An Introduction to Derivative Securities, Financial Markets, and Risk Management, 1st Edition Solution Manual

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SOLUTIONS MANUALAn Introduction to DerivativeSecurities, Financial Markets,and Risk ManagementRobert A. JarrowCORNELL UNIVERSITYArkadev ChatterjeaTHE UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL

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1CHAPTER 1Derivatives and Risk Management1.1.What is a derivative security? Give an example of a derivative and explain why it isa derivative.ANSWERA derivative security is a financial contract that derives its value from the price of anunderlying asset such as a stock or a commodity, or from the value of an underlying notionalvariable such as a stock index or an interest rate (see Section 1.1).Consider a forward contract to trade 50 ounces of gold three months from today at aforward price ofF=$1,500 per ounce. The spot price of the underlying commodity golddetermines this derivative’s payoff. For example, if the spot price of gold isS(T)=$1,510 perounce at timeT=3 months, then the buyer of this forward contract buys gold worth $1,510 for$1,500. Her profit is [S(T) –F]⋅Number of units=(1,510 – 1,500)⋅50=$500. This is the seller’sloss because derivative trading is a zero-sum game; that is, for each buyer there is a seller.1.2.List some major applications of derivatives.ANSWERSome applications of derivatives:• They help generate a variety of future payoffs, which makes the market more “complete.”• They enable trades at lower transactions costs.• Hedgers can use them to cheaply reduce preexisting risk in their economic activities.Speculators can take leveraged positions without tying up too much capital.• They help traders overcome market restrictions. For example, an exchange may restricttraders from short-selling a stock in a falling market, but a trader can adopt a similarposition by buying a put option.• They promote a more efficient allocation of risk by allowing the risk of economictransactions to be shifted to dealers who can better manage these risks.

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2|Chapter 1• They facilitate the process of price discovery. For example, futures traders, by placing bidsand offers to trade various quantities of the underlying commodity at different prices,reveal some of their information, which gets built into the market price of the underlyingcommodity. Many people watch the futures price to get a sense of the demand and supplysituation in the months and years ahead.1.3.Evaluate the following statement: “Hedging and speculation go hand in hand in thederivatives market.”ANSWERThis statement provides a good description of derivatives market activity. Many traders buy orsell derivatives to hedge some preexisting risk in a portfolio or business. It is often very hardto find counterparties with exactly opposite hedging needs. For this reason, a speculatorusually takes the other side of the hedger’s trade. Since derivatives trade in zero-supplymarkets, for each buyer there must be a seller. Speculators make the market more liquid.Consider an example: A gold mining firm sells 100,000 ounces of gold through aforward contract. The gold mining firm may not find a jewelry manufacturer who wants tosimultaneously buy the same quantity of gold on the same future date. So a speculator (whois often a dealer) steps in and becomes the counterparty to the trade providing liquidity to theforward market.1.4.What risks does a business face?ANSWERA business may face a variety of risks such as credit risk, legal risk, operational risk, andregulatory risk. However, there are three major kinds of market risk that affect mostbusinesses: currency risk, interest rate risk, and (in case of nonfinancial companies)commodity price risk (see Section 1.7).1.5.Explain why financial futures have replaced agricultural futures as the most activelytraded contracts.ANSWERBefore the 1970s, governments succeeded in keeping many macroeconomic variables likeexchange rates and interest rates relatively stable. Traders were mostly concerned aboutcommodity price risk and they used agricultural futures to manage this risk.During the 1970s, many of these macroeconomic variables became volatile.Dismantling of the Bretton Woods system (1971) made exchange rates more volatile. Oil shocksand other supply-side disturbances led to double-digit inflation. Inflation premiums soon gotbuilt into interest rates, which increased to double-digit levels and became more volatile.Exchanges responded to this increased volatility by creating financial futures forhedging these risks. Many of these products became very popu lar and eventually replacedagricultural futures as the most actively traded contracts. Because the demand for hedgingfinancial risks in larger than the demand for hedging price risks for agriculturalcommodities, financial futures have become the more actively traded contracts.

