Suppose a portfolio is delta-neutral and has a gamma of -5600. A call option trades with...
Suppose a portfolio is delta-neutral and has a gamma of -5600. A call option trades with a delta of 0.5 and a gamma of 0.8. You buy this option to gamma-hedge. How many shares of stock do you need to buy (sell) to delta-hedge your portfolio after you added the option?
a. Sell 3500 shares
b. Buy 5000 shares
c. Buy 3500 shares
d. Sell 5000 shares
Homework Answers
Delta of Existing POrtfolio = 0 (Neutral)
Gamma of Existing POrtfolio = - 5600
Delta of Call option = 0.50
Gamma of Call option = 0.80
Since we have 100 shares in one contract
Delta Position of Call Option = 0.50 * 100 = 50
Gamma Position of Call Option = 0.80 * 100 = 80
Call Option we need to buy to gamma hedge the portfolio = 5600 / 80 = 70
Therefore to to delta hedge the new portolio we need to sell = 70 * 50 * 1 = 3500 shares
Option A is correct.
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