Schweser practice exam 3 AM (Vol 2) - Q 47 (Delta neutral hedging)

CFA Level II
#1

Hi all,

In this question, basically this person wants to hedge a large equity position in his portfolio. Question is: what option strategy would be the most effective in delta neutral hedging the risk of stock?

I’m down to 2 choices:

A. Add put options to the portfolio as the put option delta moves closer to zero

C. Add put options to the portfolio as the put option delta moves toward -1

The answer is A. According to the answer, because the delta of put is negative, as the option delta moves closer to -1, the number of options necessary to maintain the hedge falls.

I’m not sure if the answer should have been C? Based on their answer, fewer options is required in C vs. A so it should be a more effective strategy?

Thanks!!

#2

i came across this question too, i might be wrong but i believe the reason is you want to do a delta neutral hedging, and you currently have a long exposure by longing the stock, long stock has a positive delta, you hedge it with a put which has negative delta. As put option delta moves closer to zero it means the stock is up and your neutral hedge is gone, so in order to neutralize the delta, you add put again to bring the positive delta down.

C cannot be right, if the put option delta moves toward -1 your delta is hedged and you dont have to add extra put options.

if i am someone please correct me. THX.

#3

If portfolio ( x times stock and y times put option) is delta zero small changes in price will not affect the value of the portfolio.

Stock delta is always 1, put delta always negativ. If put delta increases up to zero you will need more of the same put options to keep the portfolio delta zero. Example: One Stock, and two put options of delta = -0,5. This is delta hedged. If the put options increase to -0,25 (e.g. closer to zero), you will need four instead of two put options to sustain the hedge.

Best

#4

Thanks! Yeah but that’s why i thought C is the correct answer. Following your logic, if delta put is now -1, then we only need 1 put to hedge. As delta put moves towards -1, less puts are required to hedge. So this will be more effective than when delta put is closer to 0?

#5

Thanks! Yeah but that’s why i thought C is the correct answer. Following your logic, if delta put is now -1, then we only need 1 put to hedge. As delta put moves towards -1, less puts are required to hedge. So this will be more effective than when delta put is closer to 0?

#6

So we have a portfolio of stock and put: delta of portfolio = No. of stocks x Delta of stock (which is 1) + No. of puts x delta of put (negative)

What we need to do is to ensure the delta of portfolio = 0. I thought the more negative delta put, the less puts we need to hedge.

For example, if we have 1 stock, and delta of put is - 0.25 (closer to 0) => we need 4 puts to hedge.

If now the delta is - 0.75 (closer to -1) => we need 1.33 puts to hedge. so as we need less puts, this is more effective than the above?

Please let me know if my understanding is wrong? :frowning:

#7

Here is my understanding:

Options needed to hedge = (shares)/Delta

As Delta moves to -1 or 1, the denominator gets larger. Hence, larger denominator = less options needed to hedge exposure.

#8

But does ‘less needed’ means more effective? instead of using 4 puts to hedge, now we only need 1.33?

I’m so confuseddd!!!

#9

if the solution’s reasoning is due to lower amount of puts needed to hedge, then yes.

perhaps they are factoring into account stuffs like commission, transaction costs, impact on market prices of options etc

#10

I don’t want to see questions like this in the real exam :frowning: