An Introduction to Derivatives and Risk Management: With Stock-Trak Coupon

Don M. Chance, Robert Brooks

Chapter 6 Basic Option Strategies - all with Video Answers

Educators

Chapter Questions

Problem 1

We briefly mentioned the synthetic call, which consists of stock and an equal number of puts. Assume that the combined value of the puts and stock exceeds the value of the actual call by less than the present value of the exercise price. Show how an arbitrage profit can be made. Note: Do not use the data from the chapter. Show your point as it was illustrated in the text for the synthetic put.

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Problem 2

A short position in stock can be protected by holding a call option. Determine the profit equations for this position, and identify the breakeven stock price at explration and maximum and minimum profits.

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Problem 3

You have inherited some stock from a wealthy relative. The stock has had poor performance recently, and analysts believe it has little growth potential. You would like to write calls against the stock; however, the will stipulates that you must agree not to sell it unless you need the funds for a personal financial emergency. How can you write covered calls and minimize the likelihood of exercise?

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Problem 4

Explain the considerations facing a covered call writer regarding the choice of exercise prices.
The following option prices were observed for a sloch for fuly 6 of a particular your. Une this information in problems 5 through IO. Ignore dividemds on the stock. The stock is priced at rist:fres rates are 0.0503 , 0.0535, and 0.0571 , respectiveth. The slandard derviation is 0.21 . Assume that the ofitions are European.
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Problem 5

In problons 5 through 10 , Determine the profits for possibte stock prias of $150,155,160,165$, 170, 175, and 180. Answer any other questions es reguested. Note: Your Excel spreadsheel Strallyz7e.xls will bs useful here for obtaining graphs as requested, but it does not allow you to cal. culate the profits for several userspecified atset prios. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz 7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profits for the prices of $150,160, \ldots, 180 \mathrm{bg}$ hand for positions held to expiration. For positions dosed frior to expiration, use the spreadshed BSMbin 7e.xils or the Windows program BSMbain 7e exe to deternime the oftion pria when the position is dosed; then calculate the profit by hand.
Buy one August 165 call contract. Hold it until the options expire. Determine the profits and graph the results. Then identify the breakeven stock price at expiration. What is the maximum possible loss on this cransaction?

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00:13

Problem 6

Determine the profits for possibte stock prias of $150,155,160,165$, 170, 175, and 180. Answer any other questions es reguested. Note: Your Excel spreadsheel Strallyz7e.xls will bs useful here for obtaining graphs as requested, but it does not allow you to cal. culate the profits for several userspecified atset prios. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz 7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profits for the prices of $150,160, \ldots, 180 \mathrm{bg}$ hand for positions held to expiration. For positions dosed frior to expiration, use the spreadshed BSMbin 7e.xils or the Windows program BSMbain 7e exe to deternime the oftion pria when the position is dosed; then calculate the profit by hand.
Repeat problem 5, but close the position on August 1. Use the spreadsheet to find the profits for the possible stock prices on August 1. Generate a graph and use it to identify the approximate breakeven stock price.

Amy Jiang

Numerade Educator

00:13

Problem 7

Determine the profits for possibte stock prias of $150,155,160,165$, 170, 175, and 180. Answer any other questions es reguested. Note: Your Excel spreadsheel Strallyz7e.xls will bs useful here for obtaining graphs as requested, but it does not allow you to cal. culate the profits for several userspecified atset prios. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz 7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profits for the prices of $150,160, \ldots, 180 \mathrm{bg}$ hand for positions held to expiration. For positions dosed frior to expiration, use the spreadshed BSMbin 7e.xils or the Windows program BSMbain 7e exe to deternime the oftion pria when the position is dosed; then calculate the profit by hand.
Buy one October 165 put contract. Hold it until the options expire. Determine the profits and graph the results. Identify the breakeven stock price at expiration. What are the maximum possible gain and loss on this transaction?

Amy Jiang

Numerade Educator

00:13

Problem 8

Determine the profits for possibte stock prias of $150,155,160,165$, 170, 175, and 180. Answer any other questions es reguested. Note: Your Excel spreadsheel Strallyz7e.xls will bs useful here for obtaining graphs as requested, but it does not allow you to cal. culate the profits for several userspecified atset prios. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz 7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profits for the prices of $150,160, \ldots, 180 \mathrm{bg}$ hand for positions held to expiration. For positions dosed frior to expiration, use the spreadshed BSMbin 7e.xils or the Windows program BSMbain 7e exe to deternime the oftion pria when the position is dosed; then calculate the profit by hand.
Buy 100 shares of stock and write one October 170 call contract. Hold the position until expiration. Determine the profits and graph the results. Identify the breakeven stock price at expiration, the maximum profit, and the maximum loss.

Amy Jiang

Numerade Educator

00:13

Problem 9

Determine the profits for possibte stock prias of $150,155,160,165$, 170, 175, and 180. Answer any other questions es reguested. Note: Your Excel spreadsheel Strallyz7e.xls will bs useful here for obtaining graphs as requested, but it does not allow you to cal. culate the profits for several userspecified atset prios. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz 7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profits for the prices of $150,160, \ldots, 180 \mathrm{bg}$ hand for positions held to expiration. For positions dosed frior to expiration, use the spreadshed BSMbin 7e.xils or the Windows program BSMbain 7e exe to deternime the oftion pria when the position is dosed; then calculate the profit by hand.
Repeat problem 8 , but close the position on September 1 . Use the spreadsheet to find the profits for the possibie stock prices on September 1. Generate a graph and use it to approximate the breakeven stock price.

