but has no strong opinion
regarding the movement of either currency against the USD. In this case, the intercurrency spread
is analogous to an outright currency trade, with the implied short or long in the USD replaced by
another currency. If, however, the two currencies are far more closely related to each other than to
the USD, the connotation normally attributed to aspread might be at least partially appropriate.
Chapter 33

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If an intercurrency spread is motivated by the second of these factors, the position should be
 balanced in terms of equal dollar values. (This may not always be possible for the small trader.)
Otherwise, equity losses can occur, even if the exchange rate between the two currencies remains
unchanged.
For example, consider along 4 December SF/short 4 December euro spread position imple-
mented when the December SF = $1.000 and the December euro = $1.250. At the trade initiation,
the exchange rate between the SF and euro is 1 euro = 1.25 SF. If the SF rises to $1.100 and the
euro climbs to $1.375, the exchange rate between the SF and euro is unchanged: 1 euro = 1.25 SF.
However, the spread position will have lost $12,500:
Equity change numbe ro fc ontrac ts number of unitsp er contra ct ga=× × iin/loss peru nit
Equity change in long SF 41 25 000 01 0= 50 000=× ×,$ .$ ,
Equity change in short euro 4 125 000 01 25 62 500=× ×− =−,$ .$ ,
Netp rofit/loss 12 500=− $,
The reason the spread loses money even though the SF/euro exchange rate remains unchanged
is that the original position was unweighted. At the initiation prices, the spread represented along
SF position of $500,000 but ashort euro position of $625,000. Thus, the spread position was biased
toward gaining if the dollar weakened against both currencies and losing if the dollar strengthened. If,
however, the spread were balanced in terms of equal dollar values, the equity of the position would
have been unchanged. For example, if the initial spread position were long 5 December SF/short 4
December euro (aposition in which the dollar value of each side = $625,000), the aforementioned
price shift would not have resulted in an equity change:
Equity change in long SF 51 25 000 01 06 25 00=× ×=,$ .$ ,
Equity change in short euro 4 125 000 01 25 62 500=× ×− =−,( $. )$ ,
Netprofit/loss 0=
The general formula for determining the equal-dollar-value spread ratio (number of contracts of
currency 1 per contract of currency 2) is:
Equal-dollar-spread rati onumbe ro funits per
contra ct of currenc= yy2
priceo fcurrenc y2
numbe ro funits per
contra ct of currenc y1
() ()
(() ()
priceo fcurrenc y1
For example, if currency 1, the British pound (BP) = $1.50, and currency 2, the euro = $1.20,
and the BP futures contract consists of 62,500 units, while the euro futures contract consists of
125,000 units, the implied spread ratio would be:
(, )($ .)
(, )($ .) .125 0001 20
62 5001 50 16=

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SPreAD TrADINg IN CUrreNCY FUTUreS
Thus, the equal dollar value spread would consist of 1.6 BP contracts per euro contract, or 8 BP to
5 euro.
equity fluctuations in an equal-dollar-value intercurrency spread position will mirror the price
ratio (or exchange rate) between currencies. It should be emphasized that price ratios (as opposed to
price spreads) are the only meaningful means of representing intercurrency spreads. For example, if
the BP = $1.50 and SF = $1.00, an increase of $0.50 in both the currencies will leave the price spread
between the BP and SF unchanged, even though it would drastically alter the relative values of the two
currencies: adecline of the BP vis-à-vis the SF from 1.5 SF to 1.33 SF.
 ■ Intracurrency Spreads
An intracurrency spread—the price difference between two futures contracts for the same currency—
directly reflects the implied forward interest rate differential between dollar-denominated accounts
and accounts denominated in the given currency. For example, the June/December euro spread
indicates the expected relationship between six-month eurodollar and euro rates in June.
1
Todemonstrate the connection between intracurrency spreads and interest rate differentials, we
compare the alternatives of investing in dollar-denominated versus euro-denominated accounts:
S = spot exchange rate ($/euro)
F = current forward exchange rate for date at end of investment period ($/euro)
r
1 = simple rate of return on dollar-denominated account for investment period (nonannualized)
r2 = simple rate of return on euro-denominated account for investment period (nonannualized)
alternative a:
Invest in Dollar-Denominated account
alternative B:
Invest in euro-Denominated account
1. Invest $1 in dollar-denominated account. 1. Convert $1 to euro at spot.
2. Funds at end of period = $1 (1 + r1) exchange rate is S, which yields 1/Seuro. (By definition, if Sequals dollars
per euro, 1/S = euro per dollar.)
2. Invest 1/Seuro in euro-denominated account at r
2.
3. Lock in forward exchange rate by selling the anticipated euro proceeds
at end of investment period at current forward rate F.2
4. Funds at end of period = 1/S (1 + r2) euro.
5. Converted to dollars at rate F, funds at end of period = $F/S (1 + r2)
(since F = dollars per euro).
1 The eurocurrency rates are interest rates on time deposits for funds outside the country of issue and hence free
of government controls. For example, interest rates on dollar-denominated deposits in London are eurodollar
rates, while rates on sterling-denominated deposits in Frankfurt are eurosterling rates. The quoted eurocurrency
rates represent the rates on transactions between major international banks.
2 Ashort forward position can be established in one of two ways: (1) selling futures that are available for forward
dates at three-month intervals; and (2) initiating along spot/short forward position in the foreign exchange (FX)
swap market and simultaneously selling spot.

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SPreAD TrADINg IN CUrreNCY FUTUreS
Of course, the market forces just described would come into play well before the forward/spot
ratio increased to 0.82/0.80 = 1.025. The intervention of arbitrageurs will assure the six-month
forward/spot ratio would not rise significantly above 1 + r 1/1 + r2 = 1.0099. Asimilar argument
could be used to demonstrate that arbitrage intervention would keep the forward/spot ratio from
declining significantly below 1.0099. In short, arbitrage activity will assure that the forward/spot
ratio will be approximately defined by the above equation. This relationship is commonly referred to
as the interest rate parity theorem.
Since currency futures must converge with spot exchange rates at expiration, the price spread
between aforward futures contract and anearby expiring contract must reflect the prevailing interest
rate ratio (between the eurodollar rate and the given eurocurrency rate).
4 Hence, aspread between
two forward futures contracts can be interpreted as reflecting the market’sexpectation for the inter-
est rate ratio at the time of the nearby contract expiration. Specifically, if P
1 = price of the more
nearby futures expiring at t1 and P2 = price of the forward futures contract expiring at time t 2, then
P2/P1 will equal the expected interest rate ratio (expressed as 1+r1/1+r2) for term rates of duration
t2 − t1 at time t1. It should be stressed that the forward interest rate ratio implied by spreads in futures
will usually differ from the prevailing interest rate ratio.
If the market expects the eurodollar rate to be greater than the foreign eurocurrency rate, forward
futures for that currency will trade at apremium to more nearby futures—the wider the expected
differential, the wider the spread. Conversely, if the foreign eurocurrency rate is expected to be
greater than the eurodollar rate, forward futures will trade at adiscount to nearby futures.
The above relationships suggest that intracurrency spreads can be used to trade expectations
regarding future interest rate differentials between different currencies. If atrader expected eurodol-
lar rates to gain (move up more or down less) on aforeign eurocurrency rate (relative to the expected
interest rate ratio implied by the intracurrency futures spread), this expectation could be expressed
as along forward/short nearby spread in that currency. Conversely, if the trader expected the foreign
eurocurrency rate to gain on the eurodollar rate, the implied trade would be along nearby/short
forward intracurrency spread.
As atechnical point, a 1:1 spread ratio would fluctuate even if the implied forward interest rate
ratio were unchanged. For example, if P
2 = $0.81/euro and P1 = $0.80/euro, a 10-percent increase
in both rates would result in a 810-point price gain in the forward contract and only a 800-point gain
in the nearby contract, even though the implied forward interest rate ratio would be unchanged (since
an equal percentage change in each month would leave F/Sunchanged). In order for the spread posi-
tion to be unaffected by equal percentage price changes in both contracts, adevelopment that would
not affect the implied forward interest rate ratio, the spread would have to be implemented so that the
dollar value of the long and short positions were equal. This parity will be achieved when the contract
ratio is equal to the inverse of the price ratio. For example, given the above case of P
2 = $0.81 and
4 All references to interest rate ratios in this section should be understood to mean (1 + r1)/(l + r2) where r1
and r2 are the nonannualized rates of return for the time interim between Sand F. Thus, in the above example,
the interest rate ratio for the six-month period given annualized rates of 4.04 percent and 2.01 percent is equal
to 1.02/1.01 = 1.0099. The reader should be careful not to misconstrue the intended definition of interest rate
ratio with aliteral interpretation, which in the above example would suggest afigure of 0.02/0.01 = 2.

