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 for 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 of $45 are selling at $2, and January puts with a strike price of $35 are selling at $3.
1. 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
2. Compare these proceeds to what you would realize if you simply continued to hold the shares.

Answer 1

Answer:

1. 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  ⇒ $170,000

(b) $40   ⇒ $195,000

(c) $50  ⇒ $220,000

call strike price $45

call premium received $2

put strike price $35

put premium paid $3

you pay $2 - $3 = -$1

                                                           stock price

                                             $30              $40               $50

stock value                           $30              $40               $50

put value                                $5                 -                     -

call value                                 -                   -                   -$5

premium paid                        -$1                -$1                 -$1

net stock value                     $34              $39               $44

total # of stocks                 5,000          5,000           5,000

portfolio's value             $170,000     $195,000    $220,000

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

if you hold the stocks:

(a) $30  ⇒ $150,000 - $170,000 = -$20,000 (you gain by using a collar)

(b) $40   ⇒ $200,000 - $195,000 = $5,000 (you lose by using a collar)

(c) $50  ⇒ $250,000 - $220,000 = $30,000 (you lose by using a collar)