An investor does a lot of investing in the stock market and is a frequent user of the stock-index options. The investor is convinced the market is about to undergo a broad retreat and has decided to buy a put on the S&P 100 index. The put carries a strike price of 690 and is quoted in the financial press at 4.50. Although the S&P 100 stocks is currently at 686.45, Dorothy thinks it will drop to 665 by the expiration date of the option.

1. How much profit will she make, and what will be her holding period return if she is right?

2. How much will she lose if the S&P 100 goes up (rather than down) by 25 points and reaches 715 by the date of expiration?

We don't normally do homework on here, but I always found this difficult to understand. I'm going to write out the response in detail so you can understand it.

A put option gives the holder the right to sell a stock at an agreed-upon price at any time up to an agreed-upon date. The holder is betting that the stock will decline in value. The difference between the stock price that day and the agreed-upon put value, less the cost of the transaction (or premium) is the holder's profit.

1. If she is right, her profit is the difference between the strike price ($690) less the market price ($665), minus her cost to buy this option at 4.50. Her profit is $20.50 (690-665-4.50) per share sold. There would normally be a sales commission, but that is not mentioned here. For stock options, each contract covers 100 shares. The holding return = (price at start of put purchase - price at end of put purchase)/ price at start of put purchase = (686.45-665)/686.45.

2. If the price goes up, she will not exercise her option. Her risk of loss is limited to her premium, or 4.50 per share purchased.