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P1 = $0.80, an 80-contract forward/81-contract nearby spread would not be affected by equal price
changes (e.g., a 10-percent price increase would cause atotal 64,800-point change in both legs of the
spread). As can be seen in this example, abalanced spread will only be possible for extremely large
positions. This fact, however, does not present aproblem, since the distortion is sufficiently small so
that a 1:1 contract ratio spread serves as areasonable approximation.
Intracurrency spreads can also be combined to trade expectations regarding two foreign euro-
currency rates. In this case, the trader would implement along nearby/short forward spread in the
currency with the expected relative rate gain, and along forward/short nearby spread in the other
currency. For example, assume that in February the June/December euro spread implies that the
June six-month eurodollar rate will be 1 percent above the euro rate, while the June/December JY
spread implies that the June eurodollar rate will be 2 percent above the euroyen rate. In combina-
tion, these spreads imply that the June euro rate will be higher than the June euroyen rate. If atrader
expected euroyen rates to be higher than euro rates in June, the following combined spread positions
would be implied: long June JY/short December JY plus long December euro/short June euro.
Tosummarize, intracurrency spreads can be used to trade interest rate differentials in the follow-
ing manner:
expectation Indicated trade
eurodollar rate will gain on given eurocurrency rate
(relative to rate ratio implied by spread).
Long forward/short nearby
spread in given currency
eurodollar rate will lose on given eurocurrency rate
(relative to rate ratio implied by spread).
Long nearby/short forward
spread in given currency
eurocurrency rate 1 will gain on eurocurrency rate 2
(relative to rate ratio implied by spreads in both markets).
Long nearby/short forward spread in market 1 and long
forward/short nearby spread in market 2

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Aput might more properly be called astick. For the whole point of aput—its purpose, if you
will—is that it gives its owner the right to force 100 shares of some godforsaken stock onto
someone else at aprice at which he would very likely rather not take it. So what you are really
doing is sticking it to him.
—Andrew Tobias
Getting By on $100,000 a Year (and Other Sad Tales)
 ■ Preliminaries
There are two basic types of options: calls and puts. The purchase of acall option on futures1 provides
the buyer with the right, but not the obligation, to purchase the underlying futures contract at aspeci-
fied price, called the strike or exercise price, at any time up to and including the expiration date. 2 Aput
option provides the buyer with the right, but not the obligation, to sell the underlying futures contract
at the strike price at any time prior to expiration. (Note, therefore, that buying aput is abearish trade,
while selling aput is abullish trade.) The price of an option is called the premium, and is quoted in
An Introduction to
Options on Futures
Chapter 34
1 Chapters 34 and 35 deal specifically with options on futures contracts. However, generally speaking, analogous
concepts would apply to options on cash (physical) goods or instruments (e.g., bullion versus gold futures).
Some of the advantages of basing an option contract on futures as opposed to the cash asset are discussed in the
next section.
2 For some markets, the expiration date on the option and the underlying futures contract will be the same; for other
markets, the expiration date on the option will be aspecified date prior to the expiration of the futures contract.

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A Complete Guide to the Futures mArket either dollars (or cents) per unit or points. Table 34.1 illustrates how to calculate the dollar value of
apremium. As aspecific example, atrader who buys a $1,000 August gold call at apremium of $50
pays $50/oz ($5,000 per contract) for the right to buy an August gold futures contract at $1,000
(regardless of how high its price may rise) at any time up to the expiration date of the August option.
Because options are traded for both puts and calls and anumber of strike prices for each futures
contract, the total number of different options traded in amarket will far exceed the number of
futures contracts—often by afactor of 10 to 1 or more. This broad variety of listed options provides
the trader with myriad alternative trading strategies.
Like their underlying futures contracts, options are exchange-traded, standardized contracts.
Consequently, option positions can be offset prior to expiration simply by entering an order opposite
to the position held. For example, the holder of acall could liquidate his position by entering an order
to sell acall with the same expiration date and strike price.
The buyer of acall seeks to profit from an anticipated price rise by locking in aspecific purchase
price. His maximum possible loss will be equal to the dollar amount of the premium paid for the
option. This maximum loss would occur on an option held until expiration if the strike price were
above the prevailing futures price. For example, if August gold futures were trading at $990 upon the
expiration of the August option, a $1,000 call would be worthless because futures could be purchased
more cheaply at the existing market price.
3 If the futures were trading above the strike price at expira-
tion, then the option would have some value and hence would be exercised. However, if the difference
table 34.1 Determining the Dollar Value of Option premiums
Contracts Quoted on an Index
Option premium (in points) × $ value per point = $ value of the option premium
Examples:
E-mini S&P 500 options
8.50 (option premium) × $50 per point = $425 (option premium $ value)
U.S. dollar index options
2.30 (option premium) × $1,000 per point = $2,300 (option premium $ value)
Contracts Quoted in Dollars
Option premium (in dollars or
cents per unit)
× No. of units in futures contract = $ value of the option premium
Examples:
Gold options
$42 (option premium) × 100 (ounces in futures contract) = $4,200 (option premium $ value)
WTI crude oil options
$1.24 (option premium) × 1,000 (barrels in futures contract) = $1,240 (option premium $ value)
3 However, it should be noted that even in this case, the call buyer could have recouped part of the premium if
he had sold the option prior to expiration. This is true since the option will maintain some value (i.e., premium
greater than zero) as long as there is some possibility of the futures price rising above the strike price prior to
the expiration of the option.

