for the case of the New Y ork 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 Y ork coffee = $1.41/lb
and London coffee = $.80/lb, consider the effect of a 25 percent price decline on a long 3 New Y ork/
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 Y ork coffee had used the equal-dollar-value approach (assuming a 3-contract position for
New Y ork 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= $,
457
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 a price 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 T echnologies, Inc. All rights reserved.

458A COMPLETE GUIDE TO THE FUTURES MARKET
 FIGURE /uni00A031.2 Price Ratio of September 2013 Wheat to September 2013 Corn
Chart created using TradeStation. ©TradeStation T echnologies, Inc. All rights reserved.
 FIGURE /uni00A031.3 3 September 2013 Wheat Minus 4 September 2013 Corn
459
INTERCOMMODITY SPREADS: DETERMINING CONTRACT RATIOS
 In the preceding example, because wheat is a larger contract than corn (in dollar-value terms),
a long 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, a period 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 a trading range. T o illustrate
the trading implications of the spread ratio, consider a long 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 a near breakeven trade if the spread were implemented on an equal-dollar-value basis
(see Figure 31.2 or 31.3 ), but a signifi 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 a contract 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 a large premium on
 FIGURE /uni00A031.4 September 2013 Wheat and September 2013 Corn

460
A Complete Guide to the Futures mArket
nearby supplies (i.e., in markets conforming to the “general rule” defined in Chapter 30). Intercrop
spreads (which are a subset of intramarket spre


case. Wide price diff erences between
contracts in an intramarket spread can occur in extreme bull markets that place a large premium on
 FIGURE /uni00A031.4 September 2013 Wheat and September 2013 Corn

460
A Complete Guide to the Futures mArket
nearby supplies (i.e., in markets conforming to the “general rule” defined in Chapter 30). Intercrop
spreads (which are a subset of intramarket spreads) can also exhibit wide price differences. In these
cases, the greater dollar volatility implicit in the higher-priced month suggests that the spread be initi-
ated with a larger number of contracts in the lower-priced month.
It should be noted that the concept of equal dollar value is meaningless for interest rate futures.
For example, a $1 million eurodollar contract is certainly not 10 times as large as a $100,000 T -bond
contract. In fact, because of its much longer maturity, and, hence, much greater volatility, the T -bond
contract is a substantially “larger” contract by any reasonable definition.
461
The stock market is but a mirror 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 a good starting point for developing a theo-
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 a trader could accept delivery of gold on an expiring contract and
redeliver it against a subsequent 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 a risk-free profit
by performing a cash-and-carry operation. And if the premium were significantly lower, an arbitra-
geur could lock in a risk-free profit by implementing a short 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 a reasonably well-
defined band for any given combination of short-term interest rates and gold prices.
The same arguments could be duplicated substituting a stock index for gold. In a broad 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
462
A Complete Guide to the Futures mArket
dividends. Thus, the interest rate cost of holding a stock position is offset (partially, or more than
totally) by dividend income. The presence of dividends is easily incorporated into the framework of
calculating a theoretical 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 a long equity
position—equity and stock index futures—would imply an equivalent outcome can be expressed
symbolically as follows:
PP P t id21 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 a premium to nearby contracts. Conversely, if the dividend yield exceeds short-
term interest rates, forward futures will trade at a discount.
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—a consequence 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 a reminder,
to trade a ratio, 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 a contract ratio that is
inversely proportional to the contract value ratio.
For example, if the E-mini Nasdaq 100 futures contract, which has a contract value of 20 times the
index, is trading at 4,300 (a contract value of $86,000), and the Russell 2000 Mini futures contract,
463
SPREAd TRAdING IN SToCK INdEx FuTuRES
which has a contract value of 100 times the index, is trading at 1,150 (a contract 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

eBooks\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads\A Complete Guide to the Futures Market Technical Analysis, Trading Systems, Fundamental Analysis, Options, Spreads.pdf


trading at 4,300 (a contract value of $86,000), and the Russell 2000 Mini futures contract,
463
SPREAd TRAdING IN SToCK INdEx FuTuRES
which has a contract value of 100 times the index, is trading at 1,150 (a contract 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, a spread 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 a volatility 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 a contract
ratio of 1.671 instead of 1.337. If this additional adjustment is made, then a spread 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 a certain group of stocks will perform better or worse than another group
can express this view through stock index spreads. For example, a trader 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. A trader expecting relative outperfor-
mance by small-cap spreads would place the reverse spreads. As another example, a trader 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
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, a condition 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 a factor 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, a three-contract dow position
would have been balanced by a seven-contract Nasdaq position when the contract value ratio was at
its low versus only a three-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 a consequence of the contract value ratio being equal to the price ratio times
a constant—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

