Chapter 21 - R. 1. R. 2. R. 3. R. 4. R. 5. R. 6. CHAPTER 21...

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Unformatted text preview: R. 1. R. 2. R. 3. R. 4. R. 5. R. 6. CHAPTER 21 REVIEW QUESTIONS The use of derivatives and other financial tools to manage risk. Specifically,the term financial engineering is associated with modelling of risks using risk profiles or graphs and with the use of options and futures contracts to hedge or control those risks. Core business risk is the risk caused by events that are partially or fully within the control of the firm. These risks would include poor sales or high costs relative to the firm’s competitors. Core business risk should be viewed as the potential losses that the firm faces from its own decisions and policies reagrding sales, production, employment and so forth. Environmental risk is the potential losses resulting from events outside the control of the firm such as changes in market prices of supplies, economic trends, and so forth. A risk exposure profile is typically a graph that illustrates the relationship between a variable of key importance such as firm value and some source of risk such as a market price or interest rate. An example would be a graph of the change in the total value of a banking corporation’s equity (on the veritcal axis) versus the change in general interest rate levels (on the horizontal axis). An option’s profit/loss diagram relates the profit or loss in a given option (on the vertical axis) with the price of the underlying asset (on the horizontal axis). The diagram can be formed by graphing the value of the option at expiration (against the value of the underlying asset) and then subtracting the orginal cost of the option from the values at expiration. Thus in the case of the profit loss diagram of a call, the diagram would begin on the left side with a loss equal to the original cost of the call, move horizontally from left to right until under the strike price and then move upward with a slope of 1. A put option is the right to sell an underlying asset within a given time and at a given price (the strike or exercise price). A put option tends to rise in value as the underlying asset falls in value — — just the opposite of a call option. Long positions in calls, puts and forward contracts can be formed from the value of the contracts at expiration and their initial cost (if any). The case of a long call option was detailed in Review Question #4 above. The diagram of a long put position starts on the right side of the diagram with a loss equal to the original purchase price of the put and moves left horizontally until it is located directly under the strike price — — where it begins to rise to the left with a slope of one. Positions in forward contracts typically do not involve an initial cost (although they usually require a deposit to ensure performance). The value of a long position in a forward contract rises as the price of the underlying asset rises and falls as the underlying asset falls. Therefore, the profit/loss diagram of a long 166 R. 7. R. 8. R. 9. position in a foward is an upward sloping line with a slope of one that passes through the horizontal axis at a price equal to the orginally negotiated forward price. The difference between the diagrams of long and short positions is that they are the mirror images of each other. More precisely, if the diagram of a long position were placed on the far side of a pond, the reflection in the water would be the diagram of the short position (and vice versa). The principles of diagramming are the same. The short call position starts on the left side with a profit equal to the initial proceeds from writing the call. The put starts from the right side with an analogous profit. The quickest way to diagram a combination of positions is to plot each of the component positions on top of each other on a single graph. Then, at each point along the horizontal axis, net all losses from all profits and plot the combined result. Especially useful starting points include the strike price(s) and the extreme left or right side. For example, one might start at a perticular strike price and measure the losses of the components, if any, with diagrams under the strike price and net those losses from the profits on diagrams passing over the strike price. At first glance, financial engineering seems clearly in the shareholders’ best interest because it helps eliminate or control the risk that is passed through to them. However, financial theory suggests that shareholders may be better served when risks are allowed to flow through the corporation and into their stock portfolios where the risks can be more efficiently diversified and hedged. Financial theory does offer two major potential motivations for performing financial engineering. First, financial engineering may be useful in controlling the large risks that a corporation faces that could put the firm’s financial health in jeopardy. However, as Chapter 12 details, protecting the financial health of a corporation is not always in the best interest of the shareholders. A second major potential motivation for financial engineering is to protect the firm’s management from the negative consequences of large uncontrollable risks. The idea is to control some risks so that managers will maximize shareholder wealth and will focus on the risks that they can control. R. 10.False. Without the option, the firm is in a postion such that the firm suffers when the price of the raw material rises. The value of a call option generally rises in value when the underlying asset price rises. Thus a short or written call option would cause the firm to lose even more money if the raw material rose in price. 