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Fighting in The Stock Market

Of course there are. Specific risks applicable to each company and its common stock must be considered in its valuation. These risks are distinct from and in addition to the general market risks, identified in prior chapters as fluctuations in expected earnings growth, real interest rates, and inflation. Company-specific risks can be mitigated through diversification. General market risks cannot. An appropriately diversified portfolio of common stocks can mitigate the risks of separate, individually-owned common stocks. Common stocks within a portfolio may respond differently from the same event. For example, an increase in oil prices may increase the expected earnings for oil companies while simultaneously decreasing the expected earnings for airlines. Investors owning only airline common stocks lose. Investors owning only oil common stocks gain. Investors owning both oil and airline common stocks experience an offsetting effect. Their portfolios garner the average return. The portfolio return is not as large as it would have been if solely invested in oil and not as small as it would have been if solely invested in airlines. The portfolio risk has been reduced without a corresponding decrease in the average return. A completely diversified portfolio including every common stock eliminates all company-specific risks but always retains general common stock market risks.

An owner of a stock is able to protect his or her position in the stock by marrying it with an appropriate number of short call options or long put options. A short stock position may be hedged by an opposite position in options, a long call or a short put. Once the position is fully hedged, the return on it should be equal to the risk-free rate. That is why the risk-free rate is relevant to option valuation. To achieve a fully hedged position, the hedger will short the appropriate number of calls. This is determined by the hedge ratio as follows. Suppose that for every dollar change in the price of the stock the call option premium changes by $0.20. This is equivalent (mathematically) to saying that the partial derivative of the call option price with respect to the price of the underlying stock is equal to 0.20. Therefore, it would take five short call options to hedge the risk of a stock position in one hundred shares. The hedge ratio is 1/0.20 or 5. Therefore, 100 shares of stock combined with five short call options will produce, theoretically, a net position similar to holding an equivalent position in a risk-free government bond yielding the risk-free rate. All else being the same, the higher the risk-free rate, the higher the value of the call option.

With different strike prices. The call and put options had strike prices ranging from $60 to $85. The August call option with the $60 strike price is the most valuable. Looking at the same maturity (August) across higher strike prices, we observe that the price of the call option falls. That is because for each successive higher strike price the holder of the option receives less money (difference between strike and market price) if he chooses to exercise the option. We can say, therefore, that the August call option with the $60 strike price is most in-the-money, that is, it will bring in the most cash in the event it is exercised. Clearly, the option with the highest strike price will bring in the beast, if anything. In fact, the August 70 option will lose money if it were exercised (option is said to be out-of-the-money). We will explain why it still trades at a positive stock below 70. We know, consequently, that the higher the strike price, given a market price, the lower the value of option. Should one check across stock, with different market prices in Exhibit 8.2, one would discover that the higher the price of the stock, all else being the same, the higher the price of the option. We have, therefore, determined thus far that option prices (premia) are positively related to the market price of the stock and negatively related to the strike price given the market price of the stock. Taking the Cisco options from Exhibit 8.2 with a strike price of 70, we find that the longer the maturity of the option, the higher the value of the option. The October 70 is more valuable than the July 70 option. Therefore, call option premia are positively related to their life (time to maturity). But, once the maturity is fixed, the passage of time will cause the time premium to shrink with most of the shrinking occurring in the latter part of the option life. Since we already discussed that prices of stocks fall by the value of the dividends on a dividend day, we can safely conclude that dividends have a negative effect on option prices.


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