Question from FRM 2006:

“You want to implement a portfolio insurance strategy using index futures designed to protect the value of a portfolio of stocks not paying any dividends. Assuming the value of your stock portfolio decreases, which strategy would you implement to protect your portfolio...”

C. Buy an amount of index futures equivalent to the change in the calldelta X original portfolio value

D. Sell an amount of index futures equivalent to the change in the call delta X original portfolio value

C. Buy an amount of index futures equivalent to the change in the put delta X original portfolio value

D. Sell an amount of index futures equivalent to the change in the put delta X original portfolio value

David, I think portfolio insurance is basically a long protective put, no. Therefore the answer should be C. Is it? I’ve a nagging feeling that the correct answer may be D. I am confused.

--sridhar

Hi sridhar,

It is a *difficult* question, IMO. Source: Hull Chapter 15.12, Portfolio insurance.
If it helps, here is Hull’s example 15.1 input in XLS

First, you can eliminate (a) and (c) without too much effort because buying index futures would not give you a hedge (i.e., provide protection). You need to sell (short) index futures to hedge the portfolio (there is an implicit assumption here that the portfolio’s beta is the same as the index, contributing to the difficulty here, IMO).

So, to the basic idea here, given by Hull: INSTEAD of buying a protective put (sridhar, you are right about that, but Hull’s idea here is that we are conducting the synthetic equivalent of the long put. Again, i think the question is hard) you are shorting index futures.

Then, the idea is, to quote Hull “to create an option synthetically that involves maintaining a position in the underlying (or futures underlying the asset) so that the delta of the position is equal to the delta of the required option”

so, as the portfolio value declines, it must be met with selling futures in proportion to the put delta (i.e., 1-N(d)).

David