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Derivatives and Risk Management|31.6.Explain why derivatives are zero-sum games.ANSWERA derivative obtains its value from something else: a stock price, an exchange rate, an interestrate, or even an index. Unlike a stock or a bond, a derivative does not have a preexistingsupply. Hence, it is described as a “zero-supply” contract. It gets created the moment a traderdecides to trade a derivative and another trader accepts the opposite side of the transaction.These traders are called counterparties. Consequently, one counterparty’s gain creates a lossof equal magnitude for the other counterparty. Their payoffs, being of equal magnitude, addup to zero. Hence, trading derivatives is a zero-sum game (see Example 1.1).1.7.Explain why all risks cannot be hedged. Give an example of a risk that cannot be hedged.ANSWERNot all risks can be hedged because of moral hazard. For example, a trader would not like tobe in a situation where a counterparty’s actions affect the outcome. Thus, it is very hard tohedge operational risk, which is the risk of a loss due to events like human error, faultymanagement, and fraud. Because of moral hazard, no trader (visualize, as an example, aninsurance company insuring a bank against operational risk) would trade a “derivative” thatpays the counterparty for mistakes like pressing the wrong computer button and entering thewrong trade (see Section 1.7).1.8.What is a notional variable, and how does it differ from an asset’s price?ANSWERNotional variables are notions (computed variables) based on asset prices and otherquantities. Examples include interest rates, inflation rates, stock indexes, and weather indices.A traded asset, such as a stock, has a price at which it trades in the market. By contrast, acomputed stock index, which is an average of stock prices, does not directly trade and doesnot have its own market price.1.9.Explain how derivatives give traders high leverage.ANSWERA derivative’s payoff is determined by the evolution of some commodity’s price over apredetermined future time period. One can collect these payoffs by paying a premium incase of options or by posting collaterals or margin deposits in case of forwards and futures.The premium is usually a small fraction of the commodity’s price. Collaterals and marginsare also a small fraction of the commodity’s price because they depend on the past pricevolatility—an exchange may set the margin for a future contract at less than 5 percent of thecommodity price. For these reasons, derivatives provide leverage because these transactionsare significantly cheaper or require far less capital commitment than an outright purchase orshort sale of the commodity. Leverage is the amount of borrowing implicit in a derivativeposition. This leverage implies that for small changes in the underlying security’s price, largechanges in the derivative security’s price results.

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4|Chapter 11.10.Explain the essence of Merton Miller’s argument explaining what spurs financialinnovation.ANSWERMerton Miller argued in a 1986 article thatregulations and taxes cause financial innovation.The reason is that derivative securities are often created to circumvent government regulationsthat prohibit otherwise lucrative transactions. And because most countries tax income fromdifferent sources (and uses) at different rates, financial innovations are often designed to savetax dollars as well. He cites examples like Eurodollars, Eurobonds, and Swaps that wereinitiated to circumvent restrictive regulations and taxes (see Section 1.2 and Extension 1.1).1.11.Explain the essence of Ronald Coase’s argument explaining what spurs financialinnovation.ANSWERRonald Coase argued in the article, “The Nature of the Firm” (1937), that transactions incurcosts, which come from “negotiations to be undertaken, contracts . . . to be drawn up,inspections . . . to be made, arrangements . . . to be made to settle disputes, and so on,” and firmsoften appear to lower these transactions costs. With respect to financial markets, marketparticipants often trade where they can achieve their objectives at minimum costs. Financialderivatives are often created so that these costs are minimized as well.An example is the migration of traders during the 1990s from Treasury securities andtheir associated derivatives to Eurodollars and their related derivatives that are free from Fedregulations, are unaffected by peculiarities of the Treasury security auction cycle, and havelower liquidity costs.Another example would be exchange-traded funds (ETFs), which are securities givingthe holder fractional ownership rights over a basket of securities. An ETF’s structure allowsit to lower many kinds of transactions costs vis-à-vis a mutual fund with a similar investmentobjective. Unlike a mutual fund, which has daily or (at the most) hourly pricing, an ETFbehaves much like a common stock—it trades continuously during trading hours, it can beshorted, it may be traded on margin, and it can even have derivatives (such as calls and puts)written on them.1.12.Does more volatility in a market lead to more use of financial derivatives? Explainyour answer.ANSWERYes, increased volatility leads to more use of financial derivatives. More volatility increasesthe risk of a trader’s portfolio or a firm’s balance sheet. This risk is often unwanted, and it canbe hedged with derivatives. This hedging motive in the presence of volatile prices generatesthe demand for the trading of derivatives. Examples of this include options trading on stockmarket indexes, foreign currencies, interest rates, and commodities. Without price volatility, thevast derivatives market would disappear leaving behind just credit derivatives for managingcredit risk. Note, however, that although volatility is the lifeblood of derivatives trading,extreme volatility sometimes destroys markets (as it happens during times of market crashes).

