Question

Joseph Jones, a manager at Computer Science, Inc. (CSI), received 10,000 shares of company stock as part of his compensation package. The stock currently sells at \(40 a share. Joseph would like to defer selling the stock until the next tax year. In January, however, he will need to sell all his holdings to provide for a down payment on his new house. Joseph is worried about the price risk involved in keeping his shares. At current prices, he would receive \)40,000 for the stock. If the value of his stock holdings falls below \(35,000, his ability to come up with the necessary down payment would be jeopardized.

On the other hand, if the stock value rises to \)45,000, he would be able to maintain a small cash reserve even after making the down payment. Joseph considers three investment strategies:

a. Strategy A is to write January call options on the CSI shares with strike price \(45. These calls are currently selling for \)3 each.

b. Strategy B is to buy January put options on CSI with strike price \(35. These options also sell for \)3 each.

c. Strategy C is to establish a zero-cost collar by writing the January calls and buying the January puts.

Evaluate each of these strategies with respect to Joseph’s investment goals. What are the advantages and disadvantages of each? Which would you recommend?

Short answer

Strategy C is the best advised strategy.

Step-by-step solution

Explanation on strategy ‘a’

In case the price exceeds $45 per share, the most to gain from this = Present value + Premium income

= $45 x 10,000 + $30,000

=$480,000

So the payoff structure would be:

Less than $45(10,000 times stock price) + $30,000

Greater than $45$450,000 + $30,000 = $480,000

Less than $45(10,000 times stock price) + $30,000

Greater than $45$450,000 + $30,000 = $480,00

For less than $45 = (10,000 times stock price) + $30,000

For more than $45 = $45 x 10,000 + $30,000 =$480,000

This implies that in the extreme cases, if the stock price falls to zero, Jones will have $30,000 which can go up to $480000 in best cases.

Explanation on strategy ‘b’

With put option $35 strike price and premium of $30,000, the minimum value would be :- Present value - Premium income

= $35 x 10,000 - $30,000

=$320,000

So the payoff structure would be:

Less than $45(10,000 times stock price) + $30,000

Greater than $45$450,000 + $30,000 = $480,000

Less than $45(10,000 times stock price) + $30,000

Greater than $45$450,000 + $30,000 = $480,00

For less than $35 = $35 x 10,000 - $30,000 =$320,000

For more than $35 = (10,000 times stock price) - $30,000

Explanation on the strategy ‘c’

Since the net cost of the collar is zero, the value of portfolio =

For less than $35 = $35 x 10,000 =$350,000

Between $35 and $45 = (10,000 times stock price)

For more than $45 = ($45 x 10,000) = $450,000

Comparison of strategies and suggested best strategy

Since strategy C offers the possibility of preserving principal $350,000 while retaining the possibility of getting $450,000, it is the best advised strategy.