博迪《金融学》课后习题答案 中文+英文博迪《金融学》课后习题答案 中文+英文

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CHAPTER 10 AN OVERVIEW OF RISK MANAGEMENT Objectives  To explore how risk affects financial decision-making.  To provide a conceptual framework for the management of risk.  To explain how the financial system facilitates the efficient allocation of risk-bearing. Outline 10.1 What Is Risk? 10.2 Risk and Economic Decisions 10.3 The Risk Management Process 10.4 The Three Dimensions of Risk Transfer 10.5 Risk Transfer and Economic Efficiency 10.6 Institutions for Risk Management 10.7 Portfolio Theory: Quantitative Analysis for Optimal Risk Management 10.8 Probability Distributions of Returns Summary  Risk is defined as uncertainty that matters to people. Risk management is the process of formulating the benefit- cost trade-offs of risk-reduction and deciding on a course of action to take. Portfolio theory is the quantitative analysis of those trade-offs to find an optimal course of action.  All risks are ultimately borne by people in their capacity as consumers, stakeholders of firms and other economic organizations, or taxpayers.  The riskiness of an asset or a transaction cannot be assessed in isolation or in the abstract; it depends on the specific frame of reference. In one context, the purchase or sale of a particular asset may add to one’s risk exposure; in another, the same transaction may be risk-reducing.  Speculators are investors who take positions that increase their exposure to certain risks in the hope of increasing their wealth. In contrast, hedgers take positions to reduce their exposures. The same person can be a speculator on some exposures and a hedger on others.  Many resource-allocation decisions, such as saving, investment, and financing decisions, are significantly influenced by the presence of risk and therefore are partly risk-management decisions.  We distinguish among five major categories of risk exposures for households: sickness, disability, and death; job loss; consumer-durable asset risk; liability risk; and financial asset risk.  Firms face several categories of risks: production risk, price risk of outputs, and price risk of inputs.  There are five steps in the risk-management process: risk identification, risk assessment, selection of risk- management techniques, implementation, review.  There are four techniques of risk management: risk avoidance, loss prevention and control, risk retention, risk transfer.  There are three dimensions of risk transfer: hedging, insuring, and diversifying.  Diversification improves welfare by spreading risks among many people, so that the existing uncertainty matters less.  From society’s perspective risk-management institutions contribute to economic efficiency in two important ways. First, they shift risk away from those who are least willing or able to bear it to those who are most willing to bear it. Second, they cause a reallocation of resources to production and consumption in accordance with the new distribution of risk-bearing. By allowing people to reduce their exposure to the risk of undertaking certain business ventures, they may encourage entrepreneurial behavior that can have a benefit to society.  Over the centuries, various economic organizations and contractual arrangements have evolved to facilitate a more efficient allocation of risk-bearing by expanding the scope of diversification and the types of risk that are shifted.  Among the factors limiting the efficient allocation of risks are transactions costs and problems of adverse selection and moral hazard.Instructor’s Manual Chapter 10 Page 126 Solutions to Problems at End of Chapter On the Nature of Risk and Risk Management 1. Suppose that you and a friend have decided to go to a movie together next Saturday. You will select any movie for which tickets are available when you get to the theater. Is this a risky situation for you? Explain. Now suppose that your friend has already purchased a ticket for a movie that is going to be released this Saturday. Why is this a risky situation? How would you deal with the risk? SOLUTION: No, the uncertainty doesn’t represent risk since you do not care which movie you see. However, if your friend has a ticket already, and if you wait till Saturday to buy yours, the show may be sold out. To eliminate the risk that you may not be able to sit with your friend and see the same movie, you might buy your ticket in advance. 2. Suppose you are aware of the following investment opportunity: You could open a coffee shop around the corner from your home for $25,000. If business is strong, you could net $15,000 in after-tax cash flows each year over the next 5 years. a. If you knew for certain the business would be a success, would this be a risky investment? b. Now assume this is a risky venture and that there is a 50% chance it is a success and a 50% chance you go bankrupt within 2 years. You decide to go ahead and invest. If the business subsequently goes bankrupt, did you make the wrong decision based on the information you had at the time? Why or why not? SOLUTION: a. No, this investment would not be risky. b. No, you did not make a “wrong” decision. When you made your decision, you did not know for certain that the company would go bankrupt. You decided to invest for many reasons, including the