Chapter 30: Stock Index Hedging Strategies 541 
or adjusted capitalization, in order to compensate for the higher volatility of the port­
folio. 
A similar process can be used for far larger portfolios. The estimate of volatili­
ty is, of course, crucial in these calculations, but as long as one is consistent in the 
source from which he is extracting his volatilities, he should have a reasonable hedge. 
There is no way to judge the future performance of a portfolio of stocks versus the 
ZYX Index. Thus, one has to expect a rather large tracking error. In this type of 
hedge, one hopes to keep the tracking error down to a few percent, which could be 
several points in the futures contracts over a long enough period of time. Of course, 
the tracking error can work in one's favor also. The main point to recognize here is 
that the vast majority of the risk of owning the portfolios has been eliminated by sell­
ing the futures contracts. The upside profit potential of the portfolios has been elim­
inated as well, but the premise was that the investor was bearish on the market. 
Note that if the futures are overpriced when one enacts his bearishly-oriented 
portfolio hedge, he will gain an additional advantage. This will act to offset some neg­
ative tracking error, should such tracking error occur. However, there is no guaran­
tee that overpriced futures will be available at the time that the investor or portfolio 
manager decides to tum bearish. It is better to sell the futures and establish the 
hedge at the time one turns bearish, rather than to wait and hope that they will 
acquire a large premium before one sells them. 
HEDGING PORTFOLIOS WITH INDEX OPTIONS 
As mentioned earlier, one could substitute options for futures wherever appropriate. 
If he were going to sell futures, he could sell calls and buy puts instead. In this sec­
tion, we are also going to take a more sophisticated look at using index options against 
stock portfolios. 
First, let us examine how the investor from the previous example might use 
index options to hedge his portfolio. 
Example: Suppose that an investor owns the same portfolio as in the previous exam­
ple: 3,000 COCO, 5,000 UTIL, and 2,000 OIL. He decides to hedge with index 
UVX, which has options worth $100 per point. Assume that the volatility of the UVX 
is 15%. This investor would then compute his total adjusted capitalization in the same 
manner as in the previous example, again arriving at a figure of $720,000. 
Suppose that the UVX Index is at 175.60. This investor would want to hedge his 
$720,000 of adjusted capitalization with 4,100 "shares" of UVX ($720,000 + 175.60). 
Since a 1-point move in UVX options is worth $100, this means that one would sell 
41 UVX calls and buy 41 UVX puts. He would probably use the 175 strike or possi-