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Chapter 10: Risk Chapter 10: Risk ManagementManagement

Copyright © Prentice Hall Inc. 1999. Author: Nick Bagley

Objective•Risk and Financial Decision Making

•Conceptual Framework for Risk Management

•Efficient Allocation of Risk-Bearing

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Chapter 10 ContentsChapter 10 Contents• 10.1 10.1 What is Risk?What is Risk?

• 10.2 Risk and Economic Decisions10.2 Risk and Economic Decisions

• 10.3 The Risk Management Process10.3 The Risk Management Process

• 10.4 The Three Dimensions of Risk Transfer10.4 The Three Dimensions of Risk Transfer

• 10.5 Risk Transfer and Economic Efficiency10.5 Risk Transfer and Economic Efficiency

• 10.6 Institutions for Risk Management10.6 Institutions for Risk Management

• 10.7 Portfolio Theory: Quantitative 10.7 Portfolio Theory: Quantitative Analysis for Optimal Risk ManagementAnalysis for Optimal Risk Management

• 10.8 Probability Distributions of Returns10.8 Probability Distributions of Returns

• 10.9 Standard Deviation as a Measure of 10.9 Standard Deviation as a Measure of RiskRisk

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10.1 10.1 What is Risk? What is Risk?

• UncertaintyUncertainty– An unrealized event is uncertain for an An unrealized event is uncertain for an

observer at a given time if he/she does observer at a given time if he/she does not know its outcome at that timenot know its outcome at that time

– I enter a sealed bid on a public contract I enter a sealed bid on a public contract • The value of my bid is certain to meThe value of my bid is certain to me

• Before unsealing, my bid is uncertain to Before unsealing, my bid is uncertain to youyou

• After unsealing, my bid is known to youAfter unsealing, my bid is known to you

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Uncertainty that matters Uncertainty that matters

• Risk is uncertainty that “matters” to Risk is uncertainty that “matters” to the observerthe observer– You manage “The Herrings” and have a You manage “The Herrings” and have a

choice between two contracts for the choice between two contracts for the concert hallconcert hall• 1 Pay the hall owner $2 for each ticket sold1 Pay the hall owner $2 for each ticket sold

• 2 Pay a specified lump-sum for the hall that 2 Pay a specified lump-sum for the hall that has a lower expected cost than (1)has a lower expected cost than (1)

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Contractual OutcomesContractual Outcomes

• ““Ticket sales” is the “risk that matters” Ticket sales” is the “risk that matters” – While each fan may be certain about While each fan may be certain about

attending or not attending, management is attending or not attending, management is not fully informed, and is at risk because not fully informed, and is at risk because • if sales are in fact higher than N*, it pays if sales are in fact higher than N*, it pays

more if it selected choice 1more if it selected choice 1

• if sales are in fact lower than N*, it pays if sales are in fact lower than N*, it pays more if it selected choice 2more if it selected choice 2

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Strategies for Controlling Strategies for Controlling RiskRisk

• Herring’s management has several Herring’s management has several strategies for reducing cost-uncertaintystrategies for reducing cost-uncertainty– Do research to determine the number of fans Do research to determine the number of fans

and the percentage of fans who will attendand the percentage of fans who will attend

– For a fee, obtain the right to select between For a fee, obtain the right to select between contract 1 and 2 at a later date contract 1 and 2 at a later date

– Hedge with contracts to third parties, (radio Hedge with contracts to third parties, (radio station, concessionaires, contractors, …)station, concessionaires, contractors, …)

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Naming the Strategies: Naming the Strategies: ResearchResearch

• The first strategy is purchasing The first strategy is purchasing information by researchinformation by research– There is a cost associated with collecting There is a cost associated with collecting

information, but information enables one to information, but information enables one to make better-informed decisionsmake better-informed decisions

– Information is often collected Information is often collected incrementally, and a decision is made at incrementally, and a decision is made at each step whether to continue collecting each step whether to continue collecting further informationfurther information

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Naming the Strategies: Naming the Strategies: Insurance or OptionInsurance or Option

