Question

1. If own 200 shares of Apple at $300, How can I hedge those shares using a put option? How many puts, and at what strike price should I use to perfectly hedge my position? I Apple goes to $250 what is my overall change dollar wise if the put cost me $10

Answer 1

We own 200 shares of Apple at $300.

We can hedge these shares by buying put options.

Each put option contract is for 100 shares of the underlying and the delta of at the money ($300 strike) put option is -0.5. The delta of each share is 1.

The strike price we need to hedge our shares is at the money, $300. To hedge perfectly we need to make the position delta neutral.

Number of put option contracts to hedge perfectly = (Delta of shares * Number of shares)/(Positive value of delta of put option * 100)

Number of put option contracts to hedge perfectly = (1 * 200)/(0.50 * 100)

Number of put option contracts to hedge perfectly = 4

The delta of 4 put option contracts = 4 * 100 * -0.50 = -200

The delta of 200 shares of apple = 200 * 1 = 200

The delta of our position = 200 - 200 = 0. Perfectly hedged!

If Apple goes to $250, we lose $50 per share. Total loss = 50 * 200 = $10,000

Gain from put option = 50 * 4 * 100 - 10 * 4 * 100 = 16,000

Overall change dollar wise = 16,000 - 10,000 = $6,000