465
SPREAd TRAdING IN SToCK INdEx FuTuRES
 FIGURE  32.2 Contract Value Ratio: S&P 500/Nasdaq 100 E-Mini Futures
 FIGURE  32.3 Contract Value Ratio: S&P 500/Russell 2000 Mini Futures

466A CoMPLETE GuIdE To THE FuTuRES MARKET
 FIGURE  32.4 Contract Value Ratio: Nasdaq 100/dow E-Mini Futures
 FIGURE  32.5 Contract Value Ratio: Nasdaq 100/Russell 2000 Mini Futures
467
SPREAd TRAdING IN SToCK INdEx FuTuRES
 FIGURE  32.6 Contract Value Ratio: dow/Russell 2000 Mini Futures
 FIGURE  32.7 S&P 500/dow E-Mini Futures Ratio vs. S&P

468A CoMPLETE GuIdE To THE FuTuRES MARKET
 FIGURE  32.8 S&P 500/Nasdaq 100 E-Mini Futures Ratio vs. S&P
 FIGURE  32.9 S&P 500/Russell 2000 Mini Futures Ratio vs. S&P
469
SPREAd TRAdING IN SToCK INdEx FuTuRES
 FIGURE  32.10 Nasdaq


s
467
SPREAd TRAdING IN SToCK INdEx FuTuRES
 FIGURE  32.6 Contract Value Ratio: dow/Russell 2000 Mini Futures
 FIGURE  32.7 S&P 500/dow E-Mini Futures Ratio vs. S&P

468A CoMPLETE GuIdE To THE FuTuRES MARKET
 FIGURE  32.8 S&P 500/Nasdaq 100 E-Mini Futures Ratio vs. S&P
 FIGURE  32.9 S&P 500/Russell 2000 Mini Futures Ratio vs. S&P
469
SPREAd TRAdING IN SToCK INdEx FuTuRES
 FIGURE  32.10 Nasdaq 100/dow E-Mini Futures Ratio vs. dow
 FIGURE  32.11 Nasdaq 100/Russell 2000 Mini Futures Ratio vs. Russell 2000
470A CoMPLETE GuIdE To THE FuTuRES MARKET
 FIGURE  32.12 dow/Russell 2000 Mini Futures Ratio vs. Russell 2000
 Generally speaking, at least during the 14-year period depicted in these charts, Figures 32.7
through 32.12 refl ect a tendency for larger-cap indexes to lose ground to smaller-cap indexes dur-
ing market uptrends and to outperform (i.e., decline less) during market downtrends. For example,
Figure 32.12 compares the index ratio of the largest cap of the four indexes (dow) to the smallest cap
of the four indexes (Russell 2000) with the Russell 2000 index. on balance, there is a clear inverse
correlation between the index ratio and the market direction. As another example, in Figure 32.7 , in
which both indexes in the spread are large-cap, but in which the smaller-cap of the two (S&P) is in the
numerator of the ratio, the ratio is clearly positively correlated with the market direction. Another
interesting aspect of Figure 32.7 is that there appears to be some tendency for the S&P/dow ratio to
lead major trend reversals in the outright market.
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 a manner which not one man in a million is able to diagnose.
—John Maynard Keynes
 ■ Intercurrency Spreads
Conceptually, intercurrency spreads are identical to outright currency trades. After all, a net long or short
currency futures position is also a spread in that it implies an opposite position in the dollar. For example,
a net 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 a long 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 a long JY/short USD and a long USD short euro
position, in which the opposite USD positions offset each other. (T o be 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, a long 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 a spread might be at least partially appropriate.
Chapter 33
472
A Complete Guide to the Futures mArket
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 a long 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 a long
SF position of $500,000 but a short 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 (a position 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-


alue 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 o
numbe ro f units per
contra ct of currenc= yy2
priceo f
currenc y2
numbe ro f units per
contra ct of currenc y1
() ()
(() ()
priceo f
currenc 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=
473
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 $0.50 in both the currencies will leave the price spread
between the BP and SF unchanged, even though it would drastically alter the relative values of the two
currencies: a decline of the BP vis-à-vis the SF from 1.5 SF to 1.33 SF.
 ■ Intracurrency Spreads
An intracurrency spread—the price difference between two futures contracts for the same currency—
directly reflects the implied forward interest rate differential between dollar-denominated accounts
and accounts denominated in the given currency. For example, the June/December euro spread
indicates the expected relationship between six-month eurodollar and euro rates in June.
1
T o demonstrate the connection between intracurrency spreads and interest rate differentials, we
compare the alternatives of investing in dollar-denominated versus euro-denominated accounts:
S = spot exchange rate ($/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/S euro. (By definition, if S equals dollars
per euro, 1/S = euro per dollar.)
2. Invest 1/S euro 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 A short 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 a long spot/short forward position in the foreign exchange (FX)
swap market and simultaneously selling spot.
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A Complete Guide to the Futures mArket
If the proceeds of the two above alternatives are to be equivalent, then:
11 12+= +r F
S r()
Thus, at this equilibrium level, given values for S, r1, and r2, F would be automatically determined.
For example, if S = $0.80/euro, r 1 = 2 percent per six-month period (4.04 percent annualized),
and r2 = 1 percent per six-month period (2.01 percent annualized), at equilibrium, the six-month
forward rate would be:
F Sr
r= +
+ ==()
()
.( .)
(. ) .1
1
0810 2
10 1 08 07921
2
At forward rate of F = 0.80792, both alternatives will yield $1.02. This result is obvious for the
dollar-denominated account; for the euro-denominated account:
$/ () $. (. )
. $.FS r1 0 80792 10 1
08 0 10 22+= =
Consider what would happen if the forward exchange rate F were greater than the equilibrium
level (i.e., greater than $0.80792/euro in the above example). For instance, using an assumed value
of F = $0.82/euro, the proceeds of Alternative B would be:
$. (. )
. $.08 21 01
08 0 10 3525=
Thus, if F = $0.82/euro, arbitrageurs could borrow dollars at r1 convert the dollars into euro, invest
the euro at r2, and hedge the anticipated six-month forward euro proceeds at $0.82/euro. In doing so,
they would pay $1.02 for the dollar loan, but would earn $1.03525, thereby netting a risk-free profit of
$0.01525 per dollar borrowed. If such a wonderful opportunity existed (and it will soon be clear why
it could not), all arbitrageurs who were awake and could add would rush to implement the above set of
transactions. This activity by arbitrageurs would impact both the spot and forward exchange rates. In the
spot market, the concentration of conversions of dollars into euros would cause the euro to gain against
the dollar, and hence the spot rate S would rise. Similarly, in the forward market, heavy sales of euro
against the dollar would cause the euro to weaken against the dollar and hence the forward rate F would
fall.
3 These market forces would narrow the gap between the forward and spot rates until:
F
S
r
r= +
+
1
1
1
2
3 In the futures market, such sales would occur directly. In the cash FX ma