• The second strategy entails purchasing The second strategy entails purchasing the right to make a choice before a the right to make a choice before a specified timespecified time– Having the right take an action when Having the right take an action when

information becomes clearer can be valuableinformation becomes clearer can be valuable

– In this case, the option is the right to delay In this case, the option is the right to delay selection of the exact contractual termsselection of the exact contractual terms• The obligation to rent the hall might be a good The obligation to rent the hall might be a good

quid pro quo for the optionquid pro quo for the option

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Naming the Strategies: Naming the Strategies: HedgingHedging

• The third strategy creates secondary The third strategy creates secondary contracts that reduce overall exposure to contracts that reduce overall exposure to the risk created by the primary contractthe risk created by the primary contract– A primary fixed-fee rental contract creates a A primary fixed-fee rental contract creates a

forward position in (unknown) future salesforward position in (unknown) future sales

– Herring may offset this risk by requiring its Herring may offset this risk by requiring its concessionaires to enter into fixed rental fee concessionaires to enter into fixed rental fee contracts rather than % of sales contractscontracts rather than % of sales contracts

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What is Risk? Risk What is Risk? Risk Aversion Aversion

• Herring’s ultimate contracting Herring’s ultimate contracting strategy will depend upon its level strategy will depend upon its level of of risk aversionrisk aversion

• Risk aversionRisk aversion– A measure of an individual’s A measure of an individual’s

willingness to pay for a reduction in willingness to pay for a reduction in exposure to riskexposure to risk

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What is Risk? Upside-What is Risk? Upside-DownDown

• Herring has a choice of contracts, Herring has a choice of contracts, and each has an and each has an upsideupside and a and a downside,downside, depending on the variable depending on the variable that controls the “risk that matters”that controls the “risk that matters”

• Upside: favorable outcomeUpside: favorable outcome

• Downside : unfavorable outcomeDownside : unfavorable outcome

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What is Risk? Both Upside What is Risk? Both Upside and Downsideand Downside• Some risks are more complex. A Some risks are more complex. A

computer mother-board manufacturer computer mother-board manufacturer that that – underestimates demand will lose current underestimates demand will lose current

sales and market sharesales and market share

– overestimates demand will own an overestimates demand will own an inventory with a market price that is being inventory with a market price that is being eroded by rapid technological eroded by rapid technological obsolescenceobsolescence

• AnyAny deviation is unfavorable deviation is unfavorable

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What is Risk? 20/20 What is Risk? 20/20 HindsightHindsight

• The appropriateness of a risk-The appropriateness of a risk-management decision should be management decision should be determined using only the information determined using only the information available when the decision was madeavailable when the decision was made

• We should avoid coloring our judgement We should avoid coloring our judgement of a earlier decision with facts know after of a earlier decision with facts know after the decisionthe decision

• But ...But ...

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What is Risk? Preserving What is Risk? Preserving your Optionsyour Options

• But …But …– a decision that preserves the ability to a decision that preserves the ability to

make in-flight corrections (at a small make in-flight corrections (at a small cost) over one that disposes of that cost) over one that disposes of that ability characterizes a well-made ability characterizes a well-made decisiondecision

– ““Preserve your options”Preserve your options”

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What is Risk? Knowing What is Risk? Knowing when to Purchase when to Purchase InformationInformation

• But …But …– a decision that was based on timely a decision that was based on timely

and carefully purchased information and carefully purchased information characterizes a well-made decisioncharacterizes a well-made decision• ““Know when to buy a vowel”Know when to buy a vowel”

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What is Risk? What is Risk? Tailor the ContractTailor the Contract• But …But …

– Risk reduction clauses may often be Risk reduction clauses may often be included in a contract at very little cost included in a contract at very little cost when the contract is written, but are when the contract is written, but are expensive to add as a contract expensive to add as a contract amendmentamendment

– Develop a standard set of risk-related Develop a standard set of risk-related clauses that may be incorporated into clauses that may be incorporated into draft contractsdraft contracts• When negotiating, think in terms of both When negotiating, think in terms of both

expected costs expected costs andand their associated risks their associated risks