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AN INTrOduCTION TO OPTIONS ON FuTureS
between the futures price and the strike price were less than the premium paid for the option, the
net result of the trade would still be aloss. In order for the call buyer to realize anet profit, the dif-
ference between the futures price and the strike price would have to exceed the premium at the time
the call was purchased (after adjusting for commission cost). The higher the futures price, the greater
the resulting profit. Of course, if the futures reach the desired objective, or the call buyer changes his
market opinion, he could sell his call prior to expiration.
4
The buyer of aput seeks to profit from an anticipated price decline by locking in asales price.
Similar to the call buyer, his maximum possible loss is limited to the dollar amount of the premium
paid for the option. In the case of aput held until expiration, the trade would show anet profit if the
strike price exceeded the futures price by an amount greater than the premium of the put at purchase
(after adjusting for commission cost).
While the buyer of acall or put has limited risk and unlimited potential gain,
5 the reverse is true
for the seller. The option seller (“writer”) receives the dollar value of the premium in return for
undertaking the obligation to assume an opposite position at the strike price if an option is exercised.
For example, if acall is exercised, the seller must assume ashort position in futures at the strike
price (since by exercising the call, the buyer assumes along position at that price).
upon exercise,
the exchange’sclearinghouse will establish these opposite futures positions at the strike price. After
exercise, the call buyer and seller can either maintain or liquidate their respective futures positions.
The seller of acall seeks to profit from an anticipated sideways to modestly declining market. In
such asituation, the premium earned by selling acall will provide the most attractive trading oppor-
tunity. However, if the trader expected alarge price decline, he would usually be better off going
short futures or buying aput—trades with open-ended profit potential. In asimilar fashion, the seller
of aput seeks to profit from an anticipated sideways to modestly rising market.
Some novices have trouble understanding why atrader would not always prefer the buy side of an
option (call or put, depending on his market opinion), since such atrade has unlimited potential and
limited risk. Such confusion reflects the failure to take probability into account. Although the option
seller’stheoretical risk is unlimited, the price levels that have the greatest probability of occurring
(i.e., prices in the vicinity of the market price at the time the option trade occurs) would result in anet
gain to the option seller.
roughly speaking, the option buyer accepts alarge probability of asmall loss
in return for asmall probability of alarge gain, whereas the option seller accepts asmall probability
of alarge loss in exchange for alarge probability of asmall gain. In an efficient market, neither the
consistent option buyer nor the consistent option seller should have any advantage over the long run.
6
4 even if the call is held until the expiration date, it will usually still be easier to offset the position in the options
market rather than exercising the call.
5 Technically speaking, the gains on aput would be limited, since prices cannot fall below zero; but for practical
purposes, it is entirely reasonable to speak of the maximum possible gain on along put position as being unlimited.
6 Tobe precise, this statement is not intended to imply that the consistent option buyer and consistent option seller
would both have the same expected outcome (zero excluding transactions costs). Theoretically, on average, it is rea-
sonable to expect the market to price options so there is some advantage to the seller to compensate option sellers for
providing price insurance—that is, assuming the highly undesirable exposure to alarge, open-ended loss. So, in effect,
option sellers would have amore attractive return profile and aless attractive risk profile than option buyers, and it
is in this sense that the market will, on average, price options so that there is no net advantage to the buyer or seller.

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 ■ Factors That Determine Option Premiums
An option’spremium consists of two components:
Premiu mi ntri nsic valuet imev alue=+
The intrinsic value of acall option is the amount by which the current futures price is above the strike
price. The intrinsic value of aput option is the amount by which the current futures price is below the
strike price. In effect, the intrinsic value is that part of the premium that could be realized if the option were
exercised and the futures contract offset at the current market price. For example, if July crude oil futures
were trading at $74.60, acall option with astrike price of $70 would have an intrinsic value of $4.60. The
intrinsic value serves as afloor price for an option. Why? Because if the premium were less than the intrinsic
value, atrader could buy and exercise the option, and immediately offset the resulting futures position,
thereby realizing anet gain (assuming this profit would at least cover the transaction costs).
Options that have intrinsic value (i.e., calls with strike prices below the current futures price and
puts with strike prices above the current futures price) are said to be in-the-money. Options with no
intrinsic value are called out-of-the-money options. An option whose strike price equals the futures
price is called an at-the-money option. The term at-the-money is also often used less restrictively to refer
to the specific option whose strike price is closest to the futures price.
An out-of-the-money option, which by definition has an intrinsic value of zero, nonetheless retains
some value because of the possibility the futures price will move beyond the strike price prior to the expi-
ration date. An in-the-money option will have avalue greater than the intrinsic value because aposition in
the option will be preferred to aposition in the underlying futures contract.
reason: Both the option and
the futures contract will gain equally in the event of favorable price movement, but the option’smaximum
loss is limited. The portion of the premium that exceeds the intrinsic value is called the time value.
It should be emphasized that because the time value is almost always greater than zero, one should
avoid exercising an option before the expiration date. Almost invariably, the trader who wants to
offset his option position will realize abetter return by selling the option, atransaction that will yield
the intrinsic value plus some time value, as opposed to exercising the option, an action that will yield
only the intrinsic value.
The time value depends on four quantifiable factors
7:
 1. the relationship between the strike price and the current futures price. As illus-
trated in Figure 34.1, the time value will decline as an option moves more deeply in-the-money
or out-of-the-money.
deeply out-of-the-money options will have little time value, since it is
unlikely the futures will move to (or beyond) the strike price prior to expiration. deeply in-
the-money options have little time value because these options offer very similar positions to
the underlying futures contracts—both will gain and lose equivalent amounts for all but an
extreme adverse price move. In other words, for adeeply in-the-money option, the fact that the
7 Theoretically, the time value will also be influenced by price expectations, which are anon-quantifiable factor.

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AN INTrOduCTION TO OPTIONS ON FuTureS
risk is limited is not worth very much, because the strike price is so far away from the prevailing
futures price. As Figure 34.1 shows, the time value will be at amaximum at the strike price.
 2. time remaining until expiration. The more time remaining until expiration, the greater
the time value of the option. This is true because alonger life span increases the probability
of the intrinsic value increasing by any specifi ed amount prior to expiration. In other words,
the more time until expiration, the greater the probable price range of futures. Figure 34.2
illustrates the standard theoretical assumption regarding the relationship between time value
and time remaining until expiration for an at-the-money option. Specifi cally, the time value is
 FIGURE  34.1 Theoretical Option Premium Curve
 Source: Chicago Board of Trade, Marketing department.
Call Option
Strike price
Intrinsic value
T -bond futures price130
132
134
136
138
140
Time value premium
8
6
4
2 Option premium
Strike price
Intrinsic
value
T-bond futures price
124
126
128
130
8
6
4
2 Option premium
Put Option
Time value premium
 FIGURE  34.2 Time Value decay
 Source: Options on Comex Gold Futures, published by Commodity
exchange, Inc. (COMeX), 1982.
Time value decay
94 10
Time remaining until expiration (months)
Time value premium

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table 34.2 Option prices as a Function of Volatility in
e-Mini S&p 500 Futures pricesa
annualized Volatility put or Call premium
10 22.88 ($1,144)
20 45.75 ($2,288)
30 68.62 ($3,431)
40 91.46 ($4,573)
50 114.29 ($5,715)
a At-the-money options at astrike price of 2000 with 30 days to expiration.
8 James Bowe, Option Strategies Trading Handbook (New York, NY: Coffee, Sugar, and Cocoa exchange, 1983).
assumed to be afunction of the square root of time. (This relationship is aconsequence of the
typical assumption regarding the shape of the probability curve for prices of the underlying
futures contract.) Thus, an option with nine months until expiration would have 1.5 times the
time value of afour-month option with the same strike price
(; ;. )93 42 32 15== ÷=
and three times the time value of aone-month option (; ;)93 11 31 3== ÷= .
 3. Volatility. Time value will vary directly with the estimated volatility of the underlying futures
contract for the remaining lifespan of the option. This relationship is the result of the fact that
greater volatility raises the probability the intrinsic value will increase by any specified amount
prior to expiration. In other words, the greater the volatility, the larger the probable range of
futures prices. As Table 34.2 shows, volatility has astrong impact on theoretical option pre-
mium values.
Although volatility is an extremely important factor in determining option premium values,
it should be stressed that the future volatility of the underlying futures contract is never pre-
cisely known until after the fact. (In contrast, the time remaining until expiration and the rela -
tionship between the current price of futures and the strike price can be exactly specified at any
juncture.) Thus, volatility must always be estimated on the basis of historical volatility data. As
will be explained, this factor is crucial in explaining the deviation between theoretical and actual
premium values.
 4. Interest rates. The effect of interest rates on option premiums is considerably smaller than
any of the above three factors. The specific nature of the relationship between interest rates and
premiums was succinctly summarized by James Bowe
8:
The effect of interest rates is complicated because changes in rates affect not only the
underlying value of the option, but the futures price as well. Taking it in steps, abuyer
of any given option must pay the premium up front, and of course the seller receives
the money. If interest rates go up and everything else stays constant, the opportunity
cost to the option buyer of giving up the use of his money increases, and so he is will-
ing to bid less. Conversely, the seller of options can make more on the premiums by

