What is the relationship between delta and position sizing for a long call option in a hedging strategy?

• A. Delta should be ignored when sizing hedges.
• B. Delta is the sensitivity of the option price to changes in time to maturity; not correct.
• C. Delta represents the approximate number of shares to trade to hedge one option; you adjust as delta changes.
• D. Delta is constant across all underlying price levels.

Answer: (C)

Delta is the sensitivity of the option price to moves in the underlying asset. For a long call, delta is positive, meaning the option’s value rises when the stock goes up. In hedging, you translate that exposure into a position in the underlying to offset the option’s delta. The rule of thumb is to hedge by trading delta shares per option contract. Since one option contract typically controls 100 shares, you would short approximately delta × 100 shares for each call option you hold to achieve a delta-neutral hedge. Because delta changes as the stock moves (and as time to expiration changes, through gamma), you adjust the hedge over time by re-estimating delta and trading the underlying accordingly. Delta tends to be near 1 for deep in-the-money calls, near 0 for far out-of-the-money calls, and around 0.5 for at-the-money options, which explains how position sizing evolves with moneyness and time.