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What is Risk? Looking What is Risk? Looking BackBack

• But …But …– Revisit risky decisions in the light of their Revisit risky decisions in the light of their

outcomes to improve future decision making outcomes to improve future decision making • This is not to praise lucky management nor This is not to praise lucky management nor

scold unlucky managementscold unlucky management

• Ask: “How could the infrastructure supporting Ask: “How could the infrastructure supporting decision making be improved by preparing for decision making be improved by preparing for them in advance?” (e.g. them in advance?” (e.g. MaintainMaintain current current data base of key variables)data base of key variables)

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What is Risk? Risk What is Risk? Risk ExposureExposure

• If you face a particular kind of risk If you face a particular kind of risk because of the nature of your job, because of the nature of your job, business, or pattern of consumption business, or pattern of consumption you have a particular you have a particular risk exposurerisk exposure

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What is Risk? Risk-What is Risk? Risk-Controlling ToolsControlling Tools

• Many tool that may be used to reduce Many tool that may be used to reduce risk may also be used to increase riskrisk may also be used to increase risk– If If youyou insure insure youryour house against fire, you house against fire, you

are reducing your risk (Hedger) are reducing your risk (Hedger)

– If If II insure insure youryour house against fire, I am house against fire, I am increasing my risk (Speculator)increasing my risk (Speculator)• (Probably not an insurable risk: (Probably not an insurable risk:

– moral hazardmoral hazard– lack of a legitimate economic purpose)lack of a legitimate economic purpose)

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10.2 10.2 Risk and Economic Risk and Economic DecisionsDecisions

• Risk exposure of households:Risk exposure of households:– Sickness, disability, & death risksSickness, disability, & death risks

– Unemployment riskUnemployment risk

– Consumer-durable asset riskConsumer-durable asset risk

– Liability riskLiability risk

– Financial asset riskFinancial asset risk

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Risk exposure of firmsRisk exposure of firms

• Input/output channelsInput/output channels strike, boycott, embargo, war, safety, supply/ demandstrike, boycott, embargo, war, safety, supply/ demand

• Loss of production facilitiesLoss of production facilities fire, legislation, civil action, strike, nationalization, warfire, legislation, civil action, strike, nationalization, war

• Liability riskLiability risk customer, employee, community , environmentcustomer, employee, community , environment

• Price risksPrice risks input, output, foreign exchange, interestinput, output, foreign exchange, interest

• Competitor riskCompetitor risk technology, intellectual property, economictechnology, intellectual property, economic

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Government:Government:

– Major calamitiesMajor calamities• weather, forest fires, riotsweather, forest fires, riots

– GuaranteesGuarantees• exports, small business loans, mortgages, exports, small business loans, mortgages,

and student loans, crop pricesand student loans, crop prices

– InterventionsInterventions• bank failures, strategic firm failures, crop bank failures, strategic firm failures, crop

failures, medical coveragefailures, medical coverage

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10.3 10.3 The Risk The Risk Management ProcessManagement Process

• Risk identificationRisk identification

• Risk assessmentRisk assessment

• Selection of risk-management Selection of risk-management techniquestechniques

• ImplementationImplementation

• ReviewReview

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Risk identificationRisk identification

• Some risks are commonly under-Some risks are commonly under-identified, and so are not hedgedidentified, and so are not hedged– disability coverage is often too lowdisability coverage is often too low

• Some risks that do not exist are ‘hedged’Some risks that do not exist are ‘hedged’– life insurance is often over-prescribedlife insurance is often over-prescribed

• Some risks offset each otherSome risks offset each other– liability of a car within a fleet; price/quantityliability of a car within a fleet; price/quantity

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Risk assessmentRisk assessment

• The quantification of the identified The quantification of the identified risksrisks– quantification of exposure to risk quantification of exposure to risk

requires specialized skills requires specialized skills • ActuariesActuaries

• Investment counselorsInvestment counselors

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Selection of risk-Selection of risk-management techniquesmanagement techniques