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AN INTrOduCTION TO OPTIONS ON FuTureS
investing the cash received and so is willing to accept less; the value of the options fall.
However, in futures markets, part of the value of distant contracts in acarry market
reflects the interest costs associated with owning the commodity. An increase in the
interest rate might cause the futures price to increase, leading to the value of existing
calls going up. The net effect on calls is ambiguous, but puts should decline in value
with increasing interest rates, as the effects are reinforcing.
 ■ Theoretical versus Actual Option Premiums
There is avariety of mathematical models available that will indicate the theoretical “fair value” for an
option, given specific information regarding the four factors detailed in the previous section. Theoret-
ical values will approximate, but by no means coincide with, actual premiums.
does the existence of
such adiscrepancy necessarily imply that the option is mispriced? definitely not. The model-implied
premium will differ from the actual premium for two reasons:
 1. The model’sassumption regarding the mathematical relationship between option prices (premi-
ums) and the factors that affect option prices may not accurately describe market behavior. This
is always true because, to some extent, even the best option-pricing models are only theoretical
approximations of true market behavior.
 2. The volatility figure used by an option-pricing model will normally differ somewhat from the
market’sexpectation of future volatility. This is acritical point that requires further elaboration.
recall that although volatility is acrucial input in any option pricing formula, its value can
only be estimated. The theoretical “fair value” of an option will depend on the specific choice of avolatility figure. Some of the factors that will influence the value of the volatility estimate are the
length of the prior period used to estimate volatility, the time interval in which volatility is mea-
sured, the weighting scheme (if any) used on the historical volatility data, and adjustments (if any)
to reflect relevant influences (e.g., the recent trend in volatility). It should be clear that any specific
volatility estimate will implicitly reflect anumber of unavoidably arbitrary decisions.
different
assumptions regarding the best procedure for estimating future volatility from past volatility will
yield different theoretical premium values. Thus, there is no such thing as asingle, well-defined fair
value for an option.
All that any option pricing model can tell you is what the value of the option should be given
the specific assumptions regarding expected volatility and the form of the mathematical relationship
between option prices and the key factors affecting them. If agiven mathematical model provides aclose approximation of market behavior, adiscrepancy between the theoretical value and the actual
premium means the market expectation for volatility, called the implied volatility, differs from the
historically based volatility estimate used in the model. The question of whether the volatility assump-
tions of aspecific pricing model provide more accurate estimates of actual volatility than the implied
volatility figures (i.e., the future volatility suggested by actual premiums) can only be answered
empirically. Abias toward buying “underpriced” options (relative to the theoretical model fair value)

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and selling “overpriced” options would be justified only if empirical evidence supported the conten-
tion that, on balance, the model’svolatility assumptions proved to be better than implied volatility in
predicting actual volatility levels.
If amodel’svolatility estimates were demonstrated to be superior to implied volatility estimates,
it would suggest, from astrict probability standpoint, abullish trader would be better off selling puts
than buying calls if options were overpriced (based on the fair value figures indicated by the model),
and buying calls rather than selling puts if options were underpriced. Similarly, abearish trader would
be better off selling calls than buying puts if options were overpriced, and buying puts rather than
selling calls if options were underpriced. The best strategy for any individual trader, however, would
depend on the specific profile of his price expectations (i.e., the probabilities the trader assigns to
various price outcomes).
 ■ Delta (the Neutral Hedge Ratio)
Delta, also called the neutral hedge ratio, is the expected change in the option price given aone-unit
change in the price of the underlying futures contract. For example, if the delta of an August gold
call option is 0.25, it means that a $1 change in the price of August futures can be expected to result
in a $0.25 change in the option premium. Thus, the delta value for agiven option can be used to
determine the number of options that would be equivalent in risk to asingle futures contract for small
changes in price. It should be stressed that delta will change rapidly as prices change. Thus, the delta
value cannot be used to compare the relative risk of options versus futures for large price changes.
Table 34.3 illustrates the estimated delta values for out-of-the-money, at-the-money, and in-the-
money call options for arange of times to expiration. Where did these values come from? They are
derived from the same mathematical models used to determine atheoretical value for an option pre-
mium given the relationship between the strike price and the current price of futures, time remaining
table 34.3 Change in the premium of an e-Mini S&p 500 Call Option for 20.00 ($1000) Move in the
Underlying Futures Contracta
Increase in the 2000 call option premium if the futures price rises:
From 1900 to 1920 From 2000 to 2020 From 2100 to 2120
Time to expiration $ Delta $ Delta $ Delta
1 week $10 0.01 $500 0.5 $1,000 1
1 month $120 0.12 $510 0.51 $870 0.87
3 months $260 0.26 $510 0.51 $750 0.75
6 months $330 0.33 $520 0.52 $690 0.69
12 months $390 0.39 $520 0.52 $650 0.65
aAssumed volatility: 15 percent; assumed interest rate: 2 percent per year.
Source: CMe Group (www .cmegroup.com).

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until expiration, estimated volatility, and interest rates. For any given set of values for these factors,
delta will equal the absolute difference between the option premium indicated by the model and the
model-indicated premium if the futures price changes by one point. Table 34.3 illustrates anumber
of important observations regarding theoretical delta values:
 1. Delta values for out-of-the-money options are low. This relationship is aresult of the
fact that there is ahigh probability that any given price increase
9 will not make any actual differ-
ence to the value of the option at expiration (i.e., the option will probably expire worthless).
 2. Delta values for in-the-money options are relatively high, but less than one. In-
the-money options have high deltas because there is ahigh probability that aone-point change
in the futures price will mean aone-point change in the option value at expiration. However,
since this probability must always be equal to less than one, the delta value will also always be
equal to less than one.
 3. Delta values for at-the-money options will be near 0.50. Since there is a 50/50 chance
that an at-the-money option will expire in-the-money, there will be an approximately 50/50
chance that aone-point increase in the price of futures will result in aone-point increase in the
option value at expiration.
 4. Delta values for out-of-the-money options will increase as time to expiration
increases. Alonger time to expiration will increase the probability that aprice increase in
futures will make adifference in the option value at expiration, since there is more time for
futures to reach the strike price.
 5. Delta values for in-the-money options will decrease as time to expiration
increases. Alonger time to expiration will increase the probability that achange in the futures
price will not make any difference to the option value at expiration since there is more time for
futures to fall back to the strike price by the time the option expires.
 6. Delta values for at-the-money options are not substantially affected by time to
maturity until near expiration. This behavioral pattern is true because the probability that
an at-the-money option will expire in-the-money remains close to 50/50 until the option is
near expiration.
9 This section implicitly assumes that the option is acall. If the option is aput, read “price decrease” for all refer-
ences to “price increase.”

