Explanation

Gamma-negative positions are the most risky because:

• Gamma measures the rate of change of delta with respect to changes in the underlying asset price
• Gamma-negative means the position becomes more sensitive to price movements as the market moves (convexity risk)
• Delta-neutral means the position is initially hedged against small price movements
• However, when gamma is negative, the delta hedge becomes ineffective as prices move significantly
• This creates a situation where the position can experience large losses during volatile market conditions
• Gamma-positive positions are generally safer as they benefit from volatility

Among the options:

• A (Gamma-negative, delta-neutral): Most risky - hedge breaks down with price movements
• B (Gamma-positive, delta-positive): Less risky - benefits from volatility
• C (Gamma-negative, delta-positive): Risky but directional bias
• D (Gamma-positive, delta-neutral): Least risky - benefits from volatility while hedged

The gamma-negative, delta-neutral position is most vulnerable to large losses during market turbulence.