Protective put question not getting it

CFA Level III Derivatives
#1

Exhibit 1.

Option Data for Company A, 25 November 2019

Option Expiration Strike Premium Delta Theta
Call February 2020 140 5.40 0.510 –0.035
Call July 2020 140 8.64 0.517 –0.021
Put February 2020 140 6.15 –0.508 –0.034
Put July 2020 140 10.55 –0.507 –0.019

Wendy Manetti Case Scenario

Manetti states, “Now consider a situation in which a client owns shares of Company A and wants to protect against a sudden decline in share price. A strategy to consider is the purchase of put options. I might suggest that the client purchase the February 2020 put option because it is cheaper than the July 2020 option and has the lowest time decay. If it were possible to purchase a February put option with a strike price lower than $140, it would be cheaper, but there would be a greater risk of loss in the position.”

If the client executes Fillizola’s suggested strategy at the current price, her position delta will most likely be the same as the position delta of a portfolio that is:

  1. long 2,000 shares and short forward 980 shares.
  2. long 1,020 shares and short forward 980 shares.
  3. long 2,000 shares and short forward 1,020 shares.

Solution

Solution

C is correct. The delta for the February 2020 $140 call strike option on Company A is 0.51. The delta for a long position in one share of Company A is 1. She is long 2,000 shares of Company A. The position delta for the covered call is (1 – 0.51) × 2,000 = 980. This position delta can be replicated by going long 2,000 shares and taking a short forward position in 1,020 shares. Forwards have deltas of 1.0 for non-dividend-paying stocks. Position delta for Option C = (2,000 – 1,020) = 980.

My confusion - why use covered call delta? I arrived at c by simply doing 2000 *-0.508=1016 shares. This is a protective put and we are given the long put’s delta. What is the need to use a call delta here? Not getting this.

#2

Nor am I.

Your approach makes sense.

#3

Thanks Bill

#4

My pleasure.

#5

If this can clear confusion, you are looking at the wrong paragraph to answer this question.
The question states “If the client executes Fillizola’s suggested strategy”, and you pasted what Manetti states.

The correct paragraph for this question is just above :
“Fillizola suggests that the client write 20 contracts of February 2020 call options with an exercise price of $140. The implied volatility of this option is 21.05%. Fillizola notes that if the share prices moves to $140 and the option is called, the client would effectively sell her shares at $145.40. If, however, shares prices move lower to $130 her effective sale price would be $135.40. Fillizola notes that this strategy would be appropriate if the expected stock’s volatility is higher than the implied volatility of 21.05%.”

Hence the use of call delta.