t
the dollar, and hence the spot rate S would rise. Similarly, in the forward market, heavy sales of euro
against the dollar would cause the euro to weaken against the dollar and hence the forward rate F would
fall.
3 These market forces would narrow the gap between the forward and spot rates until:
F
S
r
r= +
+
1
1
1
2
3 In the futures market, such sales would occur directly. In the cash FX market, downward pressure on the implied
forward rate would manifest itself through the initiation of long spot/short forward swaps (spreads).
475
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. A similar 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 a forward futures contract and a nearby expiring contract must reflect the prevailing interest
rate ratio (between the eurodollar rate and the given eurocurrency rate).
4 Hence, a spread between
two forward futures contracts can be interpreted as reflecting the market’s expectation 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 a premium 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 a discount 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 a trader expected eurodol-
lar rates to gain (move up more or down less) on a foreign eurocurrency rate (relative to the expected
interest rate ratio implied by the intracurrency futures spread), this expectation could be expressed
as a long 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 a long nearby/short
forward intracurrency spread.
As a technical 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/S unchanged). In order for the spread posi-
tion to be unaffected by equal percentage price changes in both contracts, a development 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 S and 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 a literal interpretation, which in the above example would suggest a figure of 0.02/0.01 = 2.
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A Complete Guide to the Futures mArket
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 a total 64,800-point change in both legs of the
spread). As can be seen in this example, a balanced spread will only be possible for extremely large
positions. This fact, however, does not present a problem, since the distortion is sufficiently small so
that a 1:1 contract ratio spread serves as a reasonable approximation.
Intracurrency spreads can also be combined to trade expectations regarding two foreign euro-
currency rates. In this case, the trader would implement a long nearby/short forward spread in the
currency with the expected relative rate gain, and a long 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 a trader
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/sho


une/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 a trader
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.
T o summarize, 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
477
A put might more properly be called a stick. For the whole point of a put—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 a price at which he would very likely rather not take it. So what you are really
doing is sticking it to him.
—Andrew T obias
Getting By on $100,000 a Year (and Other Sad T ales)
 ■ Preliminaries
There are two basic types of options: calls and puts. The purchase of a call option on futures1 provides
the buyer with the right, but not the obligation, to purchase the underlying futures contract at a speci-
fied price, called the strike or exercise price, at any time up to and including the expiration date. 2 A put
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 a put is a bearish trade,
while selling a put is a bullish 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 a specified date prior to the expiration of the futures contract.
478
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
a premium. As a specific example, a trader who buys a $1,000 August gold call at a premium 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 a number of strike prices for each futures
contract, the total number of different options traded in a market will far exceed the number of
futures contracts—often by a factor 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 a call could liquidate his position by entering an order
to sell a call with the same expiration date and strike price.
The buyer of a call seeks to profit from an anticipated price rise by locking in a specific 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.
479
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 a loss. In order for the call buyer to realize a net profit, th


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.
479
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 a loss. In order for the call buyer to realize a net 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 a put seeks to profit from an anticipated price decline by locking in a sales 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 a put held until expiration, the trade would show a net 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 a call 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 a call is exercised, the seller must assume a short position in futures at the strike
price (since by exercising the call, the buyer assumes a long position at that price).
upon exercise,
the exchange’s clearinghouse 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 a call seeks to profit from an anticipated sideways to modestly declining market. In
such a situation, the premium earned by selling a call will provide the most attractive trading oppor-
tunity. However, if the trader expected a large price decline, he would usually be better off going
short futures or buying a put—trades with open-ended profit potential. In a similar fashion, the seller
of a put seeks to profit from an anticipated sideways to modestly rising market.
Some novices have trouble understanding why a trader would not always prefer the buy side of an
option (call or put, depending on his market opinion), since such a trade has unlimited potential and
limited risk. Such confusion reflects the failure to take probability into account. Although the option
seller’s theoretical 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 a net
gain to the option seller.
roughly speaking, the option buyer accepts a large probability of a small loss
in return for a small probability of a large gain, whereas the option seller accepts a small probability
of a large loss in exchange for a large probability of a small 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 T echnically speaking, the gains on a put 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 a long put position as being unlimited.
6 T o be 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 a large, open-ended loss. So, in effect,
option sellers would have a more attractive return profile and a less 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.
480
A Complete Guide to the Futures mArket
 ■ Factors That Determine Option Premiums
An option’s premium consists of two components:
Premiu mi ntri nsic v aluet imev alue=+
The intrinsic value of a call option is the amount by which the current futures price is above the strike
price. The intrinsic value of a put 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, a call option with a strike price of $70 would have an intrinsic value of $4.60. The
intrinsic value serves as a floor price for an option. Why? Because if the premium were less than the intrinsic
value, a trader could buy and exercise the option, and immediately offset the resulting futures position,
thereby realizing a net 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 wh


