Question

Imagine that you are holding 6,200 shares of stock, currently selling at $30 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 $35 are selling at $4, and January puts with a strike price of $25 are selling at $6. What will be the value of your portfolio in January (net of the proceeds from the options) if the stock price ends up at $22, $30, $42? What will the value of your portfolio be if you simply continued to hold the shares?

Answer 1

Collar is option strategy where we buy out of money put option and sell out of money call option to finance the put option

Call option is right to buy at certain strike price

Put option is right to sell at a strike price

Our holding shares is 6200 to hedge risk we buy out option at strike price of 25 and sell call option at strike price of 35

Value of portfolio if price is 22

= 6200×22 +3×6200 = 155000

As because at spot price of 22 our put option will expire in money and it's value is 3

Value of portfolio if held only shares = 6200×22 = 136400

(Value of portfolio if price is 30)

If the price is 30 our put option will be out of money and call option buyer also will not use his right

So value of portfolio with options and without options is same that is 30×6200 = 186000

(Value of position at price 42)

At price 42 our put option will be out of money but buyer of call option will exercise his right and it's value is 7

= 6200×42 -7(6200) = 217000

Value of portfolio without options is

6200×42 = 260400