# call and put delta

Assume call delta is 0.6736 and put delta -0.3264. Compute the number of shares of stock necessary to create a delta neutral portfolio consisting of 100 long put options in Exhibit 2 and the stock. A) 67.36. B) -32.64. C) 32.64. Your answer: B was incorrect. The correct answer was C) 32.64. This is simply -100 times the put option delta. Since each share has a delta of 1, we only need 32.64 shares (long) to create a delta neutral portfolio. (Study Session 17, LOS 62.e) -------------------------------------------------------------------------------- Assume call delta is 0.6736 and put delta -0.3264. Compute the number of shares of stock necessary to create a delta neutral portfolio consisting of 100 long call options in Exhibit 2 and the stock. A) -32.64. B) 67.36. C) -67.36. Your answer: B was incorrect. The correct answer was C) -67.36. This is simply -100 times the call option delta. Since each share has a delta of 1, we only need 67.36 (short) shares to create a delta neutral portfolio. (Study Session 17, LOS 62.e) why is 100 a negative in both questions? if you think about it logically it makes sense that for the put question its a positive # of shares because youre long and for the call question its a negative number of shares because youre short, but i am trying to see why 100 is negative in both. thanks.

Because if you are long a CALL, then you have to SHORT those n-number of stocks. If you are long a PUT, then you have to long those stocks. So a negative sign will take care of this relationship, as the call delta is positive and hence you get a final negative answer (meaning SHORT stocks) and put delta is negative, so you have -(-n) = n (a positive number) (meaning LONG stocks) Sorry it that got you more confused.

Is this the full question? I may be wrong but this is what I think: call = N(d) * no. of options = 0.6736 * - 100 = -67.36 (we are long here so for hedge we need to buy put) put = N(d) - 1 * no. of options = -0.3264 * -100 (put) =32.64 (for hedge, we need to go long as we already hold short position)

cfaboston28 Wrote: ------------------------------------------------------- > Is this the full question? > > I may be wrong but this is what I think: > > call = N(d) * no. of options = 0.6736 * - 100 = > -67.36 (we are long here so for hedge we need to > buy put) > > put = N(d) - 1 * no. of options = -0.3264 * -100 > (put) =32.64 (for hedge, we need to go long as we > already hold short position) im not sure i agree. if you have a certain number of shares of stock (i.e. you are long), you can achieve a delta neutral hedge by either short calls or buying puts. the # of shares needed will be different obviously, but you will get a delta neautral hedge in both instances.

^ Yeps you are correct

swaptiongamma Wrote: ------------------------------------------------------- > Because if you are long a CALL, then you have to > SHORT those n-number of stocks. If you are long a > PUT, then you have to long those stocks. > > So a negative sign will take care of this > relationship, as the call delta is positive and > hence you get a final negative answer (meaning > SHORT stocks) and put delta is negative, so you > have -(-n) = n (a positive number) (meaning LONG > stocks) > > Sorry it that got you more confused. in both questions, the person is long the stock. so he would either long puts or short calls to achieve the hedge.

^ yes - He is long the stock in both - so he will have to short the calls or long the put to have a delta hedge.

We need an expert here. Where is cpk?

look at the graph for a long put and a long call. Long Call: _/ Delta moves from 0 -> 1 If you are long call - you need to short stock. and since delta of the call is positive - you need to do a -100 * delta call. Long Put: _ Delta moves from -1 to 0 If you are long a put - you need to be long stock. delta of put is -ve so you need to do -100 * delta put.

ok im extremely confused now. this is question 88529 (5 and 6 of item set). as you can seee from the first question above, long puts have a positive sign in front of them (the 32.64). but question 88528 is very similar, and it asks you how many options you need to buy/sell, the result comes out as a negative number, and it says that means you buy put options.

Options required = Shares/delta Remember, the number of options required to hedge your stock will almost ALWAYS be greater than the number of shares since options are never a perfect hedge (unless you are deep in or out of the money and delta approaches 1) If you are long the stock, You buy puts to protect a decline in stock price (protective put strategy) shorting calls won’t work as all you’ll get is a premium If you are short the stock You buy calls to protect from an increase in stock price shorting puts won’t work, as all you’ll get is a premium

ali man, great explanation–i agree. the issue i am having is what is the sign of the # of shares needed to hedge. i feel like there are inconsistencies in schweser, if you look at the 2 questions i have posted above your post.

Just remember the negative sign in terms of how the deltas are quoted (I don’t think even in software they quote put deltas in negative numbers). But in CFA case, it’s always negative for a put. What’s important is to just know it’s negative for shorting stock and positive for buying stock. In the first case, we bought puts, so we hedge with going long the stock (positive) In the second question, we bought calls, so we hedge with shorting the stock (negative)

How do you break down the term long call? Do you guys view this as 2 different things… like the first part of the term (long) is in reference to the stock… and the second part of the term (call) is to the option?.. So regardless if this says long call or long put, you are longing the stock? And regardless of it saying long put or short put, you will be buying a put option? I always have trouble reading these…

^ no. a long call means you’re long the call. a call gives you the right to buy stock… so if you choose to exercise the call, you go long the stock. a long put means you’re long the put option. a put option gives you the right to sell stock. so you would be short the stock if you exercised (and you weren’t hedged by stock already in which case you’d be flat)

bannisja, thats a good breakdown and i have heard it that way before… Thanks for the clarification…

TheAliMan Wrote: ------------------------------------------------------- > Just remember the negative sign in terms of how > the deltas are quoted (I don’t think even in > software they quote put deltas in negative > numbers). But in CFA case, it’s always negative > for a put. > > What’s important is to just know it’s negative for > shorting stock and positive for buying stock. > > In the first case, we bought puts, so we hedge > with going long the stock (positive) > > In the second question, we bought calls, so we > hedge with shorting the stock (negative) look at 88528. there, you buy puts and the # of shares has a negative sign in front of it.

Well that’s just messed…

that ones gotta be incorrect right? if negative there is wrong then im all set