lls 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 a value greater than the intrinsic value because a position in
the option will be preferred to a position 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’s maximum
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 a better return by selling the option, a transaction 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 a deeply in-the-money option, the fact that the
7 Theoretically, the time value will also be influenced by price expectations, which are a non-quantifiable factor.
481
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 a maximum 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 a longer 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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A Complete Guide to the Futures mArket
table 34.2 Option prices as a Function of V olatility in
e-Mini S&p 500 Futures pricesa
annualized V olatility 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 a strike price of 2000 with 30 days to expiration.
8 James Bowe, Option Strategies T rading Handbook (New Y ork, NY: Coffee, Sugar, and Cocoa exchange, 1983).
assumed to be a function of the square root of time. (This relationship is a consequence 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 a four-month option with the same strike price
(; ;. )93 42 32 15== ÷=
and three times the time value of a one-month option (; ;)93 11 31 3== ÷= .
 3. V olatility. 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 a strong 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


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, a buyer
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
483
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 a carry 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 a variety 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 a discrepancy 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’s assumption 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’s expectation of future volatility. This is a critical point that requires further elaboration.
recall that although volatility is a crucial 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 a
volatility 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 a number 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 a single, 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 a given mathematical model provides a
close approximation of market behavior, a discrepancy 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 a specific 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. A bias toward buying “underpriced” options (relative to the theoretical model fair value)
484
A Complete Guide to the Futures mArket
and selling “overpriced” options would be justified only if empirical evidence supported the conten-
tion that, on balance, the model’s volatility assumptions proved to be better than implied volatility in
predicting actual volatility levels.
If a model’s volatility estimates were demonstrated to be superior to implied volatility estimates,
it would suggest, from a strict probability standpoint, a bullish 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, a bearish 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 a one-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 a given option can be used to
determine the number of options that would be equivalent in risk to a single futures contract for small
changes


ice 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 a given option can be used to
determine the number of options that would be equivalent in risk to a single 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 a range of times to expiration. Where did these values come from? They are
derived from the same mathematical models used to determine a theoretical 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).
485
AN INTrOduCTION TO OPTIONS ON FuTureS
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 a number
of important observations regarding theoretical delta values:
 1. Delta values for out-of-the-money options are low. This relationship is a result of the
fact that there is a high 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 a high probability that a one-point change
in the futures price will mean a one-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 a one-point increase in the price of futures will result in a one-point increase in the
option value at expiration.
 4. Delta values for out-of-the-money options will increase as time to expiration
increases. A longer time to expiration will increase the probability that a price increase in
futures will make a difference 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. A longer time to expiration will increase the probability that a change 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 a call. If the option is a put, read “price decrease” for all refer-
ences to “price increase.”

487
Brokers are fond of pointing out to possible buyers of options that they are a splendid thing to
buy, and pointing out to sellers that they are a splendid 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 a profit. 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, a trader who is bullish can either go long or initiate a bull 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 a variety of bullish option spreads. Frequently, one of these option-related
strategies will offer significantly better profit potential for a given level of risk than an outright futures
position. Thus, the trader who considers both option-based strategies and outright positions should
have a decided advantage over the trader who restricts his trades to only futures.
Option Trading
Strategies
Chapter 35
488
A Complete Guide to the Futures mArket
There is no single best trading approach. The optimal trading strategy in any given situat


iven level of risk than an outright futures
position. Thus, the trader who considers both option-based strategies and outright positions should
have a decided advantage over the trader who restricts his trades to only futures.
Option Trading
Strategies
Chapter 35
488
A Complete Guide to the Futures mArket
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 a
wide 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 a diagram indicating the profit or loss implied by a position (vertical axis)
for a range 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 a single option series, for a single market, on a single 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 ($1,200/oz), thereby providing a nearly precise at-the-money
option—a factor that greatly facilitates the illustration of theoretical differences among out-of-
the-money, in-the-money, and at-the-money options. The specific closing values for the option
premiums on that date were as follows ($/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 a level of complexity that would
place the discussion beyond the scope of this book. However, the key point to keep in mind
489
OPTION TrAdINg STrATegIeS
is that the profit/loss profile for strategies that include a net 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
a price 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 a single option is equivalent to a smaller position size than a
single futures contract (see section entitled “
delta—the Neutral Hedge ratio” in the previous
chapter). Similarly, an out-of-the-money option is equivalent to a smaller 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 $1,200. (See Table 35.1 and Figure 35.1.)
Comment. The simple long position in futures does not require much explanation and is included
primarily for purposes of comparison to other less familiar trading strategies. As every trader knows,
the long futures position is appropriate when one expects a significant price advance. However, as will
tabLe 35.1 profit/Loss Calculations: Long Futures
Futures price at expiration ($/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
490A COMPleTe gUIde TO THe FUTUreS MArKeT
be illustrated later in this section, for any given price scenario, some option-based strategy will often
provide a more attractive trade in terms of reward/risk characteristics.
 Strategy 2: Short Futures
ex