Amy Jiang

Numerade Educator

00:13

Problem 10

Determine the profits for possibte stock prias of $150,155,160,165$, 170, 175, and 180. Answer any other questions es reguested. Note: Your Excel spreadsheel Strallyz7e.xls will bs useful here for obtaining graphs as requested, but it does not allow you to cal. culate the profits for several userspecified atset prios. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz 7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profits for the prices of $150,160, \ldots, 180 \mathrm{bg}$ hand for positions held to expiration. For positions dosed frior to expiration, use the spreadshed BSMbin 7e.xils or the Windows program BSMbain 7e exe to deternime the oftion pria when the position is dosed; then calculate the profit by hand.
Buy 100 shares of stock and buy one August. 165 put contract. Hold the position until expiration. Determine the profits and graph the results. Determine the breakeven stock price at expiration, the maximum profit, and the maximum loss.

Amy Jiang

Numerade Educator

Problem 11

Explain the advantages and disadvantages to a call buyer of ciosing out a position prior to expiration rather than holding it all the way until expiration.

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Problem 12

Explain how a protective put is like purchasing insurance on a stock.

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Problem 13

Suppose that you wish to buy stock and protect yourself against a downside movement in its price. You consider both a covered call and a protective put. What factors will affect your decision?

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Problem 14

The Black-Scholes-Merton option pricing model assumes the stock price changes are lognormally distributed. Show graphically how this distribution changes when an investor is long the stock and long the put.

James Kiss

Numerade Educator

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Problem 15

James Kiss

Numerade Educator

Problem 16

For problems 16,17 , and 18 , Determine the profit from the following basic forrign curneng option transactions for each of the following spot rates at expiration: $$\$ 0.90$$, $$\$ 0.95$$, $$\$ 1.00$$, $$\$ 1.05$$, and $$\$1.10$$. Consinuct a profit groph. Find the breakeven spot rate at expiration. Assume that each contract covers 100,000 Euros.
A call option on the euro expiring in six months has an exercise price of $$\$ 1.00$$ and is priced at $$\$ 0.0385$$. Construct a simple long position in the call.

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Problem 17

Determine the profit from the following basic forrign curneng option transactions for each of the following spot rates at expiration: $$\$ 0.90$$, $$\$ 0.95$$, $$\$ 1.00$$, $$\$ 1.05$$, and $$\$1.10$$. Consinuct a profit groph. Find the breakeven spot rate at expiration. Assume that each contract covers 100,000 Euros.
A euro put with an exercise price of $$\$ 1.00$$ is priced at $$\$ 0.0435$$. Construct a simple long position in the put.

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01:54

Problem 18

Determine the profit from the following basic forrign curneng option transactions for each of the following spot rates at expiration: $$\$ 0.90$$, $$\$ 0.95$$, $$\$ 1.00$$, $$\$ 1.05$$, and $$\$1.10$$. Consinuct a profit groph. Find the breakeven spot rate at expiration. Assume that each contract covers 100,000 Euros.
Use the information in problem 16 to construct a euro covered call. Assume that the spot rate at the start is $$\$ 0.9825$$.

Anand Jangid

Numerade Educator

Problem 19

A short stock can be protected by selling a put. Determine the profit equations for this position, and identify the breakeven stock price at expiration and maximum and minimum profits.

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Problem 20

(Concept Problem) In each case examined in this chapter and in the preceding problems, we did not account for the interest on funds invested. One useful way to observe the effect of interest is to look at a conversion or a reverse conversion. Evaluate the August 165 puts and calls, and recommend a conversion or a reverse conversion. Determine the profit from the transaction if the options are held to expiration. Make sure that the profit properly accounts for the interest that accrues over the holding period.

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Problem 21

Suppose that one is considering buying a call at a particular exercise price. What reasons could be given for the alternative of buying a call at a higher exercise price? At a lower exercise price?

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Problem 22

Why is choosing an exercise price on a protective put like deciding which deductible to take on an insurance policy?

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Problem 23

Discuss and compare the two bullish strategies of buying a call and writing a put. Why would one strategy. be preferable to the other?

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Problem 24

Explain the advantages and disadvantages to a covered call writer of closing out the position prior to expiration.

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Problem 25

(Concept Problem) Another consideration in evaluating option strategies is the effect of transaction costs. Suppose that purchases and sales of an option incur a brokerage commission of 1 percent of the option's value. Purchases and sales of a share of stock incur a brokerage commission of 0.5 percent of the stock's value. If the option is exercised, there is a transaction cost on the purchase or sale of the stock. Determine the profit equations for the following strategies, assuming that the options are held to expiration and exercised if in-the-money rather than sold back. Assume that one option and/or share is used and that any shares left in the portfolio are sold.
a. Long call
b. Long put
c. Covered call
d. Protective put

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