Hedging - stock index futures

Q: A trader is hedging a £10m portfolio worth of shares using stock index options. The index is currently trading at 5100 pts and a put option with a strike of 5000 is available. Given £5 per half index point - how many contracts needed?

7city say the answer is divide the portfolio amount by the index level (5100) * £10

BPP have a similar question and say that the strike 5000 should be used instead becuase its heding using options - and that the level of the index is used only in a siutation of delta hedging???

CONFUSED - please help - its an FSA Derivatives exam question.

You should figure this one out yourself...

Simple questions you need to ask are:
a) How many index contract equivalents is your £10MM portfolio worth?
b) What is the delta of your 5000 strike put (very roughly)?

Once you have done that, the answer should become clear. You can verify if your solution is correct by doing a simple sense check that consists of revaluing your full portfolio after a hypothetical market move.

a) 10m / 5100 *10 = 196
b) Delta is ATM so ~ 0.5

...not too sure what after that?

Well, your portfolio is 196 contracts long. How many put options do you need to buy to entirely offset that, given that each put options is, roughly, worth -1/2 of a contract?

392

??

Yeehaw! You should check this to see that everything all adds up and that your new portfolio is, in fact, hedged. Finally, I assume this question doesn't require you to consider the second-order effects of owning options (otherwise, the answer might be that you want less than the number of options you have given)

i agree with ur method - but in terms of the exam - say the delta was not given - 7city says the answer should be just divide the portfolio value by the current index value * 10 and totally ignoring the strike value of the put.

is that right?

Well, you have the methodology to check who's right who's wrong, don't you? Just try to see what happens to the portfolio in each of the two cases and you will have your answer.

surely strike merely dictates WHERE the hedge starts to kick in. If you have a £10m portfolio, you need to have £10m worth of options protection in order to be fully hedged if the world ends. Or am I having a 'senior moment'.

If you're hedging options with the underlying then I agree, the delta of the options position comes into play, but hedging a portfolio of stocks with downside puts as protection against a big move I would have thought means you need the equivalent notional.

Let me know if I'm missing something

GJ