162 Part II: Call Option Strategies 
Number of 
round lots = Current delta x Number of short calls - Round lots held long 
to buy 
Note: If a negative number results, stock should be sold, not bought. 
These formulae can be verified by using the numbers from the examples above. For 
example, when the delta of the October 50 was .80 with the stock at 57, it was seen 
that buying 100 shares of stock would reestablish a neutral ratio. 
Number of round lots to buy= .80 x 5 3 = 4- 3 = 1 
Also, if the position was to be rolled up to the October 60 (delta = .40), it was seen 
that 7.5 October 60's would theoretically be sold: 
Number of calls to sell = __l_ = 7.5 .40 
There is a more general approach to this problem, one that can be applied to 
any strategy, no matter how complicated. It involves computing whether the position 
is net short or net long. The net position is reduced to an equivalent number of shares 
of common stock and is commonly called the "equivalent stock position" (ESP). Here 
is a simple formula for the equivalent stock position of any option position: 
ESP = Option quantity x Delta x Shares per option 
Example: Suppose that one is long 10 XYZ July 50 calls, which currently have a delta 
of .45. The option is an option on 100 shares of XYZ. Thus, the ESP can be computed: 
ESP = 10 x .45 x 100 = 450 shares 
This is merely saying that owning 10 of these options is equivalent to owning 450 
shares of the underlying common stock, XYZ. The reader should already understand 
this, in that an option with a delta of .45 would appreciate by .45 points if the com­
mon stock moved up 1 dollar. Thus, 10 options would appreciate by 4.5 points, or 
$450. Obviously, 450 shares of common stock would also appreciate by $450 if they 
moved up by one point. 
Note that there are some options - those that result from a stock split- that are 
for more than 100 shares. The inclusion of the term "shares per option" in the for­
mula accounts for the fact that such options are equivalent to a different amount of 
stock than most options. 
The ESP of an entire option and stock position can be computed, even if sev­
eral different options are included in the position. The advantage of this simple cal-