Shares to short against ten ATM calls

Question

A stock trades at $25$ and you buy $10$ at-the-money calls with strike $25$ . How many shares must you hold to be delta-neutral? Give a negative number for a short position.

Short answer

$-5$ . An at-the-money call has delta of about $0.5$ , so ten calls carry delta $5$ . Shorting five shares offsets it.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Greeks and Numerical Sensitivities
Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
Option Trading Strategies: Spreads, Combinations, and Payoff Engineering

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