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Answer: Sell the 1-month option and buy the 4-month option.
## Explanation **C is correct.** Although gamma is similar to vega in that it is greatest for an option that is at-the-money and approaches zero as the option moves deep-in-the-money or deep-out-of-the-money, one important difference is that while vega increases as the time to maturity increases, gamma decreases. Since the 1-month option has a lower vega and a higher gamma than the 4-month option, a portfolio with a short position in the 1-month and a long position in the 4-month will have positive vega and negative gamma. Adding this to the original portfolio would reduce the gamma and increase the vega of the original portfolio. ### Key Points: - **Gamma**: Higher for shorter-term options (1-month > 4-month) - **Vega**: Higher for longer-term options (4-month > 1-month) - **Current Portfolio**: Positive gamma, Negative vega - **Hedging Strategy**: Need to reduce gamma (add negative gamma) and increase vega (add positive vega) - **Transaction**: Sell 1-month (high gamma, low vega) and Buy 4-month (low gamma, high vega) This combination effectively reduces the overall gamma while increasing the overall vega of the portfolio.
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An options trader wants to hedge the gamma and vega risks of a portfolio of several options on a single non-dividend paying stock. The portfolio currently has a positive gamma and a negative vega. There are two at-the-money call options available on this stock, one with a 1-month expiration and the other with a 4-month expiration. Which combination of transactions in these two options would reduce the gamma and increase the vega of the current portfolio?
A
Buy both the 1-month and the 4-month options.
B
Buy the 1-month option and sell the 4-month option.
C
Sell the 1-month option and buy the 4-month option.
D
Sell both the 1-month and the 4-month options.
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