# The price of a stock is currently \$30. The price of a two­year European call option on the stock with a strike price of \$40 is \$15

###### byKatelyn Kraus

Q1. The price of a stock is currently \$30. The price of a two­year European call option on the
stock with a strike price of \$40 is \$15 and the price of a two­year European put option on the stock with a strike price of \$20 is \$12.
Suppose that an investor buys 100 shares of stock, shorts 100 call options, and buys 100 put options. Construct a table showing the investor’s profit (not payoff) as a function of the stock price at expiration. The difference between profit and payoff is explained in week 1. In addition, please
remember that when the investor shorts an option, he receives the option price upfront. For example, if you short sell 1 call option, you will receive \$15 today.
Hints: To answer part a, construct a column in Excel of stock prices at expiration ranging from \$1 to \$60 in increments of \$1. Then use the next 3 columns to calculate the stock, call, put profits (one column for each position). Pay attention to whether the investor is taking a long or a short position of the option. Then add all the profits from these three positions (stock, call, put). Finally, use Excel to graph the portfolio profit (y­axis) as a function of stock price (x­axis). Specifically, use scatterplot in Excel. If you don’t know how, then type “scatterplot” in Excel help and follow the instruction. Your profit for long put option should look similar to Figure 9.2 in page 213 and the profit for short call should look similar to figure 9.3.

b. The set of actions in part A is called a “collar” strategy. Explain when an investor is likely to use this collar strategy.

c. Suppose now that the investor buys 100 stocks, shorts 200 call options, and buys 200 put options. Construct a table showing the investor’s profit or loss as a function of the stock price at expiration. Graph the portfolio profit as a function of stock price. The total profit should look like a zigzag (down/up/down) pattern.

Q3: If you exercise an in­the­money call option, you will make a profit. Explain whether this is true or false.

Q2: What are the differences between (a) exchange­traded call options and (b) warrants/employee stock options/convertibles?

Q4. The current price of a stock is \$94, and a three­month European call option with a
strike price of \$95 currently sells for \$4.70. An investor who feels that the price of the stock will
increase is trying to decide between investing in 100 stocks and investing in 2,000 call options (20 contracts) for 3 months. Both strategies cost an initial investment of \$9,400. How high does the stock price have to rise in3 months for the option strategy to be more profitable than the stock strategy? In other words, at what stock price, will the 2 strategies result in the same profit?

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