167 3. .21. CHAPTER 21 PROBLEMS Risk Exposure Profile Charge -0 —Rama Corporation 5201) ~ l 515 0 — $101) 1 $50 $0.0 Change in Firm Value (millions of dollars) ($5.0) ($10.0) l l -0,01 0 0,01 0.02 0.03 (LCM 005 Change in Interest Rate 1 v0.04 —003 -0.02 40.05 b. The risk exposure profile resembles the risk exposure profile of a long call .a. a. .a. or a long futures contract. Thus, the best choices to hedge the risk would be a short position in a futures contract or a short position in a (low strike price) call. $50 + $X b. $50 — $X c. $50 + $X d. $50 — $X Long a call earns a profit of $X at: $50 + $2X Long a put earns a profit of $X at: $50 — $2X Writing a call earns a profit of $X at: $50 or less Writing a put earns a profit of $X at: $50 or more These answers ignore the time value of money and report a simple profit or loss without interest. Profit/Loss Diagram Short 3 Call Option Net P/L of the Posmon Value of the Underlying Asset 168 .a. Profit/Loss Diagram Long a Share of Stock I " " 1 / '8 D.- E l 3 ! CL. E * //// // _. /// / E l J l l l l L l J 1 Value of the Underlying Asset Profit/Loss Diagram A Covered Call .5 a E Q4 0 5 _ “5 a n4 2‘; _ A / Value of the Underlying Asset Note: the above three diagrams do not use the same scales. Profit/Loss Dlagram Long Call and Long Put (Straddle) 15.0 .. _ 100 A \ 1 / 33 \ // E 3,0 A \ // “E \ /.// ‘5 S 0.0 \ / 4 ~ E \\ \ E 45.0 ~— \ -10,“ I- v _. 4 , 1 _, A I I ., i 1 A . r _, I .. I 35 37.5 40 42,5 45 17 5 50 52,5 55 575 60 32 5 55 Value of the Underlying Asset Note: The previous diagram assumes a combined cost of $5 for the options. 169 Profit/Loss Diagram Long Call and Long Put (Strangle) 10.0 -_ so A \ 51‘! w \_ l \ 4.0 l~ \ 2,0 — Net P/L of the Position 0.0 ‘20 _ 4&0 J l i l l A r t l l l l ' 30 32.5 35 375 40 A25 45 47.5 50 52,5 55 57,5 60 Value of the Underlying Asset Note: The above diagram assumes a combined net cost of $2 for the options. 5. C. In both cases, the result would be a mirror image -— — with profits switched to 6. a. losses and Vice versa. The result would be like placing the orginal diagram on the far side of a smooth pond and viewing the reflection in the water. We show such a mirror image below only for the result of 5b. Profit/Loss Diagram Short Call and Short Put (Strangle) 2.0 v 0,0 // 72,0 — // — A ,0 V // \ Net FL of the Position \ / «so v / z\ -xvo A. / \ -1” i i l i i I r i i i t l i 30 32.5 35 37.: w 425 45 47.5 50 52.5 55 57.5 60 Value of the Underlying Asset Profit/Loss Diagram 2'10 Long Call and Short Put 15.0 v 100 ~ 5.0 A 0.0 —' » ~- '— 40 ~ // Net P/L of the Position *101‘ 4 45,0 [w l _20‘0 r l l i l l i J l J. l l t ,-< 35 37‘s 40 425 65 47.5 50 32,5 53 575 60 62.5 65 Value of the Underlying Asset 170 7. b. a. Note: The above diagram assumes that the call and put have the same initial price Profit/Loss Diagram Sbon Call and Long Put 15,0 w \\_ \\ 10,0 i—~ ‘\ , ; 2 10 ~ 0.0 ‘50 < Net P/L of the Position 4100 — v1.5.0 ._I_ / / A200 J I l l l 1 r > x l r l J 35 37.5 40 «12 5 ‘5 47.5 50 525 SS 57 S 60 62.5 65 Value of the Underlying Asset Note: The above diagram assumes that the call and put have the same initial price Profit/Loss Diagram Bull Spread (using Calls) 4.0 4 ~ 30 “ 0.0 Net P/L of the Position - 1.0 A /’ *ZO _3.0 I I l l l l l r l 415 45 415 50 57.5 55 57.5 60 615 Value of the Underlying Asset Note: The above diagram assumes that the $50 call cost $2 more than the $55 call. Profit/ Loss Diagram Bear Spread (using Puts) 3.0 ., 2.0 A \ 1,0 ' 0,0 _ m- Net P/L of the Position — 170 A \ A30 1 _ l , l | l | l ,l _ l 41 5 ‘3 ‘7 5 50 5.13 ‘5 S7 3 60 52 5 Value of the Underlying Asset 171 Note: The above diagram assumes that the $55 put cost $2.50 more than the $55 put. c. In both cases, the result would be a mirror image — — with profits switched to losses and vice versa. The result would be like placing the orginal diagram on the far side of a smooth pond and viewing the reflection in the water. We show such a mirror image below only for the result of 5b. Profit/Loss Diagram Butterfly Spread 21) I ‘— m —» ———-————a [aw—aw__ | \ l \ 0.0 A” V / so - \\\ {/V/ -{g c. Net P/L of the Position A10 I J l t l r l 1 ,_«~ I 40 IZVS 45 47,5 50 525 55 S75 60 Value of the Underlying Asset Note: The above diagram assumes an initial price of $1 for the $45 call. Profit/ Loss Diagram 4.0 Condor Spread 3.0 — / \ E 2.0 — / \ v / \ \ é °‘° / \i i’ -m - / \\ / \ vw A ———~——4 ,10 1 I l L I _4 . - 40 £13 45 47.3 50 52,5 55 S7 5 60 62.5 65 Value nfrhe Ilndprluina Amar Note: The above diagram assumes an initial price of $2 for the $45 call. Please note: The textbook has an error. The second line of problem 8b should have the word "short" replaced by the word "long" in both places. c. As difficult as it might be to believe, the shapes of both diagrams remain the same even though the call positions are replaced with put positions (i.e., each long call is changed to a long put and each short call is changed to a short put). 