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Protective call option

Protective call option assumes that buying a certain stock is followed by selling the call option on that stock (short position). So if stock price starts to fall, the investor realizes a profit based on call option.

For example, let's assume that current stock price id 50$ and an investor opens a short position on call option with strike price 50$ and the time of maturity of 60 days. Let's assume also that probability of stock price advancing by 20% for that time period is 2/3, and for falling by 10% is 1/3. At the end of a period of 60 days, in case that stock price rises to 60$, the investor will earn profit per share of 10$ and suffer a loss per option of 10$ (S - X = 60-50 = 10). In case of price falling to 45$ the investor suffers a loss on the share of the 5$, and the option becomes worthless.

Hedged position can be adjusted as:

Adjusted hedged position

This means that investor needs to buy two shares, and sell three options. Let's assume that price of the call options at the beginning of period is 4.762$. This means that investor needs to invest 100$ to purchase two shares and investor also collects money of selling three options: 3 x 4.762$ = 14.286$. So total investment is 100$ - 14.286$ = $ 85.714$.

If the stock price rises to 60$. The value of the portfolio is: 2 x 60$ (shares) and 3 x -10$ (options) = 120$ - 30$ = $ 90.

If the stock price falls to 45$, the value portfolio is: 2 x 45$ (shares) and 0$ (options) = 90$.

As you can see, for both limits (60$ and 45$) portfolio value is $ 90. Investor has invested 85.714$, so realized gain is 5% no matter if stock price rises to 60$ or declines to 45$. Of course, investor lost a chance to make bigger profit if stock price rises by 20%, but he reduced risk if stock price falls. Level of risk and profit has opposite affect - the higher the risk is, higher are the profits, and vice versa. In this case the investor wanted to reduce the risk and therefore must satisfy with a smaller potential profit.

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