630 Part V: Index Options and Futures 
be interested in neutrality. The key to determining one's neutrality, of course, is tc 
use the delta of the option. In the case of the PERCS stock, one would have to usE 
the delta of the imbedded call. 
Example: An investor is long 1,000 shares ofXYZ PERCS maturing in two years. He 
thinks XYZ is stuck in a trading range and does not expect much volatility in the near 
future. Thus, a ratio write appeals to him. How many calls should he sell in order to 
create a neutral position against his 1,000 shares? 
First, he needs to compute the delta of the imbedded option in the PER CS, and 
therefore the delta of the PERCS itself. The delta of a PERCS is not 1.00, as is the 
delta of common stock. 
Assume the XYZ PERCS matures in two years. It is redeemable at 39 at that 
time. XYZ common is currently trading at 33. The delta of a two-year call with strik­
ing price 39 and common stock at 33 can be calculated (the dividends, short-term 
interest rate, and volatility all play a part). Suppose that the delta of such an option is 
0.30. Then the delta of the PER CS can be computed: 
PERCS delta= 1.00- Delta of imbedded call 
= 1.00 - 0.30 = 0.70 in this example 
Assume the following data is known: 
Security 
XYZ Common 
XYZ PERCS 
XYZ October 40 call 
Price 
33 
34 
2 
Delta 
1.00 
0.70(!) 
0.35 
Being long 1,000 PER CS shares is the equivalent of being long 700 shares of 
common (ESP= 1,000 x 0.70 = 700). In order to properly hedge that ESP with the 
October 40 call, one would need to sell 20 October 40 calls. 
Quantity to sell = ESP of PER CS/ESP of October 40 call 
= 700/(100 shares per option x 0.35) 
= 700/35 = 20 
Thus, the position - long 1,000 PER CS, short 20 October 40 calls - is a neutral one 
and it is a ratio write. 
One may not want to have such a steep ratio, since the result of this example is 
the equivalent of being long 1,000 common and short 30 calls in total (10 are imbed­
ded in the long PERCS). Consequently, he could look at other options - perhaps 
writing in-the-money October calls - that have higher deltas and won't require so 
many to be sold in order to produce a neutral position.