Delta Neutral - Quickie

CFA Level II Portfolio Management
#1

Hi guys,

  1. Say I’m long a stock and long a put, as the stock price increases, delta for a put goes from -1 closer to 0… Would I then need to buy more puts to remain delta neutral??

  2. And if I’m long stock and long bond as the stock price decreases would I then need to sell puts to be neutral?

Or should it be the other way around for these?? Sorry I’m a little confused by this and would love any help you can offer… Cheers

#2
  1. Yes. You can deduce that using just algebra

Number of puts(calls) = number of shares / Δ of put(call)

What happens to the left hand side when you change Δ within the boundaries of 0 and1? (ignore negative signs)

#3
  1. I can’t think of a strategy where you are long a stock and a bond. These are two separate securities and one option can’t hedge them both…
#4

For the first one, I guess you wouldn’t like to delta hedge as the stock price increases. You’d love to enjoy the benefits of the stock increase and of course not exercise the put. But yes, incrementally going long puts delta neutralizes. And if I’m not wrong, going short calls also helps neutralize delta (since long stock and long put is a synthetic call)

#5

Second one - long stock and long bond itself looks like “neutral neutral” in your words (whatever it is).

#6

Note that for #1 you’re assuming that the put is in the money.

If it’s far out of the money, its delta will still increase (toward zero), but not much; you might be able to keep the number of puts constant and still be very close to delta neutral.

#7

Thanks Krokodlizm and Magician… Great feedback, really appreciate it.

I have been ignoring the negative sign when looking at the change in put option delta to determine the number of contracts required to hedge… Does anyone out there know if this is correct? Cheers

#8

It’s not a problem as long as you remember that you’re buying puts.

#9

Fantastic, cheers again

#10

My pleasure.