Question

Imagine that you are holding 5,000 shares of stock, currently selling at \(40 per share. You are ready to sell the shares but would prefer to put off the sale until next year due to tax reasons. If you continue to hold the shares until January, however, you face the risk that the stock will drop in value before year-end. You decide to use a collar to limit downside risk without laying out a good deal of additional funds. January call options with a strike price of \)45 are selling at \(2, and January puts with a strike price of \)35 are selling at \(3. What will be the value of your portfolio in January (net of the proceeds from the options) if the stock price ends up at (a) \)30? (b) \(40? (c) \)50?

Compare these proceeds to what you would realize if you simply continued to hold the shares.

Short answer

a. $150,000

b. $200,000

c. $250,000

d. net proceeds per share varies in between $34 and the $44 and total net proceeds with 5000 share will be between $170,000 and $220,000

Step-by-step solution

Given Information

Initial outlay = purchasing a put at $3 – selling a call for $2 = $1

Calculation of net proceeds at $30 ‘a’

S_T = $30

Value at expiration = Value of call + Value of put + Value of stock

= $0 + ($35 – $30) + $30

= $35

The total net proceeds with 5,000 shares = (Final Value – Original Investment) x # of shares

= ($35 – $1) x 5,000

= $170,000

Net proceeds (without using collar) = S_T x # of shares

= $30 x 5,000

= $150,000.

Calculation of net proceeds at $40 ‘b’

S_T = $40

Value at expiration = Value of call + Value of put + Value of stock

= 0 + 0 + $40

= $40

The total net proceeds with 5,000 shares: (Final value – Original investment) x # of shares

= ($40 – $1) x 5,000

= $195,000

Net proceeds (without using collar) = S_T x # of shares

= $40 x 5,000

= $200,000

Calculation of net proceeds at $50 ‘c’

S_T = $50

Value at expiration = Value of call + Value of put + Value of stock

= ($45 – $50) + 0 + $50

=$45

The total net proceeds with 5,000 shares: (Final value – Original investment) x # of shares

= ($45 – $1) x 5,000

= $220,000

Net proceeds (without using collar) = S_T x # of shares

= $50 x 5,000

= $250,000

Explanation on comparison ‘d’

With the initial outlay of $1, the net proceeds per share varies in between the lower bound of $34 and the upper bound of $44.

The total net proceeds with 5000 share will be between $170,000 and $220,000