Solutions Manual - Chapter 1 Introduction to Derivatives Question 1.1

Solutions Manual By Rüdiger Fahlenbrach For Derivatives Markets Third Edition Robert L. McDonald 1 / 4

1 ©2013 Pearson Education, Inc. Publishing as Prentice Hall Chapter 1 Introduction to Derivatives Question 1.1 This problem offers different scenarios in which some companies may have an interest to hedge their exposure to temperatures that are detrimental to their business. In answering the problem, it is useful to ask the question: Which scenario hurts the company, and how can it protect itself?

a) A soft drink manufacturer probably sells more drinks when it is abnormally hot. She dislikes

days at which it is abnormally cold because people are likely to drink less, and her business suffers. She will be interested in a cooling-degree-day futures contract because it will make payments when her usual business is slow. She hedges her business risk.

b) A ski-resort operator may fear large losses if it is warmer than usual. It is detrimental to her

business if it does not snow in the beginning of the season or if the snow is melting too fast at the end of the season. She will be interested in a heating-degree-day futures contract because it will make payments when her usual business suffers, thus compensating the losses.

c) During the summer months, an electric utility company, such as one in the south of the

United States, will sell a lot of energy during days of excessive heat because people will use their air conditioners, refrigerators, and fans more often, thus consuming a lot of energy and increasing profits for the utility company. In this scenario, the utility company will have less business during relatively colder days, and the cooling-degree-day futures offers a possibility to hedge such risk.Alternatively, we may think of a utility provider in the northeast during the winter months, a region where people use many additional electric heaters. This utility provider will make more money during unusually cold days and may be interested in a heating-degree-day contract because that contract pays off if the primary business suffers.

d) An amusement park operator fears bad weather and cold days because people will abstain

from going to the amusement park during cold days. She will buy a cooling-degree-day future to offset her losses from ticket sales with gains from the futures contract.Question 1.2 A variety of counterparties are imaginable. For one, we could think about speculators who have differences in opinion and who do not believe that we will have excessive temperature variations during the life of the futures contracts. Thus, they are willing to take the opposing side, receiving a payoff if the weather is stable.Alternatively, there may be opposing hedging needs: Compare the ski-resort operator and the soft drink manufacturer. The cooling-degree-day futures contract will pay off if the weather is relatively mild, and we saw that the resort operator will buy the futures contract. The buyer of 2 / 4

• Chapter 1/Introduction to Derivatives

©2013 Pearson Education, Inc. Publishing as Prentice Hall the cooling-degree-day futures will make a loss if the weather is cold (which means that the seller of the contract will make a gain). Since the soft drink manufacturer wants additional money if it is cold, she may be interested in taking the opposite side of the cooling-degree-day futures.Question 1.3

a) Remember that the terminology bid and ask is formulated from the market makers

perspective. Therefore, the price at which you can buy is called the ask price. Furthermore, you will have to pay the commission to your broker for the transaction. You pay:

($41.05 × 100) + $20 = $4,125.00

b) Similarly, you can sell at the market maker’s bid price. You will again have to pay a

commission, and your broker will deduct the commission from the sales price of the shares.

You receive:

($40.95 × 100) − $20 = $4,075.00

c) Your round-trip transaction costs amount to:

$4,125.00 − $4,075.00 = $50

Question 1.4 In this problem, the brokerage fee is variable and depends on the actual dollar amount of the sale/purchase of the shares. The concept of the transaction cost remains the same: If you buy the shares, the commission is added to the amount you owe, and if you sell the shares, the commission is deducted from the proceeds of the sale.

• ($41.05 × 100) + ($41.05 × 100) × 0.003 = $4,117.315

= $4,117.32

• ($40.95 × 100) − ($40.95 × 100) × 0.003 = $4,082.715

= $4,082.72

• $4,117.32 − $4,082.72 = $34.6

The variable (or proportional) brokerage fee is advantageous to us. Our round-trip transaction fees are reduced by $15.40.Question 1.5 In answering this question, it is important to remember that the market maker provides a service to the market. He stands ready to buy shares into his inventory and sell shares out of his inventory thus providing immediacy to the market. He is remunerated for this service by earning the bid-ask spread. The market maker buys the security at a price of $100, and he sells it at a 3 / 4

Chapter 1/Introduction to Derivatives 3

©2013 Pearson Education, Inc. Publishing as Prentice Hall price of $100.10. If he buys 100 shares of the security and immediately sells them to another

party, he is earns a spread of:

100 × ($100.12 − $100) = 100 × $0.12 = $12.00

Question 1.6 A short sale of XYZ entails borrowing shares of XYZ and then selling them and receiving cash.Therefore, initially, we will receive the proceeds from the sale of the asset less the proportional

commission charge:

300 × ($30.19) − 300 × ($30.19) × 0.005 = $9,057 × 0.995

= $9,011.72

When we close out the position, we will again incur the commission charge, which is added to

the purchasing cost:

300 × ($29.87) + 300 × ($29.87) × 0.005 = $8,961 × 1.005

= $9,005.81

Finally, we subtract the cost of covering the short position from our initial proceeds to receive total profits: $9,011.72 − $9,005.81 = $5.91. We can see that paying the commission charge twice significantly reduces the profits we can make.Question 1.7

a) A short sale of JKI stock entails borrowing shares of JKI, then selling them and receiving

cash, and we learned that we sell assets at the bid price. Therefore, initially, we will receive the proceeds from the sale of the asset at the bid (ignoring the commissions and interest).After 180 days, we cover the short position by buying the JKI stock, and we saw that we will

always buy at the ask. Therefore, we earn the following profit:

400 × ($25.125) − 400 × ($23.0625) = $10,050 − $9,225.00

= $825.00

b) We have to pay the commission twice. The commission will reduce our profit:

400 × ($25.125) − 400 × ($25.125) × 0.003 − (400 × [$23.0625] + 400 × [$23.0625])

= $10,050 × 0.997 − $9,225 × 1.003

= $10,019.85 − $9,252.675

= $767.175.

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