• Risk avoidanceRisk avoidance

• Loss prevention and controlLoss prevention and control

• Risk retentionRisk retention

• Risk transferRisk transfer

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ImplementationImplementation

• Risk transfer requires finding a suitable Risk transfer requires finding a suitable transfer vehicle at an acceptable pricetransfer vehicle at an acceptable price– Obtain competitive quotations and look at Obtain competitive quotations and look at

alternative ways to hedgealternative ways to hedge

– Consider the mix of upside to downside riskConsider the mix of upside to downside risk• Options shed downside risk, while Options shed downside risk, while

maintaining upside potential (at a price)maintaining upside potential (at a price)

• Futures shed both down- and up-side risksFutures shed both down- and up-side risks

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ImplementationImplementation

• Some risks may be shed only Some risks may be shed only imperfectlyimperfectly– A specialty rice grower may be able to A specialty rice grower may be able to

lower but not eliminate risk using lower but not eliminate risk using cereal futurescereal futures

– A seed grower may not be able to A seed grower may not be able to significantly reduce price risksignificantly reduce price risk

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ReviewReview

• Management of risk should be an Management of risk should be an ongoing systematic activity because ongoing systematic activity because risk exposure changes as people maturerisk exposure changes as people mature

• Maintaining flexibility will enable you to Maintaining flexibility will enable you to react more appropriately to changereact more appropriately to change– Term life insurance with an annual Term life insurance with an annual

renewable term is more flexible than renewable term is more flexible than policies without this clausepolicies without this clause

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10.4 10.4 The Three The Three Dimensions of Risk Dimensions of Risk TransferTransfer

• HedgingHedging

• InsuringInsuring

• DiversifyingDiversifying

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Hedging Hedging

• A risk is hedged when the action taken A risk is hedged when the action taken to reduce adverse risk exposure also to reduce adverse risk exposure also causes the loss of unexpected gaincauses the loss of unexpected gain– A farmer who sells her crop before it is A farmer who sells her crop before it is

harvested reduces the risk of lower prices harvested reduces the risk of lower prices and lower yields, but surrenders the right and lower yields, but surrenders the right to increased prices and yieldsto increased prices and yields

– (Note: We sometimes use “hedge” to include “insure”)(Note: We sometimes use “hedge” to include “insure”)

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InsuringInsuring

• Insuring is the payment of a premium Insuring is the payment of a premium to avoid lossesto avoid losses

• Insurance is not hedging because you Insurance is not hedging because you maintain ownership in the upside maintain ownership in the upside potentialpotential– A farmer has the right, but not the A farmer has the right, but not the

obligation to sell soy to the government at obligation to sell soy to the government at a set pricea set price

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DiversifyingDiversifying

• Diversification means holding similar Diversification means holding similar amounts of a risky asset instead of a amounts of a risky asset instead of a larger amount of a single risky assetlarger amount of a single risky asset– I have identified 10 corporations that I have identified 10 corporations that

each have an expected return each have an expected return = 0.15, a = 0.15, a standard deviation standard deviation = 0.20, and are = 0.20, and are correlated with each other with rho = 0.9 correlated with each other with rho = 0.9

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Standard Deviations of Portfolios

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.20

0 1 2 3 4 5 6 7 8 9 10

Portfolio Size

Sta

nd

are

Dev

iati

on

= 0.2000

= 0.1421

* = 0.1342Theoretical Minimum

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ObservationObservation

• Most of the diversification is obtained Most of the diversification is obtained by including just a few stock in the by including just a few stock in the portfolioportfolio

• Risk can only be reduced to a fixed Risk can only be reduced to a fixed level that depends on the correlationlevel that depends on the correlation

• Progressively adding one more new Progressively adding one more new stock has a diminishing affect on risk stock has a diminishing affect on risk

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2

11

n

nn

nstockport

Equation for Equation for Homogeneous Homogeneous Diversification with n Diversification with n StocksStocks

