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1 Chapter 10: Risk Management 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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2 Chapter 10 Contents 10.1 What is Risk?10.1 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 Analysis for Optimal Risk Management10.7 Portfolio Theory: Quantitative Analysis for Optimal Risk Management 10.8 Probability Distributions of Returns10.8 Probability Distributions of Returns 10.9 Standard Deviation as a Measure of Risk10.9 Standard Deviation as a Measure of Risk

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3 10.1 What is Risk? UncertaintyUncertainty –An unrealized event is uncertain for an observer at a given time if he/she does not know its outcome at that time –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 youBefore unsealing, my bid is uncertain to you After unsealing, my bid is known to youAfter unsealing, my bid is known to you

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4 Uncertainty that matters Risk is uncertainty that “matters” to the observerRisk is uncertainty that “matters” to the observer –You manage “The Herrings” and have a choice between two contracts for the concert 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 has a lower expected cost than (1)2 Pay a specified lump-sum for the hall that has a lower expected cost than (1)

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5 Contractual Outcomes “Ticket sales” is the “risk that matters”“Ticket sales” is the “risk that matters” –While each fan may be certain about attending or not attending, management is not fully informed, and is at risk because if sales are in fact higher than N*, it pays more if it selected choice 1if sales are in fact higher than N*, it pays more if it selected choice 1 if sales are in fact lower than N*, it pays more if it selected choice 2if sales are in fact lower than N*, it pays more if it selected choice 2

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6 Strategies for Controlling Risk Herring’s management has several strategies for reducing cost-uncertaintyHerring’s management has several strategies for reducing cost-uncertainty –Do research to determine the number of fans and the percentage of fans who will attend –For a fee, obtain the right to select between contract 1 and 2 at a later date –Hedge with contracts to third parties, (radio station, concessionaires, contractors, …)

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7 Naming the Strategies: Research The first strategy is purchasing information by researchThe first strategy is purchasing information by research –There is a cost associated with collecting information, but information enables one to make better-informed decisions –Information is often collected incrementally, and a decision is made at each step whether to continue collecting further information

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8 Naming the Strategies: Insurance or Option The second strategy entails purchasing the right to make a choice before a specified timeThe second strategy entails purchasing the right to make a choice before a specified time –Having the right take an action when information becomes clearer can be valuable –In this case, the option is the right to delay selection of the exact contractual terms The obligation to rent the hall might be a good quid pro quo for the optionThe obligation to rent the hall might be a good quid pro quo for the option

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9 Naming the Strategies: Hedging The third strategy creates secondary contracts that reduce overall exposure to the risk created by the primary contractThe third strategy creates secondary contracts that reduce overall exposure to the risk created by the primary contract –A primary fixed-fee rental contract creates a forward position in (unknown) future sales –Herring may offset this risk by requiring its concessionaires to enter into fixed rental fee contracts rather than % of sales contracts

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10 What is Risk? Risk Aversion Herring’s ultimate contracting strategy will depend upon its level of risk aversionHerring’s ultimate contracting strategy will depend upon its level of risk aversion Risk aversionRisk aversion –A measure of an individual’s willingness to pay for a reduction in exposure to risk

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11 What is Risk? Upside-Down Herring has a choice of contracts, and each has an upside and a downside, depending on the variable that controls the “risk that matters”Herring has a choice of contracts, and each has an upside and a downside, depending on the variable that controls the “risk that matters” Upside: favorable outcomeUpside: favorable outcome Downside : unfavorable outcomeDownside : unfavorable outcome

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12 What is Risk? Both Upside and Downside Some risks are more complex. A computer mother-board manufacturer thatSome risks are more complex. A computer mother-board manufacturer that –underestimates demand will lose current sales and market share –overestimates demand will own an inventory with a market price that is being eroded by rapid technological obsolescence Any deviation is unfavorableAny deviation is unfavorable

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13 What is Risk? 20/20 Hindsight The appropriateness of a risk- management decision should be determined using only the information available when the decision was madeThe appropriateness of a risk- management decision should be determined using only the information available when the decision was made We should avoid coloring our judgement of a earlier decision with facts know after the decisionWe should avoid coloring our judgement of a earlier decision with facts know after the decision But...But...

