Chapter 30: Stock Index Hedging Strategies 545 
In this case, the number of puts is determined by using the same formula as in 
the above example and then also dividing by the absolute value of the delta: 
Puts to buy = $720,000 / (100 X 180) / 0.60 
= 67 
Cost of protection: 67 x $450 = $30,150 
In this case, the portfolio manager is spending much more for the puts, but for 
his additional expense, he acquires immediate protection for his portfolio. 
Furthermore, there is some intrinsic value to the puts he bought (2 points, or $13,400 
on 67 of them). If the UVX Index drops at all, these puts will immediately begin to 
hedge his entire portfolio against loss. Of course, if the market rises, he loses his 
much more expensive insurance cost. 
When one uses options instead of futures to hedge his position, he must make 
adjustments when the deltas of the options change. This was not the case when futures 
were used; perhaps with futures, one might recalculate the adjusted capitalization of 
the portfolio occasionally, but that would not be expected to affect the quantity of 
futures to any great degree. With put options, however, the changing delta can make 
the position delta short when the market declines, or can make it delta long if the mar­
ket rises. This situation is akin to being long a straddle the position becomes delta 
short as the market declines and becomes delta long as the market rises. 
Basically, the adjustments would be same as those that a long straddle holder 
would make. If the market rallied, the position would be delta long because the delta 
of the puts would have shrunk and they would not be providing the portfolio with as 
much adjusted dollar protection as it needs. The investor might roll the puts up to a 
higher strike, a move that essentially locks in some of his stock profits. Alternatively, 
he could buy more puts at the current (low) strike to increase his protection. 
Conversely, if the market had declined immediately after the position was 
established, the investor will find himself delta short. The delta of the long puts will 
have increased and there will actually be too much protection in place. His adjust­
ment alternatives are still the same as those of a long straddle holder - he might sell 
some of the puts and thereby take a profit on them while still providing the required 
protection for the stock portfolio. Also, he might roll the puts down to a lower strike, 
although that is a less desirable alternative. 
HEDGING WITH INDEX CALLS 
Another strategy to protect a stock portfolio is to establish a ratio write using short 
calls against the long stock. This is the opposite of using puts for protection, in that 
it is more equivalent to being short a straddle.