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Derivatives and Risk Management|51.13.When the international banking regulators defined risk in their 1994 report, whatdefinition of risk did they have in mind? How does this compare with the definition of riskfrom modern portfolio theory?ANSWERThe international regulators wanted to cover all aspects of risk associated with securitytrading: market risk, credit risk (including settlement risk), liquidity risk, operational risk,and legal risk. The last four definitions of risk deal with the nitty-gritty real-world problemsof implementing a derivatives trade.The definition of risk given in connection with the capital asset pricing model andmodern portfolio theory looks at portfolio risk, both diversifiable and nondiversifiable,caused by the randomness in asset prices. The randomness in asset prices usually consideredis that due to market risk, which is essential for understanding an investor’s risk-return trade-off. This definition is more restrictive than the regulators’ definition.1.14.What’s the difference between real and financial assets?ANSWERReal assets include land, buildings, machines, and commodities. Financial assets includestocks, bonds, currencies, which are claims on real assets. Both real and financial assets havetangible values. Both real and financial assets have derivatives traded on them.1.15.Explain the differences between market risk, credit risk, liquidity risk, andoperational risk.ANSWERSee the Basel Committee’sRisk Management Guidelines for Derivatives(July 1994) fordefinitions of these risks:•Market riskis the risk to an institution’s financial condition resulting from adversemovements in the level or volatility of market prices.•Credit risk(including settlement risk) is the risk that a counterparty will fail to perform onan obligation.•Liquidity riskcan be of two types: one related to specific assets and the other related to thegeneral funding of the institution’s activities. The former is the risk that an institution maynot be able to easily unwind a particular asset position near the previous market pricebecause of market disruptions. Funding liquidity risk is the risk that the institution will beunable to meet its payment obligations in the event of margin calls.•Operational risk(also known as operations risk) is the risk that deficiencies ininformation systems or internal controls will result in unexpected loss. This risk isassociated with human error, system failures, and inadequate procedures and controls.(Legal riskis the risk that contracts are not legally enforceable or documented correctly.We include this as part of operational risk.)

