I am currently working on assignment from my derivatives class about the portfolio insurance and 1987 market crash. I was asked to perform delta-hedging during 1987 of short puts on S&P 500 index and calculate daily gain/loss on total portfolio (put and hedge). Thus, I used short index futures and risk-free rate. On 19th of October I see a huge loss on put portfolio, which couldn't be offset by gain on short futures. However, I was also asked to do the delta-gamma hedging using 1 month ATM call options on S&P 500. Thus, I gamma neutralize my put portfolio using atm call and then make my portfolio delta-neutral using short futures again. gamma-neutralizing is performed once a month and delta-hedging every day. I again calculate daily/gain loss on my total portfolio. It is even worse (not by a lot though), due to loss on long call portfolio on the crash day! Is it possible that delta-gamma hedge performs worse than delta-hedge???? I would appreciate any advice or comment...
Given the requirements stipulated by the problem, of course it's possible, even not taking into account additional transaction costs. I would be very curious as to why gamma hedging needs to be done with calls, rather than straddles. Good luck with CPPI...
I will tempt an answer although there are much smarter people here... Maybe the problem you have is with the velocity of gamma. By using ATM calls, the gamma on these guys is at its max and it will decrease and move much slower as the market tanks. On the puts, as they get closer to being ATM -when the market tanks, their gamma will get higher and doing it faster and faster. As far as the oct 19 loss on the puts that cannot be matched by the gains on the futures, they both are based on the index, yes, but they have their own logic. They will "price" time value very differently IMO and it is not surprising...
Sounds like a great exercise, should be very instructive, kudos to your prof. However, the information you've given is very spotty. Rather than waste time guessing and going back and forth, why don't you give some details - the exact positions you're comparing (with puts alone and with puts and ATM calls). Include number of options held at each strike, where the underlying is, and what implied volatility you are using. You'll get a much better answer that way.