$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
490A COMPleTe gUIde TO THe FUTUreS MArKeT
be illustrated later in this section, for any given price scenario, some option-based strategy will often
provide a more attractive trade in terms of reward/risk characteristics.
 Strategy 2: Short Futures
exAMPle . Sell August gold futures at $1,200. (See Table 35.2 and Figure 35.2 .)
 tabLe 35.2 profit/Loss Calculations: Short Futures
Futures price at expiration ($/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 –$20,000
 FIGURE  35.1 Profi t/loss Profi le: long Futures
Price of August gold futures at option expiration ($/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
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 a signifi 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 a more 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 a premium of $38.80/oz ($3,880), with August gold
futures trading at $1,200/oz. (See Table 35.3 a and Figure 35.3 a.)
Comment. The long call is a bullish strategy in which maximum risk is limited to the premium paid
for the option, while maximum gain is theoretically unlimited. However, the probability of a loss is
greater than the probability of a gain, 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 a profi t. Two spe-
cifi c characteristics 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 $0.50
change in the option price. (At-the-money options near expiration, which will change by a
greater amount, are an exception.) Thus, for small price changes, a net long futures position is
equivalent to approximately two call options in terms of risk.
 FIGURE  35.2 Profi t/loss Profi le: Short Futures
Price of August gold futures at option expiration ($/oz)
1,000 1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
Profit/loss at expiration ($)
20,000
15,000
10,000
5,000
−5,000
−10,000
−15,000
−20,000
0
492A COMPleTe gUIde TO THe FUTUreS MArKeT
 tabLe 35.3a profit/Loss Calculations: Long Call (at-the-Money)
(1) (2) (3) (4) (5)
Futures price at
expiration ($/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
493
OPTION TrAdINg STrATegIeS
Strategy 3b: Long Call (Out-of-the-Money)
exAMPle. Buy August $1,300 gold futures call at a premium 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 a smaller probability that the trade will realize a profit. 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 a profit, the futures price (as of the time of the option expiration) must exceed the strike
price by an amount greater than the premium ($9.10/oz in this example). Note that in the out-of-
the-money call position, price increases that leave futures below the option strike price will still result
in a maximum loss on the option. The long out-of-the-money call might be a particularly appropriate
position for the trader expecting a large price advance, but also concerned about the possibility of a
large price decline.
It should be emphasized that the futures price need not necessarily reach the strike price in order
for the out-of-the-money call to be profitable. If the market rises quickly, the call will increase in
value and hence can be resold at a profit. (However, this characteristic will not necessarily hold true
for slow price advances, since the depressant effect of the passage of time on the option premium
could more than offset the supportive effect of the increased price level of futures.)
For small price changes, the out-of-the-money call will change by less than a factor of one-half for
each dollar change in the futures price. Thus, for small price changes, each long futures position will
be equivalent to several long out-of-the-money calls in terms of risk.
tabLe 35.3b profit/Loss Calculations: Long Call (Out-of-the-Money)
(1) (2) (3) (4) (5)
Futures price at
expiration ($/oz)
premium of august
$1,300 Call at
Initiation ($/oz)
$ amount of
premium paid
Call Value at
expiration
profit/Loss on
position [(4) –


