Chapter 28: Mathematical Applications 483 
more than fractionally, he may have to add more calls or buy some in, to maintain a 
neutral hedge ratio. This would expose him to some risk, but the risk is substantially 
smaller than if he had not hedged at all. Of course, there would also be certain cases 
in which he would profit by the stock price change. For example, implied volatility 
could decrease, making the calls cheaper. 
A similar hedge can be established by the block trader who sells stock to accom­
modate a customer buy order. He could buy calls in accordance with the hedge ratio, 
to set up a neutral position. 
This process off acilitation is quite widely practiced, especially by brokerage 
houses that are trying to attract the business of the large institutional customer. Since 
the introduction of listed call options and their applications for facilitating orders, 
many quotes for large blocks of stock have improved considerably. The block trader 
(who works for the brokerage house) is willing to make a higher bid or a lower offer 
if he can use options to hedge his position. This facilitation with options results in a 
better market (higher bid or lower off er) from the point of view of the institutional 
customer. Without the availability of such listed options, the block trader would prob­
ably make a bid or an offer that was substantially away from the prevailing market 
price in order to work out of his stock-only position with a lessened degree of risk 
This would obviously present a poorer market for the institutional customer. 
THE NEUTRAL SPREAD 
The hedge ratios of two or more options may be used to determine a neutral spread. 
This strategy is especially useful to market-makers on the options exchanges who may 
want to reduce the risk of options bought or sold in the process of providing a pub­
lic market. If the hedge ratios of two options are known, the neutral ratio is deter­
mined by dividing the two hedge ratios. 
Example: An XYZ January 35 has a hedge ratio of .25, and an XYZ January 30 has a 
hedge ratio of .50, so a neutral ratio would be 2:1 (.50 divided by .25). That is, one 
would sell 2 January 35's against one long January 30, or, conversely, would buy 2 
January 35's against one short January 30. Thus, a market-maker who has just bought 
50 January 30's in an effort to provide a market for a public seller of that call could 
hedge his position by selling 100 January 35's. This should keep his risk small, for 
small stock price changes, until he can unwind the position. The ratio for the neutral 
spread is not as sensitive to the volatility estimate of the underlying stock as is the 
ratio concerning stock and options. This is because the same volatility estimate is 
applied to both options, and the resultant ratio for the spread would not tend to 
change greatly.