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6|Chapter 11.16.Briefly present Warren Buffett’s and Alan Greenspan’s views on derivatives.ANSWERAlthough supportive of plain vanilla derivatives that are used by farmers and other economicagents to hedge input and output price risks, Warren Buffett expressed a strong dislike forcomplex over-the-counter derivatives. In 2002, he even characterized them as “time bombs,both for the parties that deal in them and the economic system.” This prophecy proved to becorrect in light of large derivatives-related losses suffered by financial institutions during2007 and 2008, which contributed to the severe economic downturn. Interestingly, in 2008Buffett’s company sold 251 long dated European put options in the over-the-counter marketbecause they were attractively priced.By contrast, former Fed chairman Alan Greenspan (served 1987–2006) opined in a 1999speech that derivatives “unbundle” risks by carefully measuring and allocating them “to thoseinvestors most able and willing to take it,” a phenomenon that has contributed to a moreefficient allocation of capital. Greenspan reversed his position somewhat before Congress in2008 when he testified that he “had put too much faith in the self-correcting power of freemarkets and had failed to anticipate the self-destructive power of wanton mortgage lending.”1.17.Consider the situation in sunny Southern California in 2005, where house prices haveskyrocketed over the last few years and are at an all-time high. Nathan, a software engineer,buys a second home for $1.5 million. Five years back, he bought his first home in the sameregion for $350,000 and financed it with a thirty-year mortgage. He has paid off $150,000 ofthe first loan. His first home is currently worth $900,000. Nathan plans to rent out his firsthome and move into the second. Is Nathan speculating or hedging?ANSWERNathan is speculating. He has assumed the price risk on two properties whose total value is$1.5 million plus $0.9 million, or $2.4 million.1.18.During the early years of the new millennium, many economists described the pastfew decades as the period of the Great Moderation. For example,• an empirical study by economists Olivier Blanchard and John Simon found that “thevariability of quarterly growth in real output (as measured by its standard deviation) haddeclined by half since the mid-1980s, while the variability of quarterly inflation haddeclined by about two thirds.”• an article titled “Upheavals Show End of Volatility Is Just a Myth” in theWall StreetJournal, dated March 19, 2008, observed that an important measure of stock marketvolatility, “the Chicago Board Options Exchange’s volatility index, had plunged about 75%since October 2002, the end of the latest bear market, through early 2007”; the article alsonoted that “in the past 25 years, the economy has spent only 16 months in recession,compared with more than 60 months for the previous quarter century.”a.What were the explanations given for the Great Moderation?b.Does the experience of the US economy during January 2007 to December 2010 stilljustify characterizing this as a period of Great Moderation?

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Derivatives and Risk Management|7Report (1) quarterly values for changes in the gross domestic product, (2) quarterly values forchanges in the inflation rate, and (3) the volatility VIX Index value during this period tosupport your answer.ANSWERa.The chairman of the Federal Reserve System, Ben Bernanke, in a 2004 speech providedthree explanations for the Great Moderation: structural change (changes in economicinstitutions, technology, or other features of the economy), improved macroeconomicpolicies, and good luck (“the shocks hitting the economy became smaller and moreinfrequent”).b.Data presented in the following table suggests that January 2007 to December 2010 cannotbe considered a period of “Great Moderation”; rather, this period is considered to belong tothe “Great Recession.” The table reports:1. Quarterly values for changes in the gross domestic product.2. Quarterly values for changes in the inflation rate (which we have calculated from the CPIvalues, assuming 1982–84=100).3. Volatility index VIX’s value at the end of each quarter during January 2007 to December2010.QuartersGDP PercentChange(based oncurrentdollars)GDP PercentChange(based onchained 2005dollars)ConsumerPriceIndexAnnualInflation Rate(measuredover eachquarter)DateVIX at Closeon the LastTrading Dayof theQuarter201.82007q15.20.5205.3527.04063/30/200714.642007q26.53.6208.3525.84366/29/200716.232007q34.33.0208.490.26499/28/2007182007q43.61.7210.0362.966112/31/200722.52008q10.6−1.8213.5286.65033/31/200825.612008q24.01.3218.8159.90416/30/200823.952008q3−0.6−3.7218.783−0.05859/30/200839.392008q4−8.4−8.9210.228−15.641112/31/2008402009q1−5.2−6.7212.7094.72063/31/200944.142009q2−1.1−0.7215.6935.61146/30/200926.352009q31.91.7215.9690.51189/30/200925.612009q44.93.8215.949−0.037012/31/200921.682010q15.53.9217.6313.11563/31/201017.59

