Explanation

Gamma risk refers to the sensitivity of an option's delta to changes in the underlying price. Let's analyze each portfolio:

Portfolio 1: Long stock without a hedge

• Stock has zero gamma (gamma of stock = 0)
• No options involved
• Gamma risk = 0

Portfolio 2: Long stock hedged with a long put

• Long stock: gamma = 0
• Long put: gamma > 0 (puts have positive gamma)
• Gamma risk > 0

Portfolio 3: Short stock hedged with a long call

• Short stock: gamma = 0
• Long call: gamma > 0 (calls have positive gamma)
• Gamma risk > 0

Comparison:

• Portfolio 1 has zero gamma risk (no options)
• Portfolios 2 and 3 both have positive gamma risk due to the long option positions

Therefore, Portfolio 1 has the lowest gamma risk.

Correct answer: A - Portfolio 1