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 comparisons in Figure 35.4d are based upon single-unit positions. 
However, as previously explained, these alternative strategies do not represent equivalent position 
sizes. Comparisons based on positions weighted equally in terms of some risk measure (e.g., equal 
delta values) would yield different empirical conclusions.
tabLe 35.4d profit/Loss Matrix for Short Calls with Different Strike prices
Dollar amount of premium received
$1,050 $1,100 $1,150 $1,200 $1,250 $1,300 $1,350
Call Call Call Call Call Call Call
$15,520 $11,010 $7,010 $3,880 $1,920 $910 $450
position profit/Loss at expiration
Futures price at 
expiration ($/oz)
Short Futures 
at $1,200
In-the-Money 
at-the-
Money Out-of-the Money
$1,050 Call $1,100 Call a $1,150 Call $1,200 Call a $1,250 Call $1,300 Call a $500 Call
1,000 $20,000 $15,520 $11,010 $7,010 $3,880 $1,920 $910 $450
1,050 $15,000 $15,520 $11,010 $7,010 $3,880 $1,920 $910 $450
1,100 $10,000 $10,520 $11,010 $7,010 $3,880 $1,920 $910 $450
1,150 $5,000 $5,520 $6,010 $7,010 $3,880 $1,920 $910 $450
1,200 $0 $520 $1,010 $2,010 $3,880 $1,920 $910 $450
1,250 –$5,000 –$4,480 –$3,990 –$2,990 –$1,120 $1,920 $910 $450
1,300 –$10,000 –$9,480 –$8,990 –$7,990 –$6,120 –$3,080 $910 $450
1,350 –$15,000 –$14,480 –$13,990 –$12,990 –$11,120 –$8,080 –$4,090 $450
1,400 –$20,000 –$19,480 –$18,990 –$17,990 –$16,120 –$13,080 –$9,090 –$4,550
aThese calls are compared in Figure 35.4d.