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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: 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.