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Brokers are fond of pointing out to possible buyers of options that they are asplendid thing to
buy, and pointing out to sellers that they are asplendid thing to sell. They believe implicitly in
this paradox. Thus the buyer does well, the seller does well, and it is not necessary to stress the
point that the broker does well enough. Many examples can be cited showing all three of them
emerging from their adventures with aprofit. One wonders why the problem of unemployment
cannot be solved by having the unemployed buy and sell each other options, instead of mooning
around on those park benches.
—Fred Schwed
Where Are the Customers’ Yachts?
 ■ Comparing Trading Strategies
The existence of options greatly expands the range of possible trading strategies. For example, in the
absence of an option market, atrader who is bullish can either go long or initiate abull spread (in those
markets in which spread movements correspond to price direction). However, if option-related trad-
ing approaches are included, the bullish trader can consider numerous alternative strategies including:
long out-of-the-money calls, long in-the-money calls, long at-the-money calls, short out-of-the-money
puts, short in-the-money puts, short at-the-money puts, “synthetic” long positions, combined positions
in futures and options, and avariety of bullish option spreads. Frequently, one of these option-related
strategies will offer significantly better profit potential for agiven level of risk than an outright futures
position. Thus, the trader who considers both option-based strategies and outright positions should
have adecided advantage over the trader who restricts his trades to only futures.
Option Trading
Strategies
Chapter 35

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There is no single best trading approach. The optimal trading strategy in any given situation will
depend on the prevailing option premium levels and the specific nature of the expected price sce-
nario. How does one decide on the best strategy? This chapter will attempt to answer this critical
question in two steps. First, we will examine the general profit/loss characteristics (profiles) of awide range of alternative trading strategies. Second, we will consider how price expectations can be
combined with these profit/loss profiles to determine the best trading approach.
The profit/loss profile is adiagram indicating the profit or loss implied by aposition (vertical axis)
for arange of market prices (horizontal axis). The profit/loss profile provides an ideal means of
understanding and comparing different trading strategies. The following points should be noted
regarding the profit/loss profiles detailed in the next section:
 1. All illustrations are based on asingle option series, for asingle market, on asingle date: the
August 2015 gold options on April 13, 2015. This common denominator makes it easy to com-
pare the implications of different trading strategies. The choice of April 13, 2015, was not arbi-
trary. On that date, the closing price of August futures (1,200.20) was almost exactly equal to
one of the option strike prices ($1,200/oz), thereby providing anearly precise at-the-money
option—afactor that greatly facilitates the illustration of theoretical differences among out-of-
the-money, in-the-money, and at-the-money options. The specific closing values for the option
premiums on that date were as follows ($/oz):
Strike price august Calls august puts
1,050 155.2 5.1
1,100 110.1 10.1
1,150 70.1 19.9
1,200 38.8 38.7
1,250 19.2 68.7
1,300 9.1 108.7
1,350 4.5 154.1
Option pricing data in this chapter courtesy of OptionVue (www .optionvue.com).
The reader should refer to these quotes when examining each of the profit/loss profiles in
the next section.
 2. In order to avoid unnecessarily cluttering the illustrations, the profit/loss profiles do not include
transaction costs and interest income effects, both of which are very minor. (Note the assump-
tion that transaction costs equal zero imply that commission costs equal zero and that positions
can be implemented at the quoted levels—in this case, the market close.)
 3. The profit/loss profiles reflect the situation at the time of the option expiration. This assumption
simplifies the exposition, since the value of an option can be precisely determined at that point
in time. At prior times, the value of the option will depend on the various factors discussed in
the previous chapter (e.g., time until expiration, volatility, etc.). Allowing for an evaluation of
each option strategy at interim time stages would introduce alevel of complexity that would
place the discussion beyond the scope of this book. However, the key point to keep in mind

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OPTION TrAdINg STrATegIeS
is that the profit/loss profile for strategies that include anet long options position will shift
upward as the time reference point is further removed from the expiration date. The reason is
that at expiration, options have only intrinsic value; at points prior to expiration, options also
have time value. Thus, prior to expiration, the holder of an option could liquidate his position at
aprice above its intrinsic value—the liquidation value assumed in the profit/loss profile. Simi-
larly, the profit/loss profile would be shifted downward for the option writer (seller) at points
in time prior to expiration. This is true since at such earlier junctures, the option writer would
have to pay not only the intrinsic value but also the time value if he wanted to cover his position.
 4. It is important to keep in mind that asingle option is equivalent to asmaller position size than asingle futures contract (see section entitled “
delta—the Neutral Hedge ratio” in the previous
chapter). Similarly, an out-of-the-money option is equivalent to asmaller position size than an
in-the-money option. Thus, the trader should also consider the profit/loss profiles consisting
of various multiples of each strategy. In any case, the preference of one strategy over another
should be based entirely on the relationship between reward and risk rather than on the absolute
profit (loss) levels. In other words, strategy preferences should be totally independent of posi-
tion size.
 5. Trading strategies are evaluated strictly from the perspective of the speculator. Hedging applica-
tions of option trading are discussed separately at the end of this chapter.
 ■ Profit/Loss Profiles for Key Trading Strategies
Strategy 1: Long Futures
exAMPle. Buy August gold futures at $1,200. (See Table 35.1 and Figure 35.1.)
Comment. The simple long position in futures does not require much explanation and is included
primarily for purposes of comparison to other less familiar trading strategies. As every trader knows,
the long futures position is appropriate when one expects asignificant price advance. However, as will
tabLe 35.1 profit/Loss Calculations: Long Futures
Futures price at expiration ($/oz) Futures price Change ($/oz) profit/Loss on position
1,000 –200 –$20,000
1,050 –150 –$15,000
1,100 –100 –$10,000
1,150 –50 –$5,000
1,200 0 $0
1,250 50 $5,000
1,300 100 $10,000
1,350 150 $15,000
1,400 200 $20,000

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491
OPTION TrAdINg STrATegIeS
Comment. Once again, this strategy requires little explanation and is included primarily for com-
parison to other strategies. As any trader knows, the short futures position is appropriate when one
is expecting asignifi cant price decline. However, as will be seen later in this chapter, for any given
expected price scenario, some option-based strategy will often off er amore attractive trading oppor-
tunity in terms of reward/risk characteristics.
 Strategy 3a: Long Call (at-the-Money)
exAMPle . Buy 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 35.3 aand Figure 35.3 a.)
Comment. The long call is abullish strategy in which maximum risk is limited to the premium paid
for the option, while maximum gain is theoretically unlimited. However, the probability of aloss is
greater than the probability of again, since the futures price must rise by an amount exceeding the
option premium (as of the option expiration) in order for the call buyer to realize aprofi t. Two spe-
cifi ccharacteristics of the at-the-money option are the following:
 1. The maximum loss will only be realized if futures are trading at or below their current level at
the time of the option expiration.
 2. For small price changes, each $1 change in the futures price will result in approximately a $0.50
change in the option price. (At-the-money options near expiration, which will change by agreater amount, are an exception.) Thus, for small price changes, anet long futures position is
equivalent to approximately two call options in terms of risk.
 FIGURE  35.2 Profi t/loss Profi le: Short Futures
Price of August gold futures at option expiration ($/oz)
1,000 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
Profit/loss at expiration ($)
20,000
15,000
10,000
5,000
−5,000
−10,000
−15,000
−20,000
0

