Question

Imagine that you are holding 6,800 shares of stock, currently selling at $60 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 $65 are selling at $5, and January puts with a strike price of $55 are selling at $7. What will be the value of your portfolio in January (net of the proceeds from the options) if the stock price ends up at $46, $60, $66? What will the value of your portfolio be if you simply continued to hold the shares?

	Stock Price Portfolio Value $46 $60 $66 If collar is used If you continued to hold the shares $312,800 $408,000 $448,000

Answer 1

In a Collar, the lower strike price Put options are bought and higher strike price call options are sold

So, 6800 put options with strike of $55 purchased at $7 . So total cost = 6800*$7 = $47600

and, 6800 call options with strike of $65 sold at $5 . So total gain = 6800*$5 = $34000

Net cost of Collar = $47600-$34000 =$13600

Value of portfolio in January (on options expiration) = value of stocks + value of options - cost of options

If stock price is $46, put options will have value and call options will be worthless

Value of portfolio = 6800 *$46 + 6800* (55-46) - $13600 = $360400

If stock price is $60,both options will be worthless

Value of portfolio = 6800 *$60 -$13600 = $394400

If stock price is $66, call options will have value and put options will be worthless

Value of portfolio = 6800 *$66 - 6800* (66-65) - $13600 = $428400

If one simply continued to hold the shares

Value of portfolio = value of stock

When Stock price =$46, value of portfolio = 6800*$46 = $312800

When Stock price =$60, value of portfolio = 6800*$60 = $408000

When Stock price =$66, value of portfolio = 6800*$66 = $448800