Netting a whole option book down to one hedge

Question

You hold several option positions on stock $X$ (contracts cover $100$ shares):

Long $20$ calls, delta $+0.55$
Short $30$ calls, delta $+0.30$
Long $10$ puts, delta $-0.45$
Short $15$ puts, delta $-0.70$

What is your net share-delta, and how many shares do you trade to be neutral? Why net rather than hedge each leg?

Accepted Answer

Convert each leg to share-deltas (	ext{delta}	imes	ext{contracts}	imes 100, with the position sign), then add. - Long 20 calls: +0.55 	imes 20 	imes 100 = +1{,}100 - Short 30 calls: -0.30 	imes 30 	imes 100 = -900 - Long 10 puts: -0.45 	imes 10 	imes 100 = -450 - Short 15 puts: short a -0.70-delta put gives +0.70 each: +0.70 	imes 15 	imes 100 = +1{,}050 Net share-delta: 1{,}100 - 900 - 450 + 1{,}050 = +800 	ext{ shares.} You are net long 800 shares of exposure, so sell 800 shares to be delta-neutral. Why net first. Delta is additive across a single underlying, so the whole book …

Netting a whole option book down to one hedge

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