Imagine that you are holding 7,000 shares of stock, currently selling at $70 per
ID: 2753203 • Letter: I
Question
Imagine that you are holding 7,000 shares of stock, currently selling at $70 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 $75 are selling at $2, and January puts with a strike price of $65 are selling at $4. What will be the value of your portfolio in January (net of the proceeds from the options) if the stock price ends up at $57, $70, $77? What will the value of your portfolio be if you simply continued to hold the shares?
Stock Price Portfolio Value $57 $70 $77
If collar is used
If you continued to hold the shares
Explanation / Answer
Stock Price
57
70
77
If collar used
441,000
476,000
511,000
If continued to hold stocks
399,000
490,000
539,000
Number of Shares held = 7000
Current Price = $ 70
Portfolio Value = 7000 * 70 = 490,000
If continued to hold the shares
Portfolio value at $ 57 = 7000 * 57 = 399,000
Portfolio Value at $ 77 = 7000 * 77 = 539,000
If implemented collar strategy - Selling a call option and buying a put option
Call option
Strike Price = 75
Price of the option = $ 2
Put Option
Strike Price = 65
Price of the option = $ 4
Amount received on sale of Call option = 7000 * 2 = 14,000
Amount paid on buying a put option = 7000 * 4 = 28,000
Value of the Portfolio = 7000 * 70 + 14000 – 28000 = 490,000 +14000 – 28000 = 476,000
If the stock price in January is 57
As the strike price 75 is higher than the current market price of 57, the call option buyer will allow the option to expire
As the strike price of 65 is higher than the current price of 57, the investor will utilise the put option
Profit from Put option can be obtained by buying shares from market and selling the same under the put option
Profit from put option =7000 * (65-57) = 7000 * 8 = 56000
Value of the portfolio = Holding Value at current price + premium received – premium paid+ profit from put option
= 7000 * 57 + 14000 – 28000 + 56000
= 399000 + 14000 – 28000 + 56000
= 441,000
If the stock price in January is 70
As the strike price 75 is higher than the market price of 70, the call option buyer will allow the option to expire
As the strike price of 65 is lower than market price of 70, the invest will allow the put option to expire
Portfolio Value = Holding value at current market price + premium received – premium paid
= 7000 * 70 + 14000 – 28000
= 490000 + 14000 – 28000 = 476,000
If the market price in January is 77
As the strike price of 75 is lower than market price of 77, the buyer of call option will enforce the call option
Loss from call option = 7000 * (77-75) = 7000 * 2 = 14000
As the strike price of 65 is lower than market price of 77, the investor will allow the put option to expire
Portfolio Value = Holding value at current market price + premium received – premium paid – loss on call option
Portfolio value = 7000 * 77 + 14000 – 28000 – 14000
= 539000 + 14000 – 28000 – 14000
= 511,000
Stock Price
57
70
77
If collar used
441,000
476,000
511,000
If continued to hold stocks
399,000
490,000
539,000