Collapsing a whole book into one dollar-delta number

Question

You hold, all on stock A (price \50): - Long 300 shares. - Long 10 call contracts, delta 0.40 each. - Short 5 put contracts, delta -0.60 each. (Each contract covers 100 shares.) What is your net share-delta and dollar-delta, and how much do you make if A rises \1?

Accepted Answer

Convert everything to share-equivalents, being careful with signs. - Shares: +300. - Long calls: +0.40 	imes 10 	imes 100 = +400. - Short puts: the put delta is -0.60; you are short, so your delta per option is +0.60. Total = +0.60 	imes 5 	imes 100 = +300. Net share-delta: 300 + 400 + 300 = +1{,}000 	ext{ shares.} Dollar-delta (the notional stock exposure) is 1{,}000 	imes \50 = \50{,}000. A \1 rise in A makes you 1{,}000 	imes \1 = +\1{,}000. The point of the exercise: a book of stock plus options on one name reduces, to first order, to a single number, how many shares you are effect…

Collapsing a whole book into one dollar-delta number

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