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

Answer 1

Answer:

Consider the following calculations

Explanation:

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

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