# Delta Hedging

JOhn wants to hedge a large BIC equity position in his portfolio. John expects BIC equity to make a recovery from the intense market scrutiny but wants to provide his portfolio with a hedge in case BIC has a negative suprise. Is the most effective hedge: Add put options to the portfolio as option delta moves closer to 0 Add put optiont to the portfolio as option delta moves further from 0 Please explain answer.

B? As delta of a put moves from 0 to -1 (it’s getting more out-of-the-money) and the number of option contract needed to hedge decrease, as the denominator is increasing in absolute sense.

I reckon it’s: “Add put options to the portfolio as option delta moves closer to 0”. He wants to hedge his exposure. Assume he has 100 stocks. That means he has 100 deltas. When the delta moves closer to 0 it means he will need more (of the same) put options to be delta neutral (or roll the puts to a higher strike level!). With numbers: 100 Stocks -> 100 Deltas Let’s say he buys two ATM puts (contract size 100). He is completely Delta Neutral (ATM Delta = 50; or -50 for a put). The Delta moves to 0, let’s say -25 instead of the original -50, so he is 100 Delta’s long, only 50 short so to remain Delta neutral he needs more put options.

B ? this is assuming that the option delta referenced in the answer choices points to the put option’s delta, and not a call. if put option’s delta is moving away from 0, then its making money and that’s what will hedge a losing long equity position.

swaptiongamma Wrote: ------------------------------------------------------- > B? > > As delta of a put moves from 0 to -1 (it’s getting > more out-of-the-money) and the number of option > contract needed to hedge decrease, as the > denominator is increasing in absolute sense. You are right it’s B but if it’s moving from 0 to -1 it’s getting more in the money which is not what you’ve put as an ‘in the money’ put option will have a delta very close to -1. So therefore if you are buying more puts as it moves into the money surely you’ll have to constantly re-balance? Can someone please explain this to me.

sorry - that was a typo. I mean moving from 0 to -1 will bring the put more in-the-money.

If the delta is approaching -1, and you are buying more put options, doesn’t this mean you’re now speculating and not hedging?

I think that was implicitly in my reply bpdulog. I don’t agree with the assessment of the others it should be B but I could be misinterpreting the question. The further the Delta of the put options moves from zero the higher the short delta position will become. If you were Delta neutral at start you’d be delta short and have to sell puts to become neutral again, instead of increasing the delta short position.

My interpretation: The father delta is from 0, the closer the put’s strike is to the stock price, hence a better hedge.

Yes, but they are talking about a dynamic hedge. Since they consider buying extra puts. The question is when you should buy extra puts (when delta moves to 0 or away). You are talking about a static hedge. Just buy a put for your equity position, ride out the storm and at expiration your options are either 0 (not needed, spot has risen) or -1; you are hedged for that downturn. The question is probably lacking extra info.

Perhaps it is lacking info. It doesn’t say anything that implies that he wants to add a dynamic hedging strategy. It looks like a conceptual question on how delta behaves in relation to the strike-underlying spread.

I used to remember that ‘most effective hedge’ means that minimal rebalancing of put options portfolio is required.

If delta is provided, wouldn’t that imply he is using a dynamic hedge? If you have 1,000 shares of BIC and want to hedge that exposure, then just buy 10 put contracts and be done with it.

bpdulog Wrote: ------------------------------------------------------- > If delta is provided, wouldn’t that imply he is > using a dynamic hedge? > I don’t see a delta # provided. I see delta mentioned. The question could be, essentially, “Which is a more effective hedge on Stock A, a put with a delta close to zero, or a put will a delta far from zero?” The first would be far out of the money, and the second would be closer to in the money, hence a better hedge.

OK let’s go back to the definition of option delta. It is the change in value of the option with respect to change in the value of the underlying. If the option delta is close to zero - this has to mean that the stock is far above the strike. So the put option is far out of the money. Delta by definition is also the hedge ratio! So delta of 0 means you buy 0 options. As delta moves away from 0 (I am assuming this means the stock price approaches the strike), you will add put options. At the money delta will be close to -1/2 and you will buy one put for every 200 shares of stock. As the stock price drops further if delta becomes -1, you will now have doubled the amount of puts you have put on.