Chapter 7

Constructing a Hedge

If I learned all this so slowly it was because I learned by my mistakes, and some time always elapses between making a mistake and realizing it, and more time between realizing it and exactly determining it.

Edwin Lefèvre, Reminiscences of a Stock Operator

7.1. AN IDEAL HEDGE

In seeking to reduce risk, one approach is to seek to minimize risk concentration through diversification, that is, by capitalizing on a lack of correlation in assets, while another is to make use of correlation, through hedging. An ideal hedge is one for which the change in value as a result of a given change in market conditions is such that it exactly offsets the change in value of the position to be hedged, that is, the changes in price of the hedge are perfectly inversely correlated with the price changes of the unhedged position. There are two steps in determining the characteristics of this ideal hedge, if it exists.

1. Identify the combination of instruments or contracts whose aggregate change in price as a result of changing market conditions is inversely correlated with that of the position. That is, determine what hedge position has the opposite risk profile to the position we wish to hedge.

2. Determine the number of those instruments or contracts required such that the change in value of the hedge exactly equals and offsets the change in value of the position we are seeking to hedge. That is, find out how big our hedge needs to be.

7.2. A SAMPLE HEDGE

Consider ...

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