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14 What is Risk? Preserving your Options But …But … –a decision that preserves the ability to make in-flight corrections (at a small cost) over one that disposes of that ability characterizes a well-made decision –“Preserve your options”

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15 What is Risk? Knowing when to Purchase Information But …But … –a decision that was based on timely and carefully purchased information characterizes a well-made decision “Know when to buy a vowel”“Know when to buy a vowel”

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16 What is Risk? Tailor the Contract But …But … –Risk reduction clauses may often be included in a contract at very little cost when the contract is written, but are expensive to add as a contract amendment –Develop a standard set of risk-related clauses that may be incorporated into draft contracts When negotiating, think in terms of both expected costs and their associated risksWhen negotiating, think in terms of both expected costs and their associated risks

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17 What is Risk? Looking Back But …But … –Revisit risky decisions in the light of their outcomes to improve future decision making This is not to praise lucky management nor scold unlucky managementThis is not to praise lucky management nor scold unlucky management Ask: “How could the infrastructure supporting decision making be improved by preparing for them in advance?” (e.g. Maintain current data base of key variables)Ask: “How could the infrastructure supporting decision making be improved by preparing for them in advance?” (e.g. Maintain current data base of key variables)

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18 What is Risk? Risk Exposure If you face a particular kind of risk because of the nature of your job, business, or pattern of consumption you have a particular risk exposureIf you face a particular kind of risk because of the nature of your job, business, or pattern of consumption you have a particular risk exposure

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19 What is Risk? Risk-Controlling Tools Many tool that may be used to reduce risk may also be used to increase riskMany tool that may be used to reduce risk may also be used to increase risk –If you insure your house against fire, you are reducing your risk (Hedger) –If I insure your house against fire, I am increasing my risk (Speculator) (Probably not an insurable risk:(Probably not an insurable risk: –moral hazard –lack of a legitimate economic purpose)

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20 10.2 Risk and Economic Decisions Risk exposure of households:Risk exposure of households: –Sickness, disability, & death risks –Unemployment risk –Consumer-durable asset risk –Liability risk –Financial asset risk

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21 Risk exposure of firms Input/output channelsInput/output channels strike, boycott, embargo, war, safety, supply/ demand strike, boycott, embargo, war, safety, supply/ demand Loss of production facilitiesLoss of production facilities fire, legislation, civil action, strike, nationalization, war fire, legislation, civil action, strike, nationalization, war Liability riskLiability risk customer, employee, community, environment customer, employee, community, environment Price risksPrice risks input, output, foreign exchange, interest input, output, foreign exchange, interest Competitor riskCompetitor risk technology, intellectual property, economic technology, intellectual property, economic

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22 Government: –Major calamities weather, forest fires, riotsweather, forest fires, riots –Guarantees exports, small business loans, mortgages, and student loans, crop pricesexports, small business loans, mortgages, and student loans, crop prices –Interventions bank failures, strategic firm failures, crop failures, medical coveragebank failures, strategic firm failures, crop failures, medical coverage

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23 10.3 The Risk Management Process Risk identificationRisk identification Risk assessmentRisk assessment Selection of risk-management techniquesSelection of risk-management techniques ImplementationImplementation ReviewReview

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24 Risk identification Some risks are commonly under- identified, and so are not hedgedSome risks are commonly under- identified, and so are not hedged –disability 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-prescribed Some risks offset each otherSome risks offset each other –liability of a car within a fleet; price/quantity

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25 Risk assessment The quantification of the identified risksThe quantification of the identified risks –quantification of exposure to risk requires specialized skills ActuariesActuaries Investment counselorsInvestment counselors

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26 Selection of risk-management techniques Risk avoidanceRisk avoidance Loss prevention and controlLoss prevention and control Risk retentionRisk retention Risk transferRisk transfer