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8|Chapter 1QuartersGDP PercentChange(based oncurrentdollars)GDP PercentChange(based onchained 2005dollars)ConsumerPriceIndexAnnualInflation Rate(measuredover eachquarter)DateVIX at Closeon the LastTrading Dayof theQuarter2010q25.43.8217.9650.61396/30/201034.542010q33.92.5218.4390.86999/30/201023.72010q44.22.3219.1791.355112/31/201017.75The data was retrieved on March 8, 2012, from the following sources:1. Gross Domestic Product: percent change from preceding period, from www.bea.gov/national/index.htm#gdp. (Chain-weighted indexesuse “up-to-date weights in order to provide amore accurate picture of the economy, to better capture changes in spending patterns and inprices, and to eliminate the bias present in fixed-weighted indexes,” from “Chained-DollarIndexes: Issues, Tips on Their Use, and Upcoming Changes,” by J. Steven Landefeld, BrentR. Moulton, and Cindy M. Vojtech inSurvey of Current Business[Nov 2003].)2. Consumer Price Index History Table: table containing history of CPI-U in the UnitedStates, retrieved from www.bls.gov/cpi/tables.htm; All Urban Consumers (CPI-U) US cityaverage (1982–84=100).3. VIX Historical Price Data from New Methodology: VIX data for 2004 to present(updated daily); retrieved from www.cboe.com/micro/vix/historical.aspx.1.19.Drawing on your experience, give examples of two risks that one can easily hedgeand two risks that one cannot hedge.ANSWERA gold mining company can easily hedge the output price risk of its gold by selling goldfutures. A manufacturer of silver jewelries can hedge input price risk by buying silver futures.A cell phone manufacturer cannot hedge the risk that a new model of mobile phonesthat it developed will sell well. A firm cannot hedge operational risks like the risk of a lossdue to human error, faulty management, and fraud.1.20.Download Form 10-K filed by P&G from the company’s website or the US Securitiesand Exchange Commission’s website. Answer the following questions based on a study ofthis report:a.What are the different kinds of risks to which P&G is exposed?b.How does P&G manage its risks? Identify and state the use of some derivatives in thisregard.c.Name some techniques that P&G employs for risk management.d.Does P&G grant employee stock options? If so, briefly discuss this program.What valuation model does the company use for valuing employee stock options?

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Derivatives and Risk Management|9ANSWERThe 2011 Annual Report was retrieved on March 11, 2012, from the Procter & Gamble(P&G) website: www.pg.com/en_US/investors/index.shtml. Information provided on page50 under section “Other Information,” subsection “Hedging and Derivative FinancialInstruments” and on page 60, “Note 5: Risk Management Activities and Fair Value Measure-ments,” helps answers these questions.a.Being a “multinational company with diverse product offerings,” P&G is exposed to“market risks, such as changes in interest rates, currency exchange rates and commodityprices.” And it is exposed to risks that hinder smooth completion of a transaction like creditrisk. As with all firms, it is also exposed to operational risk.b.P&G manages its risks by:• Evaluating exposures on a “centralized basis to take advantage of natural exposurecorrelation and netting.”• Except within financing operations, leveraging its “broadly diversified portfolio ofexposures as a natural hedge” and prioritizing “operational hedging activities overfinancial market instruments.”• Entering into different financial transactions (read: derivatives) in case it decides to“further manage volatility associated with the net exposures.” It accounts for thesetransactions by “using the applicable accounting guidance for derivative instruments andhedging activities.”• Monitoring interest rate, currency rate, and commodity derivatives positions usingCorporateManager™ value-at-risk model using a one-year horizon and a 95 percentconfidence level.• Controlling credit risk by following its “counterparty credit guidelines” and trying to tradeonly with “investment grade financial institutions”; it monitors counterparty exposuresdaily and reviews “downgrades in counterparty credit ratings” on a timely basis.Some of the derivatives used by P&G for risk management purposes are:• Interest rate risk management. P&G manages interest cost by using a combination offixed-rate and variable-rate debt. It uses interest rate swaps to hedge risks on these debtobligations.• Foreign currency risk management. Because P&G has operations in many nations, itsrevenue and expenses are impacted by currency exchange rates. The primary objective ofthe company’s currency hedging activities is “to manage the volatility associated withshort-term changes in exchange rates.” P&G primarily uses forward contracts withmaturities of less than eighteen months. It also uses some currency options and currencyswaps with maturities of up to five years for managing foreign exchange risk.• Commodity risk management. P&G spends significant amounts on raw materials whoseprices can become volatile due to “weather, supply conditions, political and economicvariables and other unpredictable factors.” It manages volatility by using fixed pricecontracts and also by trading futures, options, and swap contracts.

