Show how options can be used to reach a chosen level of equity risk exposure
The idea
Delta converts options into equivalent shares: options needed = (target delta − current delta) ÷ option delta. A holder of 10,000 shares seeking zero delta with calls of delta 0.50 writes 20,000 calls. Protective puts, covered calls and collars trim exposure without selling shares, perhaps avoiding tax or keeping votes. Bought calls add upside with limited loss. Gamma matters because delta drifts as the price moves. A position short options is short gamma, so the hedge weakens just when prices move sharply and needs costly rebalancing. To neutralise gamma, add options to set gamma to zero, then use shares to reset delta. The trap is treating a delta hedge as permanent rather than valid for small moves only.
Formulas
Options needed to reach a target delta
options needed = (target delta − current delta) ÷ option delta
- target delta
- the position delta wanted
- current delta
- the position delta now, each share counting 1
- option delta
- the delta of one option, per share of the underlying
Delta moves with the price and with time, so the hedge drifts and has to be rebalanced, faster the larger the gamma. A negative answer means selling options, or buying ones of the opposite delta.
In the app: 1 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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