Question

Question 4 - (20 Points) You are a broker and you think that the Google share price will rise in the next three months. The current price of 1 Google share is $55. A 3-month European call options on Google shares with a strike price of $58 are currently selling for $2.75. Each option contract is written on 100 shares. You have to choose your investment, between buying 50 shares and buying 1000 call options. Both strategies involve an investment of $2750 (a) Describe pros and cons of the two strategies in relation to potential profit/loss (Take into account the cost of your strategy). (b) How high does the stock price have to rise for the option strategy to be more profitable? (Take into account the cost of your strategy)

Answer 1

(a) Buying 50 shares and buying 1000 call options both incur a cost of $2750.

Let's assume the share price of Google at the end of three months is x.

Let's analyse the buying share option first.

Profit on buying share = (x-55) * 50

Thus, if the share price rises above $55, the broker will be profitable. However, if the share price drops below $55, the broker will incur a loss with maximum loss at a share price of 0 i.e. (0-55) * 50 = -$2750.

Lets now analyse the profit/loss for buying call option strategy.

Profit on buying call option = (x-58) * 1000 - 2750

Now let's calculate the price at which buying call options strategy will have zero profit.

(x-58) * 1000 - 2750 = 0

x - 58 = 2.75

x = 60.75

If the share price is at or below $58 after three months, the broker will not exercise the call option and incur a loss of $2750. This is the maximum loss than the broker can incur. The broker will break-even if the share price rises to $60.75. Above this price, the strategy starts accumulating profit.

(b) Let's equal the profit equation under both strategies to determine the price at which both strategies have equal profit. If the price increases above this level, the call option will start accumulating more profits.

(x-58) * 1000 - 2750 = (x-55) * 50

1000x - 58000 = 50x

950x = 58000

x = 61.05

Thus, if the stock price rises to $61.06 or more, the option strategy becomes more profitable.