rice. 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 $9,090
494A COMPleTe gUIde TO THe FUTUreS MArKeT
 FIGURE  35.3b Profi t/loss Profi le: long Call (Out-of-the-Money)
Price of August gold futures at option expiration ($/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 a premium of $110.10 /oz ($11,010), with August
gold futures trading at $1,200/oz. (See Table 35.3 c and Figure 35.3 c.)
Comment. In many respects, a long in-the-money call position is very similar to a long 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 a price rise—an amount equal
to the time value portion of the premium paid for the option ($1,010 in the above example).
 2. For moderate price declines, the long futures position will lose slightly less. (Once again, the
diff erence will be equal to the time value portion of the premium paid for the option.)
 3. In the event of a large price decline, the loss on the in-the-money long call position would be lim-
ited to the total option premium paid, while the loss on the long futures position will be unlimited.
 In a sense, the long in-the-money call position can be thought of as a long futures position with a
built-in stop. This characteristic is an especially important consideration for speculators who typically
employ protective stop-loss orders on their positions—a prudent trading approach. A trader using a
protective sell stop on a long position faces the frustrating possibility of the market declining suffi ciently
to activate his stop and subsequently rebounding. The long in-the-money call position off ers the spec-
ulator an alternative method of limiting risk that does not present this danger. Of course, this benefi t
does not come without a cost; as mentioned above, the buyer of an in-the-money call will gain slightly
less than the outright futures trader if the market advances, and will lose slightly more if the market
declines moderately. However, if the trader is anticipating volatile market conditions, he might very
495
OPTION TrAdINg STrATegIeS
well prefer a long in-the-money call position to a long futures position combined with a protective
sell stop order. In any case, the key point is that the trader who routinely compares the strategies
of buying an in-the-money call versus going long futures with a protective sell stop should enjoy an
advantage over those traders who never consider the option-based alternative.
 FIGURE  35.3c Profi t/loss Profi le: long Call (In-the-Money)
Price of August gold futures at option expiration ($/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
496
A Complete Guide to the Futures mArket
Table 35.3d summarizes the profit/loss implications of various long call positions for a range of
price assumptions. Note that as calls move deeper in-the-money, their profit and loss characteristics
increasingly resemble a long 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 a long 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’t all 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’s assessment that there is a very low probability of gold prices moving to this deep in-
the-money strike price, and therefore the market places a low value on the time premium. In other
words, the market places a low value on the loss protection provided by an option with a strike price
so far below the market. Second, the $1,050 call represents a fairly illiquid option position, and the
quoted price does not reflect the bid/ask spread. No doubt, a potential buyer of the call would have
had to pay a higher 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


tion position, and the
quoted price does not reflect the bid/ask spread. No doubt, a potential buyer of the call would have
had to pay a higher 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 $4,550
aThese calls are compared in Figure 35.3d.
497
OPTION TrAdINg STrATegIeS
 Figure 35.3 d compares the three types of long call positions to a long futures position. It should be
noted that in terms of absolute price changes, the long futures position represents the largest position
size, while the out-of-the-money call represents the smallest position size. Figure 35.3 d suggests the
following important observations:
 1. As previously mentioned, the in-the-money call is very similar to an outright long futures
position.
 2. The out-of-the-money call will lose the least in a declining market, but will also gain the least in
a rising market.
 3. The at-the-money call will lose the most in a steady market and will be the middle-of-the-road
performer (relative to the other two types of calls) in advancing and declining markets.
 Again, it should be emphasized that these comparisons are based upon single-unit positions that
may diff er substantially in terms of their implied position size (as suggested by their respective delta
values). A comparison that involved equivalent position size levels for each strategy (i.e., equal delta
values for each position) would yield diff erent observations. This point is discussed in greater detail in
the section entitled “Multiunit Strategies.”
 FIGURE  35.3d Profi t/loss Profi le: long Futures and long Call Comparisons (In-the-Money,
At-the-Money, and Out-of-the-Money)
Chart created using TradeStation. ©TradeStation T echnologies, Inc. All rights reserved.
Price of August gold futures at option expiration ($/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
498A COMPleTe gUIde TO THe FUTUreS MArKeT
 Strategy 4a: Short Call (at-the-Money)
example . Sell August $1,200 gold futures call at a premium of $38.80 /oz ($3,880), with August gold
futures trading at $1,200/oz. (See Table 35.4 a and Figure 35.4 a.)
 tabLe 35.4a profit/Loss Calculations-Short Call (at-the-Money)
(1) (2) (3) (4) (5)
Futures price at
expiration ($/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 –$16,120
 FIGURE  35.4a Profi t/loss Profi le: Short Call (At-the-Money)
Chart created using TradeStation. ©TradeStation T echnologies, Inc. All rights reserved.
Price of August gold futures at option expiration ($/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
499
OPTION TrAdINg STrATegIeS
Comment. The short call is a bearish position with a maximum 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 a call enjoys a greater probability of
realizing a profit than a loss. Note the short at-the-money call position will result in a gain 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 a large price rise as being very low . If, however, the trader
anticipated a large price decline, he would probably be better off buying a put or going short futures.
Strategy 4b: Short Call (Out-of-the-Money)
example. Sell August $1,300 gold futures call at a premium 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 a smaller maximum gain (i.e.,
premium) in exchange for increasing the probability of a gain on the trade. The seller of an out-of-
the-