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27 Implementation Risk transfer requires finding a suitable transfer vehicle at an acceptable priceRisk transfer requires finding a suitable transfer vehicle at an acceptable price –Obtain competitive quotations and look at alternative ways to hedge –Consider the mix of upside to downside risk Options shed downside risk, while maintaining upside potential (at a price)Options shed downside risk, while 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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28 Implementation Some risks may be shed only imperfectlySome risks may be shed only imperfectly –A specialty rice grower may be able to lower but not eliminate risk using cereal futures –A seed grower may not be able to significantly reduce price risk

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29 Review Management of risk should be an ongoing systematic activity because risk exposure changes as people matureManagement of risk should be an ongoing systematic activity because risk exposure changes as people mature Maintaining flexibility will enable you to react more appropriately to changeMaintaining flexibility will enable you to react more appropriately to change –Term life insurance with an annual renewable term is more flexible than policies without this clause

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30 10.4 The Three Dimensions of Risk Transfer HedgingHedging InsuringInsuring DiversifyingDiversifying

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31 Hedging A risk is hedged when the action taken to reduce adverse risk exposure also causes the loss of unexpected gainA risk is hedged when the action taken to reduce adverse risk exposure also causes the loss of unexpected gain –A farmer who sells her crop before it is harvested reduces the risk of lower prices and lower yields, but surrenders the right to increased prices and yields –(Note: We sometimes use “hedge” to include “insure”)

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32 Insuring Insuring is the payment of a premium to avoid lossesInsuring is the payment of a premium to avoid losses Insurance is not hedging because you maintain ownership in the upside potentialInsurance is not hedging because you maintain ownership in the upside potential –A farmer has the right, but not the obligation to sell soy to the government at a set price

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33 Diversifying Diversification means holding similar amounts of a risky asset instead of a larger amount of a single risky assetDiversification means holding similar amounts of a risky asset instead of a larger amount of a single risky asset –I have identified 10 corporations that each have an expected return = 0.15, a standard deviation = 0.20, and are correlated with each other with rho = 0.9

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34 = 0.2000 = 0.1421 * = 0.1342 Theoretical Minimum

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35 Observation Most of the diversification is obtained by including just a few stock in the portfolioMost of the diversification is obtained by including just a few stock in the portfolio Risk can only be reduced to a fixed level that depends on the correlationRisk can only be reduced to a fixed level that depends on the correlation Progressively adding one more new stock has a diminishing affect on riskProgressively adding one more new stock has a diminishing affect on risk

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36 Equation for Homogeneous Diversification with n Stocks

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37 10.5 Risk Transfer and Economic Efficiency Institutional arrangements for transfer of risk contribute to economic efficiency byInstitutional arrangements for transfer of risk contribute to economic efficiency by –allocating existing risks to those most willing to bear them –reallocation of resources to production and consumption in accordance with the new distribution of risk-bearing

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38 10.6 Institutions for Risk Management A complete market for allocating risk would permit the separation of productive activity and risk-bearingA complete market for allocating risk would permit the separation of productive activity and risk-bearing –While technology is driving the risk market- place towards completeness, this will not be achieved because: transaction coststransaction costs incentive costsincentive costs

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39 10.7 Portfolio Theory: Quantitative Analysis for Optimal Risk Management Portfolio theoryPortfolio theory –quantitative analysis for optimal risk management Portfolio theory selects from a set of (usually divisible) risks by optimizing risk-returnPortfolio theory selects from a set of (usually divisible) risks by optimizing risk-return Consumption and risk preferences are exogenousConsumption and risk preferences are exogenous It is sometimes possible to devise a strategy that reduces the risk of all contracting partiesIt is sometimes possible to devise a strategy that reduces the risk of all contracting parties

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40 10.8 Probability Distributions of Returns Assume that there are two stock available, GENCO and RISCO, and each responds to the state of the economy according to the following tableAssume that there are two stock available, GENCO and RISCO, and each responds to the state of the economy according to the following table

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41 Returns on GENCO & RISCO

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42 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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43 Observation Both companies have the same expected return, but there is considerably more risk associated with RISCOBoth companies have the same expected return, but there is considerably more risk associated with RISCO