possibility of making a lot of money. Given your tolerance for risk and the fact that you based our decision on the information available at the time, your decision was not wrong and may have been optimal at the time. 3. Suppose you are a pension fund manager and you know today that you need to make a $100,000 payment in 3 months. a. What would be a risk-free investment for you? b. If you had to make that payment in 20 years instead, what would be a risk free investment? c. What do you conclude from your answers to Parts a and b of this question? SOLUTION: a. A risk-free investment for you would be a Treasury Bill (default risk free) which matures in exactly 3 months. b. A risk-free investment would be a zero coupon U.S. Treasury security maturing in 20 years and which would have the same single payment of $100,000. c. Because risk is dependent upon circumstances, what is risk-free for one individual may be risky for another too. There can be any number of risk-free investments depending upon circumstances. Your investment time horizon is critical to choosing the best risk-free investment (so payments in can exactly match payments out so that you are left with no risk). 4. Is it riskier to make a loan denominated in dollars or in yen? SOLUTION: It depends on the context. For people whose income and expenses are denominated in dollars (perhaps because they live in the U.S), denominating a loan in yen would be riskier than denominating it in dollars. But for someone whose income and expenses are denominated in yen, denominating the loan in yen would be less risky than in dollars.Instructor’s Manual Chapter 10 Page 127 5. Which risk management technique has been chosen in each of the following situations?  Installing a smoke detector in your home  Investing savings in T-bills rather than in stocks  Deciding not to purchase collision insurance on your car  Purchasing a life insurance policy for yourself SOLUTION:  Loss prevention and control.  Risk avoidance  Risk retention  Risk transfer 6. You are considering a choice between investing $1,000 in a conventional one-year T-Bill offering an interest rate of 8% and a one-year Index-Linked Inflation Plus T-Bill offering 3% plus the rate of inflation. a. Which is the safer investment? b. Which offers the higher expected return? c. What is the real return on the Index-Linked Bond? SOLUTION: a. The inflation-indexed T-Bill offers a fixed real rate of return of 3% over the life of the investment. The real return on the conventional T-Bill’s real return depends upon the expected rate of inflation over the life of the investment. The safer investment is the Inflation Plus T-Bill. b. The real rate of return on the conventional T-Bill depends upon the expected rate of inflation over the life of the investment. You do not know which expected return is higher unless you know what inflation is expected to be. c. The real return on the index-linked T-Bill is 3%. Hedging and Insurance 7. Suppose you are interested in financing your new home purchase. You have your choice of a myriad financing options. You could enter into any one of the following agreements: 8% fixed rate for 7 years, 8.5% fixed rate for 15 years, 9% fixed for 30 years. In addition, you could finance with a 30-year variable rate that begins at 5% and increases and decreases with the prime rate, or you could finance with a 30- year variable rate that begins at 6% with ceilings of 2% per year to a maximum of 12% and no minimum. a. Suppose you believe that interest rates are on the rise. If you want to completely eliminate your risk of rising interest rates for the longest period of time, which option should you choose? b. Would you consider that hedging or insuring? Why? c. What does your risk management decision “cost” you in terms of quoted interest rates during the first year? SOLUTION: a. You would choose the 30-year fixed rate at 9%. b. That would be a hedge because you have eliminated both the upside (declining rates) or downside ( rising rates). c. This costs me at least 4% since I could get a variable rate loan at 5%.Instructor’s Manual Chapter 10 Page 128 8. Referring to the information in problem 7, answer the following: a. Suppose you believe interest rates are going to fall, which option should you choose? b. What risk do you face in that transaction? c. How might you insure against that risk? What does that cost you (in terms of quoted interest rates?). SOLUTION: a. You would want one of the variable rate options, in particular the variable loan tied to the prime rate, currently equal to 5%. b. You face the risk of rising rates. c. You could insure against that risk by purchasing the option to have a 12% ceiling on the rate (2% increase per year. This option cost you 1% (the difference between 6% and 5%). 9. Suppose you are thinking of investing in real estate. How might you achieve a diversified real estate investment? SOLUTION:  You could own several different buildings in the same general area.  You could own several different buildings in different geographic areas.  You could sell some of your equity ownership to other owners to lower your own individual exposure to declining market values. 