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10.5 10.5 Risk Transfer and Risk Transfer and Economic EfficiencyEconomic Efficiency

• Institutional arrangements for Institutional arrangements for transfer of risk contribute to transfer of risk contribute to economic efficiency byeconomic efficiency by– allocating existing risks to those most allocating existing risks to those most

willing to bear themwilling to bear them

– reallocation of resources to production reallocation of resources to production and consumption in accordance with and consumption in accordance with the new distribution of risk-bearingthe new distribution of risk-bearing

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10.6 10.6 Institutions for Risk Institutions for Risk ManagementManagement

• A complete market for allocating A complete market for allocating risk would permit the separation of risk would permit the separation of productive activity and risk-bearingproductive activity and risk-bearing– While technology is driving the risk While technology is driving the risk

market-place towards completeness, market-place towards completeness, this will not be achieved because:this will not be achieved because:• transaction coststransaction costs

• incentive costsincentive costs

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10.7 10.7 Portfolio Theory: Portfolio Theory: Quantitative Analysis for Quantitative Analysis for Optimal Risk ManagementOptimal Risk Management

• Portfolio theoryPortfolio theory

– quantitative analysis for optimal risk quantitative analysis for optimal risk managementmanagement• Portfolio theory selects from a set of (usually Portfolio theory selects from a set of (usually

divisible) risks by optimizing risk-returndivisible) risks by optimizing risk-return

• Consumption and risk preferences are Consumption and risk preferences are exogenousexogenous

• It is sometimes possible to devise a strategy It is sometimes possible to devise a strategy that reduces the risk of all contracting parties that reduces the risk of all contracting parties

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10.8 10.8 Probability Probability Distributions of ReturnsDistributions of Returns

• Assume that there are two stock Assume that there are two stock available, GENCO and RISCO, and available, GENCO and RISCO, and each responds to the state of the each responds to the state of the economy according to the following economy according to the following tabletable

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Returns on GENCO & Returns on GENCO & RISCORISCO

State ofEconomy

Return onRISCO

Return onGENCO

Prob-ability

Strong 50% 30% 0.20

Normal 10% 10% 0.60

Weak -30% -10% 0.20

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•50%•30%

•10%•-10%

•-30%

•RISCO

•GENCO•0

•0.1

•0.2

•0.3

•0.4

•0.5

•0.6

•Probability

•Return

•Probability Distributions of Returns of GENCO and RISCO

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ObservationObservation

• Both companies have the same Both companies have the same expected return, but there is expected return, but there is considerably more risk associated considerably more risk associated with RISCOwith RISCO

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10.9 10.9 Equations: MeanEquations: Mean

%10

: Also

%1010.0

)10.0(2.010.06.03.02.0

...

1

332211

RISCO

GENCO

GENCO

r

r

r

n

iii

nnr

rP

rPrPrPrPrE

rP

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Equations: Standard Equations: Standard DeviationDeviation

2530.0

: Also

1265.0016.0

)10.010.0(2.010.010.06.010.030.02.0

...

222

1

2

2222

211

2

RISCO

GENCO

GENCO

r

r

r

n

irii

rnnrr

r

rP

rPrPrP

rErE

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ObservationObservation

• The expected returns of GENCO and The expected returns of GENCO and RISCO happen to be equal, but the RISCO happen to be equal, but the volatility, or standard deviation, of volatility, or standard deviation, of RISCO is twice that of GENCO’sRISCO is twice that of GENCO’s

• However, we would expect share However, we would expect share prices to follow a continuous prices to follow a continuous distribution, rather than the discrete distribution, rather than the discrete distribution illustrateddistribution illustrated

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Continuous DistributionsContinuous Distributions

• A very common assumption is that A very common assumption is that the returns of a stock are distributed the returns of a stock are distributed normally. Assume:normally. Assume:– NORMCO’s has an expected return of NORMCO’s has an expected return of

10% and a standard deviation of 0.126510% and a standard deviation of 0.1265

– VOLCO also has an expected return of VOLCO also has an expected return of 10%, but has a standard deviation of 10%, but has a standard deviation of 0.25300.2530

