18 April, 23:38

# The current price of a stock is \$94 & European call options with a strike of \$95 currently sell for \$4.70. An investor is trying to decide between buying 100 shares of stock and buying 2,000 call options ( = 20 option contracts).A. At what stock price would the investor be indifferent between these 2 trades?B. At what stock prices would the investor be better off with the option contract purchase?

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1. 19 April, 00:13
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The investment in call options may have higher risks which can inturn lead to higher returns especially If the stock price stays at \$94.

Hence, an investor who buys call options loses \$9,400 while an investor who buys shares will neither gains nor loses anything.

Therfore If the stock price rises to \$120, the investor who buys call options gains-

2000 * (120 - 95) - 9400 = \$40,600

And if the stock price rises to \$120, an investor who buys shares gains

100 * (120 - 94) = \$2600

Which means the strategies are equally profitable if the stock price rises to a level, S, where

100 * (S - 94) = 2000 * (S - 95) - 9400

S = \$100