172 9. a. b. 10a. Since the initial investments (or proceeds) using the puts rather than the calls will generally differ, the height of the diagram will also generally differ. In other words, the diagram will shift upward or downward to indicate different maximum profits and losses — — but the shape will be preserved. Risk Exposure Profile Condor International $200.0 $100.0 A $0.0 ($100.0) — Change in Firm Value (millions of dollars) (510,10) A 4‘ l x l x > I l . A, 0.15 0.16 0.17 0,18 0.19 0.2 0.11 0.22 0.23 0.24 0.25 Exchange Rate (SUS per French Franc) Either a futures contract or option could be used to hedge the risks. In foreign exchange the differences between long and short futures and the differences between calls and puts are not clear since two types of money are being exchanged rather than an exchange between money and some other asset such as a stock. In this example, the futures contract or option should allow Condor to give up francs in exchange for receiving dollars. In other words, the derivative should benefit Condor if the French Franc falls in value relative to the US Dollar. A futures contract would seem to offer a more pure hedge. However, Condor may prefer an option that would hedge the downside risk but would not totally eliminate the upside potential. Of course, purchasing such an option would cost money and reduce profitability over some outcomes. The shareholder of Condor would have reduced stock price volatility assuming that there were no other offsetting positions in French Francs inside Condor International. . The shareholder of the Bank would have increased stock price volatility assuming that the bank did not have or take offsetting positions in French Francs. A shareholder who diversified between the two companies would see the two risks offset each other. In theory, the risks would be exactly offset if the shareholder had an equal percentage ownership in each company. 173 11. . . . a Profit/Loss Diagram PquallPanty 1‘0 - 0.5 v 0.0 ~— Net P/L of the Position v0.5 ‘ x -1‘0 ‘4. l 1 l u ~ I l r l l L l 40 62,5 45 47 5 SCI 52.5 55 57.5 60 61.5 65 Value of the Underlying Asset Note: Assuming that the forward contract was established at zero value and that the put and call had the same strike price, there would be no initial investment and no potential for profit or loss. 174 CHAPTER 21 DISCUSSION QUESTIONS The motivation for forming and operating a corporation is generally found from the goal of making superior decisions. Thus, there are some risks that a firm is in the business of taking. These risks are the core business risks and are generally within the control or influence of the management. However, the environmental risks are not within management’s control and are not viewed in the long run as a source of increased shareholder wealth. Therefore, firms will typically perform financial engineering on the environmentla risks and not the core business risks. Generally speaking, there has been less volatility in recent years in major financial markets such as the stock market — — despite the common public’s perception to the contrary. The increased emphasis on financial engineering may be attributed to the apparently more competitive environment. In theory, the value of a call option and a put option will decline through time as the price of the underlying asset remains constant since the "time value” of the option is decaying. Also, an option price could decline because the volatility of the underlying asset is declining. A straddle, as illustrated in Problem 5a. can generate profits to its purchaser if the underlying asset rises or falls by a large amount since it involves owning (or writing) both a call and a put. A buyer of a straddle would typically be expecting unusually high volatility in the underlying stock, while the writer of the straddle would typically be expecting lower volatility than the market anticipates. Not in the long run. By the time markets have become volatile, the prices of calls and puts have already risen to reflect the greater volatilty. Thus, straddles cost more to establish and greater price movements in the underlying asset are needed to generate profits to the buyer. When markets are stable, option prices tend to fall and so the proceeds from writing straddles are reduced and the straddle will cause losses to the writer from relatively small movements in the price of the underlying asset. Such a strategy would only be consistently successful if the person could anticipate periods of market volatility and stability in advance of other market participants. As discussed in the text and in Review Question #9, the motivation for managing risk inside of a corporation is unclear when the shareholders hold their shares inside diversified portfolios. As discussed in Problem 10c, a diversified investor who owns shares in both companies involved in a derivative security is essentially moving money from one "pocket" into another. This question is also similar to Discussion Question #7 in Chapter 15. The idea is that if the objective of a corporation is determined by shareholders and if the 175 shareholders hold diversified portfolios, why would they care about having risks managed inside of each coroporation? However, risk inside of a corporation can do more than just pass through to its shareholders. These risks can effect employees, creditors and even customers. For example, managers exposed to large financial risks may demand increased compensation or may allow those risks to influence their decision making. It is important that managers accept all positive NPV prjects and reject all negative NPV prjects. If environmental risks aren’t controlled using financial engineering, it is possible that those risks will cause managers to behave in more ways that hurt shareholders in the managers’ desire to maximize their own utility. This would be an example of an agency cost. Derivatives can provide an extremely cost effective method of transferring risk and should be seriously considered when there are agency costs and/or other potential costs to allowing the risks to remain unhedged. 176 ...
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This note was uploaded on 11/30/2011 for the course FINOPMGT 301 taught by Professor Lacey during the Spring '10 term at UMass (Amherst).

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Chapter 21 - R. 1. R. 2. R. 3. R. 4. R. 5. R. 6. CHAPTER 21...

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