Question

1. Alvaro creates a covered call. A covered call consists of one long share of stock and one short call option on the stock. The spot price of PND stock is 100. The call option he will use has a strike price of 105 and one year to expiration.

The price of the call option is 9.68 . The continuously compounded risk-free rate is 4%.

1. What is Alvaro’s profit at the end of one year if the price of PND at that time is 102?

2. What is the breakeven stock price for the portfolio?

3. What is the minimum profit of the portfolio?

4. What is the maximum profit of the portfolio?

5. What ending stock price would result in a profit of 6.00?

Answer 1

(a) In this case, Alvaro has one long share of stock and one short call option on the stock. At the end of one year, the price of PND is 102. The price is less than the strike price of 105. Hence, the call option should expire worthless for the buyer and Alvaro has no obligation to purchase the stock. His profit can be provided using the formulae: -

In this case,

^{is the stock price at the end of one year, is the stock price at the beginning and is the premium obtained on selling the option.}

At the end of one year, Alvaro gets the profit on the stock and the premium that he obtains on selling the call option. Thus,

(b) The breakeven stock price for the porfolio is the price where the profit is 0. In case the breakeven stock price at the end of year 1 is ,

Here is the strike price. In case strike price is less than the stock price at the end of year 1 , the buyer exercises the call option and Alvaro should sell the stock at . Hence, the limited profits. He always keeps the premium though. We've:

On simplifying,

The breakeven stock price at the end of year 1 is 90.32.

(c) The minimum profit is when the stock price at the end of year 1 decreases to 0. In this case,

Hence, the minimum profit is -90.32.

(d) The maximum profit is when the stock price at the end of year 1 is equal to or more than the strike price . In case strike price is less than the stock price at the end of year 1 , the buyer exercises the call option and Alvaro should sell the stock at .

Hence,

Hence, the minimum profit is 14.68.

(e) Let the ending stock price be . We've,

Hence,

Thus,

The ending stock price for profit to be 6 should be 96.32.