Corpfin, Mod 20: Readings (8th edition)


Corpfin, Mod 20: Readings (8th edition)

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NEAS
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Corporate Finance, Module 20: "Introduction to Options"

Required reading, Eighth Edition:

(The attached PDF file has better formatting.)

Updated: November 22, 2005

{The Brealey and Myers textbook is excellent. We say to read certain sections and to skip others. This does not mean that certain sections are better; it means that the homework assignments and exam problems are based on the sections that you must read for this course. Some of the skipped sections are fascinating, but they are not tested.}

Modules 20, 21, 22, and 23 cover options.

Module 20 is an introduction to options; puts, calls, and put call parity.

Module 21 covers basic pricing techniques: options deltas and binomial trees.

Module 22 covers real options: follow-on investments, timing, and abandonment.

Module 23 covers advanced topics: risky bonds, Black-Scholes, and American options.

 

Read the introduction on pages 541-542. This introduction covers topics in all four of the options modules for this course. The real options discussed on page 541, from "Second, many capital investments …" through "… to decommission an offshore oil rig" are covered in real options; they won’t be clear to you until you have completed module 22. The paragraph on page 541 "In fact, we shall see that whenever a company borrows, it creates an option …" is covered in Module 23. It takes a while to get used to options theory; have patience as you review these modules.

Read section 20.1, "Calls, Puts, and Shares" on pages 542-544. Before reading page 545, make sure the previous pages are clear to you. Then read the sub-section "Position Diagrams Are Not Profit Diagrams" on pages 545-546. Review Figure 20.3 on page 545, and make sure you understand (i) why the horizontal line is above or below the x-axis by the amount of the option premium and (ii) why the break-even point is more or less than the strike price.

Read section 20.2, "Financial Alchemy with Options," on pages 546-552. Focus on the put call parity relation on page 549: "c + PV(X) = p + S." The final exam tests this relation.

Pages 552-557 are covered in Module 23. Read these pages now (or at least skim them), but don’t worry if you don’t yet grasp all the concepts. The concepts are difficult; after working through the mathematics of Module 21 and the illustrations in Module 22, these pages are easier.

Read the summary on page 558. Look at practice questions 2, 3, 4, and 5 on page 560 and 11 (parts a and b) on page 561. These questions are a good review of the material. Now look at practice questions 13 and 14 on page 561. These two questions test your understanding of the put call parity relation. It takes a while to get the hang of this relation; post your answer to these two questions on the discussion forum to see if you grasp the method.


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Rick Sutherland
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I took a shot at some of the Practice Questions on pages 560 & 561 of the textbook, as suggested by the NEAS posting above. I'm pretty shaky on this stuff, and there were a couple of questions for which I didn't even know where to start. But, here is my best shot at each question:

2) The speaker is incorrect. The buyer of the call makes money if the stock price rises above the strike price, because the buyer will execute the call. The potential profit of this call buyer is limited only by the amount by which the stock could rise. The seller of the put, on the other hand, avoids losing money if the stock price rises above the strike price, since the put will not be executed. The potential profit of this put seller can never be any more than the price paid for the put itself.

3) For the American call, you buy the call for $75 and buy one share of the stock for $50, then immediately sell the stock for its market price of $200, realizing an immediate $75 profit. For the European call, you borrow a share and sell it short for the market price of $200, then you use the proceeds to buy the call for $75 and invest the remaining $125 at the risk-free interest rate. One year later, if market share price is greater than $50, you exercise the call option to buy the stock for $50 and you return that share to the borrower, leaving you with at least $75 in your investment account. If the market share price is less than $50 one year later, you let the call option expire, buy the stock in the market for less than $50 and return that share to the borrower, again leaving you with over $75 in your investment account. So, no matter what, whether stock price goes up or down and whether you choose the American or European call, you have an arbitrage opportunity with guaranteed money.

4) Value of 3-month Call + Exercise Price Discounted 3 months = Value of 3-month Put + Current Share Price. So, 10 + ($60 Exercise Price Discounted 3 months) = 10 + Current Share Price. So, ($60 Exercise Price Discounted 3 months) = Current Share Price. We know that ($60 Exercise Price Discounted 6 months) < ($60 Exercise Price Discounted 3 months). This tells us that ($60 Exercise Price Discounted 6 months) < Current Share Price. But we know that Value of 6-month Call + ($60 Exercise Price Discounted 6 months) = Value of 6-month Put + Current Share Price. From these last two items, we conclude that Value of 6-month Call > Value of 6-month Put. 6-month Call is more valuable.

5) Value of Call + PV(Exercise Price) = Value of Put + Current Share Price. So, 9.05 + PV(50) = Value of Put + 54. This implies Value of Put = 9.05 + 50 * e ^ (-.015 * (8 / 12)) - 54 = $4.55

11a) Buy a put option and borrow at the risk-free rate. The exact number of shares on which to buy a put option and the amount to borrow vary depending on the spread of possible option prices and the spread of possible share prices. This type of scenario is described in the textbook section entitled "Valuing the Amgen Put Option" on pages 568-569.

11b) I could not figure out how to do this one.

13) I was confused by the terminology used in this question, particularly the sentence "It has a par (face value) of $350 million, but is trading at a market value of only $280 million." To what does the word "it" refer? The comapny's debt? The company's stock value? I have no idea how to take the information given and plug it into the put-call parity formula.

14-Straddle Strategy) Let PT = Stock Price at the Strike Date. Assume the price paid for the call and the put are sunk costs (since we are told that following this strategy is a given), so we are only evaluating the profit earned on the Strike Date. If PT > 100, then you exercise the call and not the put, ending up with a profit of ( PT - 100 ). If PT < 100, then you exercise the put and not the call, ending up with a profit of ( 100 - PT ). The further PT varies from 100, the greater the amount of profit. You are betting that the stock price will have high variability around 100.

14-Butterfly Strategy) Same assumptions as in Straddle Strategy above. With the Butterfly Strategy, if PT < 100, then no calls are exercised, and profit is 0. If 100 < PT < 110, then only the $100 call is exercised and your profit is ( PT - 100 ). If 110 < PT < 120, then the $100 and $110 calls are exercised and your profit is ( PT - 100 ) - 2 * ( PT - 110 ) = (120 - PT ). If 120 < PT, then all four calls are exercised and your profit is ( PT - 100 ) - 2 * ( PT - 110 ) + ( PT - 120 ) = 0. So, the profits are 0 if PT is smaller than 100 or bigger than 120, and profits are highest if PT is exactly 110. The further PT varies from 110, the smaller the amount of profit. You are betting that the stock price will have low variability around 110.

After typing up this posting, I can see why I'm the first one to post here...these are rather long answers. Still, if anyone cares to post their thoughts, especially on the questions I couldn't answer, I'll be interested to see them.


shasha
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11 a)   I think should be

Sell Call + Buy Put + Borrow X  = short shock

b)

short stock + sell put with exercise X + buy call with exercise X = loan X (borrowing X)


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