UECM2443 FINANCIAL ECONOMICS I

Test 1

1. The common stock of the P.U.T.T Corporation has been trading in a narrow price range for the past month, and you are convinced it is going to break far out of that range in the next three months. You do not know whether it will go up or down, however. The current price of the stock is $100 per share, and the price of a three-month call option at an exercise price of $100 is $10. (15 Marks)

(a) If the risk-free interest rate is 10% per year, what must be the price of a 3-month put

option on P.U.T.T stock at an exercise price of $100? The stock pays no dividend.

(b) What would be a simple options strategy to exploit your conviction about the stock price’s future movements? How far would it have to move in either direction for you to make a profit on your initial investment?

2. On January 1, 2004, Karen sold stock A short for 50 with a margin requirement of 80%. On December 31, 2004, the stock paid a dividend of 2, and an interest amount of 4 was credited to the margin account. On January 1, 2005, Karen covered the short sale at a price of X, earning a 20% return. Calculate X. (5 Marks)

3. You are given the following information:

� One share of the P&S index currently sells for $1,500.

� The P&S index does not pay dividends.

� The annual effective risk-free rate is 6%.

You would like to lock in the ability to buy this index in one year for $1,600. You create a synthetic forward position on the index with a European put option and a European call option with the same strike price. The price of the put is $154.45 and the price of the call is $145.01.

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UECM2443 FINANCIAL ECONOMICS I

Test 1

Determine the profit at time one year if the price of the index is $1,650 at that time. (15 Marks)

Solution A synthetic forward is created when a call is purchased and a put is sold on the same underlying asset with the same strike price and time to expiration. When the call is purchased, you pay $145.01 now, and the profit at the end of the year is: Max[0, 1,650 - 1,600] - 145.01(1.06) = - 103.711 When the put is sold, you receive $154.45 now, and the profit at the end of the year is: - Max[0, 1,600 - 1,650] +154.45(1.06) = 163.717 The profit from the synthetic forward is -103.711+ 163.717 = 60.006.

4. Aardvark Airlines (AA) would like to limit its exposure to fluctuations in the price of jet fuel. AA expects the market price for a gallon of jet fuel in one year to be between $2.50 and $2.75. Its expected revenue per gallon of jet fuel is $2.70.

AA has decided to hedge this risk by selling a collar using one put option and one call option. The following table contains the various option prices available to AA:

The continuously compounded risk-free interest rate is 5.35%.

Based on AA’s expectations for the market price of jet fuel in one year, which interval represents the range of possible profit one year from now on a gallon of jet fuel basis for AA? (20 marks)

Solution

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UECM2443 FINANCIAL ECONOMICS I

Test 1

5. Martha sells a six-month call and purchases a 6-month put on Imclone stock. Both options have a strike price of $52.50. The current price of Imclone stock is $50. Imclone does not pay dividends.

The annual effective risk-free interest rate is 10.25%. Determine Martha’s net cost for this transaction. (15 %)

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UECM2443 FINANCIAL ECONOMICS I

Test 1

Solution

6. Consider the following options portfolio: you write a January maturity call option on IBM with exercise price 95. You write a January IBM put option with exercise price 85.

(20 Marks) (a) Graph the payoff of this portfolio at option expiration as a function of IBM’s stock

price at that time.

(b) What will be the profit/loss on this position if IBM is selling at 87 on the option maturity date? What if IBM is selling at 100? (Call price = $9 5/8; Put price = 0 1/16)

(c) At what two stock prices will you just break even on your investment?

(d) What kind of “bet” is this investor making? That is, what must this investor believe about IBM’s stock price in order to justify this position?

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UECM2443 FINANCIAL ECONOMICS I

Test 1

7. Explain why (i) A call option’s price cannot exceed the price of the underlying asset. (ii) A put option’s price cannot be more than the strike price. (10 Marks) Solution

(i) This is because a call option gives its owner the right to buy the underlying asset,

while the price of the underlying asset gives its owner the underlying itself. Clearly, the latter is more valuable than the former.

(ii) Because the strike price is the maximum possible payoff.

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