如题

问题如下：

A stock currently trades at USD25. In one year, it will either increase in value to USD35 or decrease to USD15. An investor sells a call option on the stock, granting the buyer the right, but not the obligation, to buy the stock at USD25 in one year. At the same time, the investor buys 0.5 units of the stock. Which of the following statements about the value of the investor’s portfolio at the end of one year is correct?

选项：

A.

The portfolio has a value of USD7.50 in both scenarios.

B.

The portfolio has a value of USD25 in both scenarios.

C.

The portfolio has a value of USD17.50 if the stock goes up and USD7.50 if the stock goes down.

解释：

A is correct. Regardless of whether the stock increases or decreases in price, the investor’s portfolio has a value of USD7.50 as follows:

If stock price goes to USD35, value = 0.5×35 – 10 = 7.50.

If stock price goes to USD15, value = 0.5×15 – 0 = 7.50.

If the stock price rises to USD35, the sold call option at USD25 has a value to the buyer of USD10, offsetting the rise in the stock price.