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492A COMPleTe gUIde TO THe FUTUreS MArKeT
 tabLe 35.3a profit/Loss Calculations: Long Call (at-the-Money)
(1) (2) (3) (4) (5)
Futures price at
expiration ($/oz)
premium of august
$1,200 Call at
Initiation ($/oz)
$ amount of
premium paid
Call Value at
expiration
profit/Loss of
position [(4) – (3)]
1,000 38.8 $3,880 $0 –$3,880
1,050 38.8 $3,880 $0 –$3,880
1,100 38.8 $3,880 $0 –$3,880
1,150 38.8 $3,880 $0 –$3,880
1,200 38.8 $3,880 $0 –$3,880
1,250 38.8 $3,880 $5,000 $1,120
1,300 38.8 $3,880 $10,000 $6,120
1,350 38.8 $3,880 $15,000 $11,120
1,400 38.8 $3,880 $20,000 $16,120
 FIGURE  35.3a Profi t/loss Profi le: long Call (At-the-Money)
Price of August gold futures at option expiration ($/oz)
Futures at time of position
initiation and strike price
Breakeven price = $1,238.80
Profit/loss at expiration ($)
1,000
15,000
17,500
12,500
10,000
7 ,500
2,500
0
−2,500
−5,000
5,000
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400

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493
OPTION TrAdINg STrATegIeS
Strategy 3b: Long Call (Out-of-the-Money)
exAMPle. Buy August $1,300 gold futures call at apremium of $9.10/oz ($910), with August gold
futures trading at $1,200/oz. (See Table 35.3b and Figure 35.3b.)
Comment. The buyer of an out-of-the-money call reduces his maximum risk in exchange for accept-
ing asmaller probability that the trade will realize aprofit. By definition, the strike price of an out-of-
the-money call is above the current level of futures. In order for the out-of-the-money call position
to realize aprofit, the futures price (as of the time of the option expiration) must exceed the strike
price by an amount greater than the premium ($9.10/oz in this example). Note that in the out-of-
the-money call position, price increases that leave futures below the option strike price will still result
in amaximum loss on the option. The long out-of-the-money call might be aparticularly appropriate
position for the trader expecting alarge price advance, but also concerned about the possibility of alarge price decline.
It should be emphasized that the futures price need not necessarily reach the strike price in order
for the out-of-the-money call to be profitable. If the market rises quickly, the call will increase in
value and hence can be resold at aprofit. (However, this characteristic will not necessarily hold true
for slow price advances, since the depressant effect of the passage of time on the option premium
could more than offset the supportive effect of the increased price level of futures.)
For small price changes, the out-of-the-money call will change by less than afactor of one-half for
each dollar change in the futures price. Thus, for small price changes, each long futures position will
be equivalent to several long out-of-the-money calls in terms of risk.
tabLe 35.3b profit/Loss Calculations: Long Call (Out-of-the-Money)
(1) (2) (3) (4) (5)
Futures price at
expiration ($/oz)
premium of august
$1,300 Call at
Initiation ($/oz)
$ amount of
premium paid
Call Value at
expiration
profit/Loss on
position [(4) – (3)]
1,000 9.1 $910 $0 –$910
1,050 9.1 $910 $0 –$910
1,100 9.1 $910 $0 –$910
1,150 9.1 $910 $0 –$910
1,200 9.1 $910 $0 –$910
1,250 9.1 $910 $0 –$910
1,300 9.1 $910 $0 –$910
1,350 9.1 $910 $5,000 $4,090
1,400 9.1 $910 $10,000 $9,090

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494A COMPleTe gUIde TO THe FUTUreS MArKeT
 FIGURE  35.3b Profi t/loss Profi le: long Call (Out-of-the-Money)
Price of August gold futures at option expiration ($/oz)
Futures price at time
of position initiation Strike price
Breakeven price
= $1,309.10
Profit/loss at expiration ($)
1,000
10,000
5,000
7 ,500
2,500
−2,500
0
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
 Strategy 3c: Long Call (In-the-Money)
example . Buy 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 35.3 cand Figure 35.3 c.)
Comment. In many respects, along in-the-money call position is very similar to along futures posi-
tion. The three main diff erences between these two trading strategies are:
 1. The long futures position will gain slightly more in the event of aprice rise—an amount equal
to the time value portion of the premium paid for the option ($1,010 in the above example).
 2. For moderate price declines, the long futures position will lose slightly less. (Once again, the
diff erence will be equal to the time value portion of the premium paid for the option.)
 3. In the event of alarge price decline, the loss on the in-the-money long call position would be lim-
ited to the total option premium paid, while the loss on the long futures position will be unlimited.
 In asense, the long in-the-money call position can be thought of as along 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 sell stop on along position faces the frustrating possibility of the market declining suffi ciently
to activate his stop and subsequently rebounding. The long in-the-money call position off ers the spec-
ulator an alternative method of limiting risk that does not present this danger. Of course, this benefi tdoes not come without acost; as mentioned above, the buyer of an in-the-money call will gain slightly
less than the outright futures trader if the market advances, and will lose slightly more if the market
declines moderately. However, if the trader is anticipating volatile market conditions, he might very

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495
OPTION TrAdINg STrATegIeS
well prefer along in-the-money call position to along futures position combined with aprotective
sell stop order. In any case, the key point is that the trader who routinely compares the strategies
of buying an in-the-money call versus going long futures with aprotective sell stop should enjoy an
advantage over those traders who never consider the option-based alternative.
 FIGURE  35.3c Profi t/loss Profi le: long Call (In-the-Money)
Price of August gold futures at option expiration ($/oz)
Futures price at
time of position
initiationStrike price
Breakeven price = $1210.10
Profit/loss at expiration ($)
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
 tabLe 35.3c profit/Loss Calculations: Long Call (In-the-Money)
(1) (2) (3) (4) (5)
Futures price at
expiration ($/oz)
premium of august $1,100
Call at Initiation ($/oz)
$ amount of
premium paid
Call Value at
expiration
profit/Loss on
position [(4) – (3)]
1,000 110.1 $11,010 $0 –$11,010
1,050 110.1 $11,010 $0 –$11,010
1,100 110.1 $11,010 $0 –$11,010
1,150 110.1 $11,010 $5,000 –$6,010
1,200 110.1 $11,010 $10,000 –$1,010
1,250 110.1 $11,010 $15,000 $3,990
1,300 110.1 $11,010 $20,000 $8,990
1,350 110.1 $11,010 $25,000 $13,990
1,400 110.1 $11,010 $30,000 $18,990

