546 Part V: Index Options and Futures 
Example: In the last example, the March 180 put had a delta of -0.60. The March 
180 call should then have a delta of 0.40. If the portfolio manager wanted to hedge 
his portfolio by ratio writing calls against it, he could use the same formula as in the 
previous example: 
Calls to sell = $720,000 I (100 x 180) I 0.40 = 100 
He would sell 100 calls to hedge his portfolio. 
Adjustments would be made in much the same manner as those that a straddle 
seller would make. If the market rises, the delta of the calls will increase and the posi­
tion will be delta short. One would probably buy calls in that case. Follow-up action 
for an actual short straddle might dictate buying in some of the underlying security 
rather than buying the calls, but that is not a realistic alternative in this case, since the 
sample portfolio is probably stable. 
If, on the other hand, the market declined after the short calls were sold against 
the portfolio, the position would become delta long as the delta of the calls shrinks. 
The normal action in that case would be to roll the calls down and reestablish the 
proper amount of protection for the portfolio. 
Overall, hedging the portfolio with short index calls does not present as attrac­
tive a position as hedging with long index puts. This is due mostly to the nature of 
what the portfolio manager is trying to accomplish, as opposed to the relative merits 
of long and short straddles. As was pointed out in previous chapters, straddle selling, 
while risky, is an excellent strategy on a statistical basis. However, in this section we 
are not dealing with a strategist who is going to go out and buy stocks and then write 
index calls against them. Rather, we have an existing portfolio and the portfolio man­
ager is becoming bearish on the market. Thus, the stock portfolio is a fixed entity and 
the index options or futures are being built around it for protection. 
Long puts serve the purpose of protection far better than short calls, for the fol­
lowing reasons. First, the types of adjustments that need to be made by a straddle 
seller often involve buying stock or at least buying relatively deep in-the-money calls. 
A portfolio manager or investor holding a portfolio stock may not need or want to get 
involved in a multi-optioned position. Second, with calls there is large risk to the 
upside in case of a large market rally. Someone holding a portfolio of stocks might be 
willing to forego upside profits ( as in the sale of futures), but generally would be quite 
upset to sustain large losses on the upside. Using puts, of course, leaves room for 
upside profit potential. Third, there is risk of early assignment with short index calls, 
although that is of minor significance in this case since the portfolio of stocks would 
have been long in any case. Other calls could be written immediately on the day after 
the assignment. The only real drawback to using the puts is that premium dollars are