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Distribution of Returns on Two Stocks

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-100% -50% 0% 50% 100%

Return

Pro

bab

ilit

y D

ensi

ty

NORMCO

VOLCO

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Two New Distributions of Two New Distributions of ReturnReturn

• The next slide shows another two The next slide shows another two distributions of return that have distributions of return that have been superimposedbeen superimposed

• They appear to have the same They appear to have the same mean, namely 10%, but ODDCO mean, namely 10%, but ODDCO appears to have a higher standard appears to have a higher standard deviation than VOLCOdeviation than VOLCO

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Two More Return Densities.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

-100.00% -50.00% 0.00% 50.00% 100.00%

Return.

Pro

bab

ilit

y D

ensi

ty.

VOLCO

ODDCO

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CaveatCaveat

• The ODDCO distribution actually has The ODDCO distribution actually has nono mean nor standard deviation mean nor standard deviation

• If you drew samples from the If you drew samples from the distribution and computed these two distribution and computed these two statistics, you would quickly discover statistics, you would quickly discover that for n = 100, 200, et cetera, that for n = 100, 200, et cetera, neither statistic converges to a neither statistic converges to a constant numberconstant number

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CaveatCaveat

• The distribution of ODDCO’s returns The distribution of ODDCO’s returns follow a Cauchy Distributionfollow a Cauchy Distribution

• The Cauchy and Normal distributions are The Cauchy and Normal distributions are special cases of the Stable distributionspecial cases of the Stable distribution

• Some researchers believe that stock Some researchers believe that stock returns are not normal, but are drawn returns are not normal, but are drawn from a stable distribution without a SDfrom a stable distribution without a SD

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CaveatCaveat

• As we progress, we will assume that As we progress, we will assume that stock returns do have a mean and a stock returns do have a mean and a standard deviation, but this is a key standard deviation, but this is a key assumptionassumption

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Another CaveatAnother Caveat

• You should reconcile financial models with You should reconcile financial models with common understandingcommon understanding– The distribution we have proposed for The distribution we have proposed for

returns, the normal, theoretically takes values returns, the normal, theoretically takes values from -infinity to +infinityfrom -infinity to +infinity

– Returns on the other hand may only be from -Returns on the other hand may only be from -100% to +infinity100% to +infinity

– Theoretically, the normal distribution is at Theoretically, the normal distribution is at odds with the factsodds with the facts

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Another Caveat: Another Caveat: ResolutionResolution

• The return that is distributed normally is The return that is distributed normally is the the annual return compounded annual return compounded continuouslycontinuously, and this takes values , and this takes values from -infinity to +infinityfrom -infinity to +infinity

• The annual rate compounded annually The annual rate compounded annually has a minimum of -1, that compounded has a minimum of -1, that compounded semi-annually a minimum of -2, et semi-annually a minimum of -2, et ceteracetera

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Another Caveat: Another Caveat: ResolutionResolution

• One of the useful features of standard One of the useful features of standard deviation is that it has the same deviation is that it has the same dimensions as its random variabledimensions as its random variable– The standard deviation used with the The standard deviation used with the

normal distribution is then also an annual normal distribution is then also an annual rate compounded continuouslyrate compounded continuously• (that is, if you are being a stickler for (that is, if you are being a stickler for

detail)detail)

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Yet Another CaveatYet Another Caveat

• Recall that in Chapter 4 we Recall that in Chapter 4 we investigated a stock that investigated a stock that – paid no dividends paid no dividends

– was currently trading at its purchase pricewas currently trading at its purchase price

– yet had a significant average return!yet had a significant average return!

• The wrong average caused this The wrong average caused this problemproblem

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Yet Another Caveat: Yet Another Caveat: ResolutionResolution

• If we restrict ourselves to the annual If we restrict ourselves to the annual rate compounded continuously, rate compounded continuously, then the problem disappears, and then the problem disappears, and the correct average is the the correct average is the arithmetic mean of returnsarithmetic mean of returns