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10|Chapter 1c.P&G uses market valuation, sensitivity analysis, and value-at-risk modeling for riskmanagement.d.P&G grants stock options and restricted stock awards to key managers and directors andto a small number of employees.Some key features of the employee stock options program are:• Option’s exercise price is set at the market price of the underlying shares on the date of thegrant.• Key manager stock option awards: Such awards granted since September 2002 are vestedafter three years and have a ten-year life.• Company director stock option awards. Such awards are in the form of restricted stock andrestricted stock units.• Employee stock option awards. P&G also gives some employees minor stock option grantsand RSU grants with substantially similar terms.To calculate the compensation expense for stock options granted, P&G utilizes a binomiallattice-based valuation model. (These models are discussed in chapters 17 and 18.)

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112.1.The interest rate is 5 percent per year. Compute the six-month zero-coupon bondprice using a simple interest rate.ANSWERThe simple interest rate isi=0.05 per year. The time to maturity isT=0.5 year. Usingexpression (2.4c) of Result 2.3 of chapter 2, the six-month dollar return is1+R(0.5)=(1+i⋅T)=(1+0.05⋅0.5)=$1.0250.The six-month zero-coupon bond price isB(0.5)=1/[1+R(0.5)]=1/1.025=$0.9756.2.2.The interest rate is 5 percent per year. Compute the six-month zero-coupon bondprice using a compound interest rate with monthly compounding.ANSWERThe compound interest rate isi=0.05 per year. The time to maturity isT=0.5 year. Thenumber of times interest is compounded every year ism=12. Using expression (2.3b) ofResult 2.2 of chapter 2, the six-month dollar return is1+R(0.5)=[1+(i/m)]mT=[1+(0.05/12)]12⋅0.5=$1.0253.Six-month zero-coupon bond price isB(0.5)=1/[1+R(0.5)]=$0.9754.CHAPTER 2Interest Rates

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12|Chapter 22.3.The interest rate is 5 percent per year. Compute the six-month zero-coupon bondprice using a continuously compounded interest rate.ANSWERThe continuously compounded interest rate isr=0.05 per year. The time to maturity isT=0.5 year. Using expression (2.4d) of Result 2.3 of chapter 2, the six-month dollar return is1+R(0.5)=erT=e0.05⋅0.5=1.025315.The six-month zero-coupon bond price isB(0.5)=1/[1+R(0.5)]=$0.9753099.2.4.The interest rate is 5 percent per year. Compute the six-month zero-coupon bondprice using a banker’s discount yield (the zero-coupon bond is a US T-bill with 180 days tomaturity).ANSWERExpression (2.7b) of chapter 2 gives the T-bill price asB(0.5)=[1 – (Banker’s discount yield)⋅T/ 360]=1 – 0.05⋅(180 / 360)=$0.9750.2.5.What is a fixed-income security?ANSWERBonds or loans are called fixed-income securities because they make interest and principalrepayments according to a fixed schedule.The next three questions are based on the following table, where the interest rate is4 percent per year, compounded once a year.Time (in years)Cash Flows(in dollars)0 (today)−10517293108

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