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A Complete Guide to the Futures mArket
Table 35.3d summarizes the profit/loss implications of various long call positions for arange of
price assumptions. Note that as calls move deeper in-the-money, their profit and loss characteristics
increasingly resemble along futures position. The very deep in-the-money $1,050 call provides
an interesting apparent paradox: The profit/loss characteristics of this option are nearly the same
as those of along futures position for all prices above $1,050, but the option has the advantage of
limited risk for lower prices. How can this be? Why wouldn’tall traders prefer the long $1,050
call to the long futures position and, therefore, bid up its price so that its premium also reflected
more time value? (The indicated premium of $15,520 for the $1,050 call consists almost entirely
of intrinsic value.)
There are two plausible explanations to this apparent paradox. First, the option price reflects
the market’sassessment that there is avery low probability of gold prices moving to this deep in-
the-money strike price, and therefore the market places alow value on the time premium. In other
words, the market places alow value on the loss protection provided by an option with astrike price
so far below the market. Second, the $1,050 call represents afairly illiquid option position, and the
quoted price does not reflect the bid/ask spread. No doubt, apotential buyer of the call would have
had to pay ahigher price than the quoted premium in order to assure an execution.
tabLe 35.3d profit/Loss Matrix for Long Calls with Different Strike prices
Dollar amount of premiums paid
$1,050 $1,100 $1,150 $1,200 $1,250 $1,300 $1,350
Call Call a Call Call a Call Call a Call
$15,520 $11,010 $7,010 $3,880 $1,920 $910 $450
position profit/Loss at expiration
Futures price at
expiration ($/oz)
Long
Futures
at $1,200
In-the-Money at-the-Money Out-of-the-Money
$1,050
Call
$1,100
Calla
$1,150
Call
$1,200
Calla
$1,250
Call
$1,300
Calla
$1,350
Call
1,000 –$20,000 –$15,520 –$11,010 –$7,010 –$3,880 –$1,920 –$910 –$450
1,050 –$15,000 –$15,520 –$11,010 –$7,010 –$3,880 –$1,920 –$910 –$450
1,100 –$10,000 –$10,520 –$11,010 –$7,010 –$3,880 –$1,920 –$910 –$450
1,150 –$5,000 –$5,520 –$6,010 –$7,010 –$3,880 –$1,920 –$910 –$450
1,200 $0 –$520 –$1,010 –$2,010 –$3,880 –$1,920 –$910 –$450
1,250 $5,000 $4,480 $3,990 $2,990 $1,120 –$1,920 –$910 –$450
1,300 $10,000 $9,480 $8,990 $7,990 $6,120 $3,080 –$910 –$450
1,350 $15,000 $14,480 $13,990 $12,990 $11,120 $8,080 $4,090 –$450
1,400 $20,000 $19,480 $18,990 $17,990 $16,120 $13,080 $9,090 $4,550
aThese calls are compared in Figure 35.3d.

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497
OPTION TrAdINg STrATegIeS
 Figure 35.3 dcompares the three types of long call positions to along futures position. It should be
noted that in terms of absolute price changes, the long futures position represents the largest position
size, while the out-of-the-money call represents the smallest position size. Figure 35.3 dsuggests the
following important observations:
 1. As previously mentioned, the in-the-money call is very similar to an outright long futures
position.
 2. The out-of-the-money call will lose the least in adeclining market, but will also gain the least in
arising market.
 3. The at-the-money call will lose the most in asteady market and will be the middle-of-the-road
performer (relative to the other two types of calls) in advancing and declining markets.
 Again, it should be emphasized that these comparisons are based upon single-unit positions that
may diff er 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 diff erent observations. This point is discussed in greater detail in
the section entitled “Multiunit Strategies.”
 FIGURE  35.3d Profi t/loss Profi le: long Futures and long Call Comparisons (In-the-Money,
At-the-Money, and Out-of-the-Money)
Chart created using TradeStation. ©TradeStation Technologies, Inc. All rights reserved.
Price of August gold futures at option expiration ($/oz)
Futures price at time of position initiation
Long futures
At-the-money call
(strike price = $1,200)
Out-of-the-money
call (strike price = $1,300)
In-the-money call
(strike price = $1,100)
Profit/loss at expiration ($)
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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498A COMPleTe gUIde TO THe FUTUreS MArKeT
 Strategy 4a: Short Call (at-the-Money)
example . Sell August $1,200 gold futures call at apremium of $38.80 /oz ($3,880), with August gold
futures trading at $1,200/oz. (See Table 35.4 aand Figure 35.4 a.)
 tabLe 35.4a profit/Loss Calculations-Short Call (at-the-Money)
(1) (2) (3) (4) (5)
Futures price at
expiration ($/oz)
premium of august
$1,200 Call at
Initiation ($/oz)
$ amount of
premium received
Call Value at
expiration
profit/Loss on
position [(3) – (4)]
1,000 38.8 $3,880 $0 $3,880
1,050 38.8 $3,880 $0 $3,880
1,100 38.8 $3,880 $0 $3,880
1,150 38.8 $3,880 $0 $3,880
1,200 38.8 $3,880 $0 $3,880
1,250 38.8 $3,880 $5,000 –$1,120
1,300 38.8 $3,880 $10,000 –$6,120
1,350 38.8 $3,880 $15,000 –$11,120
1,400 38.8 $3,880 $20,000 –$16,120
 FIGURE  35.4a Profi t/loss Profi le: Short Call (At-the-Money)
Chart created using TradeStation. ©TradeStation Technologies, Inc. All rights reserved.
Price of August gold futures at option expiration ($/oz)
Futures price at time
of position initiation
and strike price Breakeven price
= $1,238.80
Profit/loss at expiration ($)
1,000
5,000
2,500
−5,000
−2,500
0
−10,000
−7,500
−17,500
−15,000
−12,500
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400

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OPTION TrAdINg STrATegIeS
Comment. The short call is abearish position with amaximum potential gain equal to the premium
received for selling the call and unlimited risk. However, in return for assuming this unattractive
maximum reward/maximum risk relationship, the seller of acall enjoys agreater probability of
realizing aprofit than aloss. Note the short at-the-money call position will result in again as long as
the futures price at the time of the option expiration does not exceed the futures price at the time
of the option initiation by an amount greater than the premium level ($38.80/oz in our example).
However, the maximum possible profit (i.e., the premium received on the option) will only be real-
ized if the futures price at the time of the option expiration is below the prevailing market price at the
time the option was sold (i.e., the strike price). The short call position is appropriate if the trader is
modestly bearish and views the probability of alarge price rise as being very low . If, however, the trader
anticipated alarge price decline, he would probably be better off buying aput or going short futures.
Strategy 4b: Short Call (Out-of-the-Money)
example. Sell August $1,300 gold futures call at apremium of $9.10/oz ($910), with August gold
futures trading at $1,200/oz. (See Table 35.4b and Figure 35.4b.)
Comment. The seller of an out-of-the-money call is willing to accept asmaller maximum gain (i.e.,
premium) in exchange for increasing the probability of again on the trade. The seller of an out-of-
the-money call will retain the full premium received as long as the futures price does not rise by an
amount greater than the difference between the strike price and the futures price at the time of the
option sale. The trade will be profitable as long as the futures price at the time of the option expiration
is not above the strike price by more than the option premium ($9.10/oz in this example). The short
out-of-the-money call represents aless bearish posture than the short at-the-money call position.
Whereas the short at-the-money call position reflects an expectation that prices will either decline
or increase only slightly, the short out-of-the-money call merely reflects an expectation that prices
will not rise sharply.
tabLe 35.4b profit/Loss Calculations: Short Call (Out-of-the-Money)
(1) (2) (3) (4) (5)
Futures price at
expiration ($/oz)
premium of august $1,300
Call at Initiation ($/oz)
$ amount of
premium received
Value of Call
at expiration
profit/Loss on
position [(3) – (4)]
1,000 9.1 $910 $0 $910
1,050 9.1 $910 $0 $910
1,100 9.1 $910 $0 $910
1,150 9.1 $910 $0 $910
1,200 9.1 $910 $0 $910
1,250 9.1 $910 $0 $910
1,300 9.1 $910 $0 $910
1,350 9.1 $910 $5,000 –$4,090
1,400 9.1 $910 $10,000 –$9,090

