YOUR KILLER EQUITIES INTERVIEW QUESTIONS: In equity derivatives, can your gamma and theta both be positive? If so, can this be achieved in a single option?

Here's the latest question sent in by site visitors who have attended equities interviews at investment banks. This question has allegedly been asked in equity derivatives trading interviews at HSBC. The answer has been suggested by the person who submitted the question (and is not being advocated by us). If you disagree with the answer, or have any superior alternative responses, please express your opinion in the comments box below.

QUESTION. In equity derivatives, can your gamma and theta both be positive? If so, can this be achieved in a single option? Or can you only do this using a strategy, and what would that strategy be?

THE SUGGESTED ANSWER

The simple answer is yes. For a deep in the money put that is not so deep in the money that it does not have any residual gamma, the option can demonstrate both positive gamma and theta.

You can also achieve this in a strategy by buying cheap (in volatility terms) options and selling expensive ones. For instance, you could use a simple bullish risk reversal strategy (sell downside put, buy upside call). Remember that volatility skew in equities is negative and can potentially yield positive gamma and positive theta.