10. Suppose the following represents the historical returns for Microsoft and Lotus Development Corporation:Historical Returns Year MSFT LOTS 1 10% 9% 2 15% 12% 3 -12% -7% 4 20% 18% 5 7% 5% a. What is the mean return for Microsoft? For Lotus? b. What is the standard deviation of returns for Microsoft? For Lotus? c. Suppose the returns for Microsoft and Lotus have normally distributed returns with means and standard deviations calculated above. For each stock, determine the range of returns within one expected standard deviation of the mean and within two standard deviations of the mean. SOLUTION: a. Mean return Microsoft: 8.0%; Lotus: 7.4% b. If you use the formula for the standard deviation based on a sample of size n: You find that the standard deviations are: MSFT: 10.94%; Lotus: 8.357%. However, if you use the formula for the population standard deviation: You find that the standard deviations are: MSFT 12.23% and LOTS 9.34%. c. Range of returns within 1 standard deviation Microsoft: -2.94% to +18.94% Range of returns within 1 standard deviation Lotus: -0.957% to + 15.76% Range of returns within 2 standard deviations Microsoft: -13.88% to +29.88% Range of returns within 1 standard deviation Lotus: -9.31% to + 24.11%  ( )      1 2 1 n r r i i n  ( )       1 1 2 1 n r r i i nCHAPTER 11 HEDGING, INSURING, AND DIVERSIFYING Objective  To explain the various methods and institutional mechanisms for the transfer of risk through the financial system by hedging, insuring, and diversifying. Outline 11.1 Using Forward and Futures Contracts to Hedge Risk 11.2 Hedging Foreign-Exchange Risk with Swap Contracts 11.3 Hedging Shortfall-Risk by Matching Assets to Liabilities 11.4 Minimizing the Cost of Hedging 11.5 Insuring versus Hedging 11.6 Basic Features of Insurance Contracts 11.7 Financial Guarantees 11.8 Caps and Floors on Interest Rates 11.9 Options as Insurance 11.10 The Diversification Principle 11.11 Diversification and the Cost of Insurance 11.12 The Fallacy of Time Diversification Summary  Market mechanisms for hedging risk exposures are: forward and futures contracts, swaps, and matching assets to liabilities.  A forward contract is the obligation to deliver a specified asset at a specified future delivery date at a specified price. Futures contracts are standardized forward contracts that are traded on exchanges.  A swap contract consists of two parties exchanging a series of payments at specified intervals over a specified period of time. A swap contract could call for the exchange of almost anything. In current practice, however, most swap contracts involve the exchange of commodities, currencies, or securities.  Financial intermediaries such as insurance companies often hedge their customer liabilities by matching their assets to their liabilities. This is done to reduce the risk of a shortfall.  When there is more than one way to hedge a given risk exposure, the mechanism chosen should be the one that minimizes the cost of achieving the desired reduction of risk.  There is a fundamental difference between insuring and hedging. When you hedge, you eliminate the risk of loss by giving up the potential for gain. When you insure, you pay a premium to eliminate the risk of loss and retain the potential for gain.  Put options on stocks protect against losses from a decline in stock prices.  Financial guarantees are insurance against credit risk. Interest rate floors and caps offer insurance against interest-rate risk to lenders and borrowers, respectively. A put option on a bond offers the bondholder insurance against both default risk and interest rate risk.  The more diversified are the risks in a portfolio of a given size, the less it will cost to insure the portfolio against a loss. Therefore there is a cost advantage to an individual or a firm to integrate the process of insuring against all of its risks.Instructor’s Manual Chapter 11 Page 130 Solutions to Problems at End of Chapter Hedging Price Risk with Futures Contracts 1. Suppose you own a grove of orange trees. The harvest is still two months away but you are concerned about price risk. You want to guarantee that you will receive $1.00 per pound in two months regardless of what the spot price is at that time. You are selling 250,000 pounds. a. Show the economics of a short transaction in the forward market if the spot price on delivery date is $0.75 per pound, $1.00 per pound, or $1.25 per pound. b. What would have happened to you if you had not entered the hedge and each scenario is equally likely? c. What is the variability of your receipts after the hedge is in place? SOLUTION: a. Orange Grower’s Transaction $0.75/pound $1.00/pound $1.25/pound Proceeds from sale of orange juice $187,500 $250,000 $312,500 Cash flow from futures contract $62,500 paid to grower $0 $62,500 paid by grower Total receipts $250,000 $250,000 $250,000 b. You would have had a 1/3 chance each of paying out $187,500 (less than expected), $250,000 (the same as expected) or $312,500 (more than expected). c. No variability. Receipts are always equal to $250,000. Mutual Benefits of Hedge Transaction 2. Suppose in six months’ time the cost of a gallon of heating oil will either be $0.90 or $1.10. The current price is $1.00 per gallon. a. What are the risks faced by a reseller of heating oil that has a large inventory on hand? What are the risks faced by a large user of heating oil with a very small inventory? b. How can these two parties use the heating oil