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44 10.9 Equations: Mean

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45 Equations: Standard Deviation

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46 Observation The expected returns of GENCO and RISCO happen to be equal, but the volatility, or standard deviation, of RISCO is twice that of GENCO’sThe expected returns of GENCO and RISCO happen to be equal, but the volatility, or standard deviation, of RISCO is twice that of GENCO’s However, we would expect share prices to follow a continuous distribution, rather than the discrete distribution illustratedHowever, we would expect share prices to follow a continuous distribution, rather than the discrete distribution illustrated

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47 Continuous Distributions A very common assumption is that the returns of a stock are distributed normally. Assume:A very common assumption is that the returns of a stock are distributed normally. Assume: –NORMCO’s has an expected return of 10% and a standard deviation of 0.1265 –VOLCO also has an expected return of 10%, but has a standard deviation of 0.2530

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49 Two New Distributions of Return The next slide shows another two distributions of return that have been superimposedThe next slide shows another two distributions of return that have been superimposed They appear to have the same mean, namely 10%, but ODDCO appears to have a higher standard deviation than VOLCOThey appear to have the same mean, namely 10%, but ODDCO appears to have a higher standard deviation than VOLCO

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51 Caveat The ODDCO distribution actually has no mean nor standard deviationThe ODDCO distribution actually has no mean nor standard deviation If you drew samples from the distribution and computed these two statistics, you would quickly discover that for n = 100, 200, et cetera, neither statistic converges to a constant numberIf you drew samples from the distribution and computed these two statistics, you would quickly discover that for n = 100, 200, et cetera, neither statistic converges to a constant number

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52 Caveat The distribution of ODDCO’s returns follow a Cauchy DistributionThe distribution of ODDCO’s returns follow a Cauchy Distribution The Cauchy and Normal distributions are special cases of the Stable distributionThe Cauchy and Normal distributions are special cases of the Stable distribution Some researchers believe that stock returns are not normal, but are drawn from a stable distribution without a SDSome researchers believe that stock returns are not normal, but are drawn from a stable distribution without a SD

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53 Caveat As we progress, we will assume that stock returns do have a mean and a standard deviation, but this is a key assumptionAs we progress, we will assume that stock returns do have a mean and a standard deviation, but this is a key assumption

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54 Another Caveat You should reconcile financial models with common understandingYou should reconcile financial models with common understanding –The distribution we have proposed for returns, the normal, theoretically takes values from -infinity to +infinity –Returns on the other hand may only be from -100% to +infinity –Theoretically, the normal distribution is at odds with the facts

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55 Another Caveat: Resolution The return that is distributed normally is the annual return compounded continuously, and this takes values from -infinity to +infinityThe return that is distributed normally is the annual return compounded continuously, and this takes values from -infinity to +infinity The annual rate compounded annually has a minimum of -1, that compounded semi-annually a minimum of -2, et ceteraThe annual rate compounded annually has a minimum of -1, that compounded semi-annually a minimum of -2, et cetera

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56 Another Caveat: Resolution One of the useful features of standard deviation is that it has the same dimensions as its random variableOne of the useful features of standard deviation is that it has the same dimensions as its random variable –The standard deviation used with the normal distribution is then also an annual rate compounded continuously (that is, if you are being a stickler for detail)(that is, if you are being a stickler for detail)

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57 Yet Another Caveat Recall that in Chapter 4 we investigated a stock thatRecall that in Chapter 4 we investigated a stock that –paid no dividends –was currently trading at its purchase price –yet had a significant average return! The wrong average caused this problemThe wrong average caused this problem

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58 Yet Another Caveat: Resolution If we restrict ourselves to the annual rate compounded continuously, then the problem disappears, and the correct average is the arithmetic mean of returnsIf we restrict ourselves to the annual rate compounded continuously, then the problem disappears, and the correct average is the arithmetic mean of returns

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Portfolio Management Lecture: 26 Course Code: MBF702.

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