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# Call and Put options

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1. Ms. Smith longs 1 XYZ Feb. 40 Call @ 3 and hold it it to expiration. Assuming no transaction costs, analyze this investment in terms of possible profit or loss. Draw a payoff diagram.

2. Ms. Smith writes 10 BETA Jan. 40 put @ 4. The put is exercised when the stock is trading at 38. Ms. Smith immediately sells the stocks in the market. What is Ms. Smiths profit or loss?

3.Ms. Smith writes 10 KLP Dec. 55 call @ 5, uncovered. The call is excersized when the stock is trading at \$58. What is Ms. Smiths profit or loss?

4. In Dec. 16 an investor buys 1 ALFA Feb 60 call @ 3 1/2. In January 10th ALFA share closes at \$63. What is the intrinsic value of the call? What is its time value?

5. Ms. Smith shorts 1 XYZ Feb. 40 Call @ 3 covered. She purchases XYZ for \$30 a share. Assuming no transaction costs, analyze this investment in terms of possible profit or loss. Draw a payoff diagram.

6. Suppose you have the following positions
Long 10 CDE Jan. 50 call @ 3
Long 10 CDE Jan. 50 put @ 4

Analyze this investment in terms of possible profit or loss. Draw a payoff diagram.

#### Solution Summary

The solution calculates payoffs from buying/writing call and put options.

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## 1) Consider a portfolio consisting of a long TM stock and a long put (K = \$70). a. Graph the profits to the position as a function of stock price. b. How might you create a similar payoff structure using a call option? Based on a comparison of these two positions, are the options priced correctly?

Answer questions 1 - 3 based on the information below. Assume r = 4% and no dividends.
Toyota Motor Corporation (TM) - Stock Price 77.70
Options expiring in one year
K Call Put
70 12.2 5.8
80 7.2 10.5
90 3.7 17.6

1) Consider a portfolio consisting of a long TM stock and a long put (K = \$70).
a. Graph the profits to the position as a function of stock price.
b. How might you create a similar payoff structure using a call option? Based on a comparison of these two positions, are the options priced correctly?

2 Charles Schwab has been recommending a naked strangle to some clients. This is a short positioning both the \$70 put and \$80 call.
a. Draw a diagram showing profit as a function of stock price.
b. Compute maximum gain, loss and breakeven point(s).

3) Assume you own \$1.5 million of Toyota stock in your retirement account and would like to protect your position. Toyota's beta is .66. Six-month S&P futures (250x the index) list for 1090. What position (long/short, number of contracts) would you take if you decided to hedge Toyota price risk with S&P forwards? How effective do you anticipate this strategy to be? Briefly explain.

Answer questions 4 - 7 based on the information below. Assume interest rates are 2% and no dividends.
Mylan Inc. (MYLAN) - Stock Price 17.42

Options Prices (6-months until expiration)
K Call Put
14 4 0.45
17 1.9 1.45
20 0.7 3.3

4 Graph the profits to the following position at expiration as a function of stock price. Compute the maximum profit, loss and breakeven points and show these distinctly in your excel file along with the formulas for computing each. A covered call (K = 20)
a) A long stock purchase.
b) A protective put (K = 17)
c) A covered call (K = 20)

5) Compute percentage gain or loss for each of the positions in #4 if the stock price in 6 months is \$25. Repeat for a price of \$10.

6) Graph the profits to a butterfly spread using the Mylan options. Compute break-even points.

7) Use the put and the call (K = 17) to create a synthetic forward. Graph the profit to this position.

** See ATTACHED file(s) for complete details **

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