futures market to reduce their risks and lock in a price of $1.00 per gallon? Assume each contract is for 50,000 gallons and they each need to hedge 100,000 gallons. c. Can you say that each party has been made better off? Why or why not? SOLUTION: a. Reseller would lose money if the price of oil fell to $0.90 per gallon because he purchased the oil at $1.00. The user of heating oil would face the risk of rising heating prices. b. Heating Oil User goes long two futures contracts Heating Oil User Transaction $.90/gallon $1.10/gallon Cost of heating oil purchased from supplier $900,000 $1,100,000 Cash flow from futures contract $100,000 paid by Oil User $100,000 paid to Oil User Total outlay $1,000,000 $1,000,000 Heating Oil Reseller goes short two futures contracts Heating Oil User Transaction $.90/gallon $1.10/gallon Proceeds from sale of heating oil $900,000 $1,100,000 Cash flow from futures contract $100,000 paid to Oil Reseller $100,000 paid by Oil Reseller Total outlay $1,000,000 $1,000,000 c. Even though it appears that in each scenario one party has benefited at the expense of the other, both have really benefited because both parties were able to lock in a price of $1.00 per gallon and eliminate all risk.Instructor’s Manual Chapter 11 Page 131 Hedging Price Risk with Futures Contract 3. Suppose you are chief financial officer of Hotels International and you purchase a large quantity of coffee each month. You are concerned about the price of coffee one month from now. You want to guarantee that you will not pay more than $1.50 per pound for 35,000 pounds. You do not want to pay for insurance but you do want to lock in a price of $1.50 per pound for 35,000 pounds. a. Show the economics of a futures transaction if the spot price on the delivery date is $1.25, $1.50, or $1.75. b. What is the variability of Hotels International total outlays under the futures contract? c. If at the time of delivery coffee is $1.25 per pound, should you have forgone entering into the futures contract? Why or why not? SOLUTION: a. CFO Hotels’ Transaction $1.25/pound $1.50/pound $1.75/pound Cost of coffee purchased from supplier $43,750 $52,500 $61,250 Cash flow from futures contract $8,750 paid by Hotels $0 $8,750 paid to Hotels Total outlay $52,500 $52,500 $52,500 b. Outlays are fixed at $52,500. c. Regardless of the outcome of the price of coffee at the delivery date, the Treasurer did the right transaction if he wanted to lock in a price of $1.50 per pound. Although he gave up any opportunity to pay a lower price, he also guaranteed that he would never pay more than $1.50 per pound. A hedge transaction is only useful if one does not know the future price of some item, hence the need to hedge the risk of uncertainty. Risk Reduction Versus Speculation 4. Suppose you are treasurer of a large municipality in Michigan and you are investing in cattle futures. You purchase futures contracts worth 400,000 pounds of cattle with an exercise price of $0.60 per pound and an expiration date in one month. a. Show the economics of a futures transaction if the price of cattle at delivery date is $0.40 per pound, $0.60 per pound, or $0.80 per pound. b. Is this a risk-reducing transaction? c. Would your answer to “b” be different if the treasurer were investing in oil futures? What about interest rate futures? SOLUTION: a. Treasurer Transaction $.40/pound $.60/pound $.70/pound Cash flow from futures contract - $80,000 $0 + $80,000 b. This is not a risk-reducing transaction because you are not hedging a similar but opposite exposure. c. Oil futures = same answer as “b” above. Interest rate futures depends upon the context. Are you offsetting some interest risk you currently have in your portfolio or are you taking what is said to be a “naked” or unhedged position?Instructor’s Manual Chapter 11 Page 132 Risk Reduction versus Speculation 5. Your cousin is a hog farmer and he invests in pork belly futures and options contracts. He has told you that he believes pork belly prices are on the rise. You decide to purchase a call option on pork bellies with a strike price of $0.50 per pound. That way, if pork belly prices go up, you can exercise the call, buy the pork bellies and sell them for the higher spot price. Assume the price of an option on 40,000 pounds is $1,000 and you purchase five options for $5,000 on 200,000 pounds. a. Would this be a risk-reducing or speculative transaction for you? b. What is your downside risk in dollars and percentage terms? c. If the price per pound increases to $0.55 per pound, how much would you net after paying for the options? SOLUTION: a. Because this would be an unhedged position for you, this would be speculative. b. $5,000 (the options expire, worthless) or -100 c. .55-.50 =$ .05/pound .05* 200,000 pounds = $10,000 Net: $10,000 - $5,000 = $5,000 Hedging Price and Availability Risk with Forward Contracts 6. Suppose you are expecting your fourth child in six months and you need a bigger car. You have your eye on a used three-year old Minivan which currently costs approximately $10,000. You are concerned about the pricing and availability of this specific car in six months’ time, but you won’t have enough money to purchase the car until six months from today. a. How could you advertise in the newspaper for a forward contract with a counterparty that