: Short Call (Out-of-the-Money)
example. Sell August $1,300 gold futures call at a premium 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 a smaller maximum gain (i.e.,
premium) in exchange for increasing the probability of a gain 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 ($9.10/oz in this example). The short
out-of-the-money call represents a less bearish posture than the short at-the-money call position.
Whereas the short at-the-money call position reflects an expectation that prices will either decline
or increase only slightly, the short out-of-the-money call merely reflects an expectation that prices
will not rise sharply.
tabLe 35.4b profit/Loss Calculations: Short Call (Out-of-the-Money)
(1) (2) (3) (4) (5)
Futures price at
expiration ($/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
500A COMPleTe gUIde TO THe FUTUreS MArKeT
 Strategy 4c: Short Call (In-the-Money)
example . Sell August $1,100 gold futures call at a premium of $110.10 /oz ($11,010), with August
gold futures trading at $1,200/oz. (See Table 35.4 c and Figure 35.4 c.)
 FIGURE  35.4b Profi t/loss Profi le: Short Call (Out-of-the-Money)
Chart created using TradeStation. ©TradeStation T echnologies, Inc. All rights reserved.
Price of August gold futures at option expiration ($/oz)
Futures price at time
of position initiation Strike price
Breakeven price
= $1,309.10
Profit/loss at expiration ($)
1,000
2,500
−5,000
−2,500
0
−10,000
−7,500
1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400
 tabLe 35.4c profit/Loss Calculations: Short Call (In-the-Money)
(1) (2) (3) (4) (5)
Futures price at
expiration ($/oz)
premium of august $1,100
Call at Initiation ($/oz)
Dollar amount of
premium received
Value of Call
at expiration
profit/Loss on
position [(3) – (4)]
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 –$18,990
501
OPTION TrAdINg STrATegIeS
Comment. For most of the probable price range, the profi t/loss characteristics of the short in-the-
money call are fairly similar to those of the outright short futures position. There are three basic dif-
ferences between these two positions:
 1. The short in-the-money call will lose modestly less than the short futures position in
an advancing market because the loss will be partially off set by the premium received for
the call.
 2. The short in-the-money call will gain modestly more than the short futures position in a mod-
erately declining market.
 3. In a very sharply declining market, the profi t potential on a short futures position is open-ended,
whereas the maximum gain in the short in-the-money call position is limited to the total pre-
mium received for the call.
 In eff ect, the seller of an in-the-money call chooses to lock in modestly better results for the prob-
able price range in exchange for surrendering the opportunity for windfall profi ts in the event of a
price collapse. generally speaking, a trader should only choose a short in-the-money call over a short
futures position if he believes that the probability of a sharp price decline is extremely small.
 Table 35.4 d summarizes the profi t/loss results for various short call positions for a range of
price assumptions. As can be seen, as calls move more deeply in-the-money, they begin to resemble
 FIGURE  35.4c Profi t/loss Profi le: Short Call (In-the-Money)
Chart created using TradeStation. ©TradeStation T echnologies, Inc. All rights reserved.
Price of August gold futures at option expiration ($/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
502
A Complete Guide to the Futures mArket
a short 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 a
zero 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 a short 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 a rising 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 a strong resemblance between this strategy and an outright
short position in futures.
It should be emphasized that the com