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OPTION TrAdINg STrATegIeS
Comment. For most of the probable price range, the profi t/loss characteristics of the short in-the-
money call are fairly similar to those of the outright short futures position. There are three basic dif-
ferences between these two positions:
 1. The short in-the-money call will lose modestly less than the short futures position in
an advancing market because the loss will be partially off set by the premium received for
the call.
 2. The short in-the-money call will gain modestly more than the short futures position in amod-
erately declining market.
 3. In avery sharply declining market, the profi tpotential on ashort futures position is open-ended,
whereas the maximum gain in the short in-the-money call position is limited to the total pre-
mium received for the call.
 In eff ect, the seller of an in-the-money call chooses to lock in modestly better results for the prob-
able price range in exchange for surrendering the opportunity for windfall profi ts in the event of aprice collapse. generally speaking, atrader should only choose ashort in-the-money call over ashort
futures position if he believes that the probability of asharp price decline is extremely small.
 Table 35.4 dsummarizes the profi t/loss results for various short call positions for arange of
price assumptions. As can be seen, as calls move more deeply in-the-money, they begin to resemble
 FIGURE  35.4c Profi t/loss Profi le: Short Call (In-the-Money)
Chart created using TradeStation. ©TradeStation Technologies, Inc. All rights reserved.
Price of August gold futures at option expiration ($/oz)
Futures price at
time of position
initiation
Strike price
Breakeven price
= $1210.10
Profit/loss at expiration ($)
1,000
10,000
15,000
−10,000
5,000
−5,000
0
−20,000
−15,000
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
ashort futures position more closely. (Sellers of deep in-the-money calls should be aware that longs
may choose to exercise such options well before expiration. early exercise can occur if the poten-
tial interest income on the premium is greater than the theoretical time value of the option for azero interest rate assumption.) Short positions in deep out-of-the-money calls will prove profitable
for the vast range of prices, but the maximum gain is small and the theoretical maximum loss is
unlimited.
Figure 35.4d compares each type of short call to ashort futures position. The short at-the-money
call position will be the most profitable strategy under stable market conditions and the middle-of-
the-road strategy (relative to the other two types of calls) in rising and declining markets. The short
out-of-the-money call will lose the least in arising market, but it will also be the least profitable
strategy if prices decline. The short in-the-money call is the type of call that has the greatest potential
and risk and, as mentioned above, there is astrong resemblance between this strategy and an outright
short position in futures.
It should be emphasized that the comparisons in Figure 35.4d are 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 different empirical conclusions.
tabLe 35.4d profit/Loss Matrix for Short Calls with Different Strike prices
Dollar amount of premium received
$1,050 $1,100 $1,150 $1,200 $1,250 $1,300 $1,350
Call Call Call Call Call Call Call
$15,520 $11,010 $7,010 $3,880 $1,920 $910 $450
position profit/Loss at expiration
Futures price at
expiration ($/oz)
Short Futures
at $1,200
In-the-Money
at-the-
Money Out-of-the Money
$1,050 Call $1,100 Call a $1,150 Call $1,200 Call a $1,250 Call $1,300 Call a $500 Call
1,000 $20,000 $15,520 $11,010 $7,010 $3,880 $1,920 $910 $450
1,050 $15,000 $15,520 $11,010 $7,010 $3,880 $1,920 $910 $450
1,100 $10,000 $10,520 $11,010 $7,010 $3,880 $1,920 $910 $450
1,150 $5,000 $5,520 $6,010 $7,010 $3,880 $1,920 $910 $450
1,200 $0 $520 $1,010 $2,010 $3,880 $1,920 $910 $450
1,250 –$5,000 –$4,480 –$3,990 –$2,990 –$1,120 $1,920 $910 $450
1,300 –$10,000 –$9,480 –$8,990 –$7,990 –$6,120 –$3,080 $910 $450
1,350 –$15,000 –$14,480 –$13,990 –$12,990 –$11,120 –$8,080 –$4,090 $450
1,400 –$20,000 –$19,480 –$18,990 –$17,990 –$16,120 –$13,080 –$9,090 –$4,550
aThese calls are compared in Figure 35.4d.

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503
OPTION TrAdINg STrATegIeS
 Strategy 5a: Long put (at-the-Money)
example . Buy August $1,200 gold futures put at apremium of $38.70/oz ($3,870), with August gold
futures trading at $1,200/oz. (See Table 35.5 aand Figure 35.5 a.)
 FIGURE  35.4d Profi t/loss Profi le: Short Futures and Short Call Comparisons (In-the-Money,
At-the-Money, and Out-of-the-Money)
Price of August gold futures at option expiration ($/oz)
Futures price at time
of position initiation
Short futures
At-the-money call
(strike price = $1,200)
Out-of-the-money call
(strike price = $1,300)
In-the-money call
(strike price = $1,100)
Profit/loss at expiration ($)
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
 tabLe 35.5a profit/Loss Calculations: Long 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 paid
put Value at
expiration
profit/Loss on
position [(4) – (3)]
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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504A COMPleTe gUIde TO THe FUTUreS MArKeT
Comment. The long put is abearish strategy in which maximum risk is limited to the premium paid
for the option, while maximum gain is theoretically unlimited. However, the probability of aloss is
greater than the probability of again, since the futures price must decline by an amount exceeding
the option premium (as of the option expiration) in order for the put buyer to realize aprofi t. Two
specifi ccharacteristics of the at-the-money option are:
 1. The maximum loss will be realized only if futures are trading at or above their current level at
the time of the option expiration.
 2. For small price changes, each $1 change in the futures price will result in approximately a $0.50
change in the option price (except for options near expiration). Thus, for small price changes, anet short futures position is equivalent to approximately 2 put options in terms of risk.
 Strategy 5 b: Long put (Out-of-the-Money)
example . Buy August $1,100 gold futures put at apremium of $10.10 /oz ($1,010). (The current
price of August gold futures is $1,200/oz.) (See Table 35.5 band Figure 35.5 b.)
Comment. The buyer of an out-of-the-money put reduces his maximum risk in exchange for accept-
ing asmaller probability that the trade will realize aprofi t. By defi nition, the strike price of an out-of-
the-money put is below the current level of futures. In order for the out-of-the-money put position
Price of August gold futures at option expiration ($/oz)
Futures price at time
of position initiation
and strike price
Breakeven price = $1,161.30
Profit/loss at expiration ($)
1,000
10,000
7,500
−5,000
5,000
−2,500
2,500
0
17,500
15,000
12,500
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
 FIGURE  35.5a Profi t/loss Profi le: long Put (At-the-Money)

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505
OPTION TrAdINg STrATegIeS
to realize aprofi t, the futures price (as of the time of the option expiration) must penetrate the strike
price by an amount greater than the premium ($10.10/oz in the above example). Note that in the
out-of-the-money put position, price decreases that leave futures above the option strike price will
still result in amaximum loss on the option. The long out-of-the-money put might be aparticularly
appropriate position for the trader expecting alarge price decline, but also concerned about the pos-
sibility of alarge price rise.
 tabLe 35.5b profit/Loss Calculations: Long put (Out-of-the-Money)
(1) (2) (3) (4) (5)
Futures price at
expiration ($/oz)
premium of august $1,100
put at Initiation ($/oz)
$ amount of
premium paid
Value of put
at expiration
profit/Loss on
position [(4) – (3)]
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
Futures price at time
of position initiation
Breakeven
price
= $1,089.90
Profit/loss at expiration ($)
1,000
7,500
10,000
5,000
−2,500
2,500
0
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
Strike price
 FIGURE  35.5b Profi t/loss Profi le: long Put (Out-of-the-Money)

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