You are long 250 call contracts with delta 0.42 and short 180 put contracts with delta -0.35, each contract on 100 shares. How many shares do you sell to be delta neutral?

You are long 250 call contracts with delta 0.42 and short 180 put contracts with delta -0.35, each contract on 100 shares. How many shares do you sell to be delta neutral?

Approach: Convert each leg into share deltas using the contract multiplier, taking care that a short position flips the sign of the quoted delta, then net the two.

16800. Each long call contributes 100 * 0.42 = 42 deltas through the contract multiplier, so 250 contracts give 10500. The short put is long delta, because the quoted delta of -0.35 flips sign when the position is short, giving 180 * 100 * 0.35 = 6300. The position delta is 10500 + 6300 = 16800. You sell 16800 shares to reach delta neutral. The sign convention on the short put delta is the whole trap here, since a long call and a short put both gain as the stock rises, so both need stock sold against them. A candidate who subtracts the put deltas answers 4200 and is left carrying 12600 shares of unwanted exposure.

Follow-up: The stock rallies 3% and the book has 500 shares of gamma per dollar. How many shares do you now buy or sell to stay neutral?

Key concepts: delta neutral, position delta, short put delta, contract multiplier.