would eliminate your risk? b. Who would be willing to take the short position on your forward contract? (Who is the likely counterparty)? SOLUTION: a. You could advertise that you are willing to pay $10,000 for a Minivan with specific characteristics but that you do not want to take delivery for 6 months. b. Anyone who wants to sell his Minivan in 6 months and is worried about finding a buyer willing to pay the current price of $10,000. Hedging Price Risk with Forward Contracts 7. Suppose you are interested in taking a safari to Kenya, Africa, next summer but are worried about the price of the trip, which has ranged from $2,500 to $3,500 over the past five years. The current price is $3,000. a. How could you enter into a forward contract with a safari sponsor to eliminate your price risk? b. Why would the safari sponsor be interested in accepting your forward contract? SOLUTION: a. Enter into an agreement today to pay $3,000 next year. b. As sponsor, they may be concerned about falling prices and may be happy to lock-in your reservation at the current price. Hedging Foreign Exchange Risk with Swap Contracts 8. Suppose you are treasurer of Photo Processing, Inc. Approximately 50% of your sales are in the United States (headquarters) whereas 40% are in Japan and 10% are in the rest of the world. You are concerned about the dollar value of your Japanese sales over the next five years. Japanese sales are expected to be 2,700,000,000 yen each year over the next five years. The current dollar/yen exchange rate is 90 yen to the U.S. dollar and you would be happy if this would remain so during all five years. a. How could you use swap contracts to eliminate the risk that the dollar depreciates against the yen? b. What is the notional amount of your swap contract per year? c. Who might take the opposite side of this swap contract (who is a logical counterparty)?Instructor’s Manual Chapter 11 Page 133 SOLUTION: a. Enter into a swap contract with a counterparty whereby you would agree now to receive or pay each year an amount of cash equal to 2,700,000,000 yen times the difference between the 90 yen/dollar forward rate and spot rate at the time. b. $30,000,000 per year or 2.7 billion yen per year. c. Anyone or any company interested in hedging a possible appreciation in the dollar versus the yen. Perhaps a Japanese company with sales in the US. Hedging Foreign Exchange Risk with Swap Contracts 9. Suppose you are a consultant living in the United States and have been engaged by a French company to perform a market study, which should take 18 months to complete. They are planning to pay you 100,000 francs monthly. The current exchange rate is $0.20 per franc. You are concerned that the French franc will strengthen versus the dollar and that you will receive fewer U.S. dollars each month. The French company does not want to have to come up with dollars to pay you each month and is not willing to agree to a fixed exchange rate of $0.20 per franc. a. How could you use swap contracts and a financial intermediary to eliminate your risk? b. Suppose that in the sixth month, the spot price of the franc is $0.18. Without the swap contract, what would be your cash revenues in dollars? With the swap contract what will they be? c. Suppose that in the tenth month, the spot price of the franc is $0.25. Without the swap contract, what would be your cash revenues in dollars? With the swap contract what will they be? SOLUTION: a. On each settlement date you agree to receive or pay an amount of cash equal to 100,000 francs times the difference between $0.20 and the spot price. b. $100,000 x .18 = $18,000. With the swap contract: You will receive 100,000 francs, which you sell for $18,000. You then receive 100,000 x (.20-.18) = $2,000 from the counterparty. Total = $20,000. c. $100,000 x .25 = $25,000. With the swap contract: You will receive 100,000 francs, which you sell for $25,000. You then pay 100,000 x (.20-.25) = -$5,000 from the swap contract Total = $20,000. Matching Assets and Liabilities 10. At Montgomery Bank and Trust most of its liabilities are customer deposits, which earn a variable interest rate tied to the three-month Treasury bill rate. On the other hand, most of its assets are fixed-rate loans and mortgages. Montgomery Bank and Trust does not want to stop selling fixed-rate loans and mortgages, but it is worried about rising interest rates, which would cut into their profits. How could Montgomery Bank and Trust develop a hedge against interest rate risk without selling the loans? Assume that its exposure is $100 million at an average fixed rate of 9% while paying out T-bills + 75 basis points. SOLUTION: Montgomery Bank and Trust could enter into an interest rate swap with a counterparty. Montgomery would pay a fixed rate which would be something less than 9% and would receive a floating rate equal to T-Bills + 75 basis points. The Bank would then be guaranteed a profit which would be the spread between the fixed rate it receives on loans and the fixed rate it pays out. The floating rate exposures cancel each other out with equivalent inflows and outflows. Choosing Among Hedging Options 11. Suppose you are chief financial officer of an Oil Company. You are constantly presented with ways to hedge your exposur
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