Answer: There is a short position in an S&P 500 futures contract that will make his portfolio insensitive to both small and large moves in the S&P 500.

## Explanation Let's analyze each statement: **A. He can make his portfolio delta neutral by shorting index futures contracts.** - **Correct**: Since he has written a put option (short put position), he has positive delta exposure. Shorting index futures (which have negative delta) can offset this delta exposure and make the portfolio delta neutral. **B. There is a short position in an S&P 500 futures contract that will make his portfolio insensitive to both small and large moves in the S&P 500.** - **Not Correct**: While short futures can make the portfolio delta neutral (insensitive to small price moves), they cannot make the portfolio gamma neutral. Gamma measures the rate of change of delta, and futures have zero gamma. Therefore, the portfolio would still be sensitive to large price moves due to gamma risk. **C. A long position in a traded option on the S&P 500 will help hedge the volatility risk of the option he has written.** - **Correct**: Long options have positive vega exposure, which can offset the negative vega exposure from writing a put option. This helps hedge volatility risk. **D. To make his hedged portfolio gamma neutral, he needs to take positions in options as well as futures.** - **Correct**: Futures have zero gamma, so they cannot hedge gamma risk. Only options have non-zero gamma, so positions in options are necessary to achieve gamma neutrality. The incorrect statement is **B** because short futures alone cannot make the portfolio insensitive to both small and large price moves - they only address delta risk, not gamma risk.

Author: LeetQuiz .