Chapter 10 Risk Management Objective Copyright Prentice Hall
Chapter 10: Risk Management Objective Copyright © Prentice Hall Inc. 1999. Author: Nick Bagley • Risk and Financial Decision Making • Conceptual Framework for Risk Management • Efficient Allocation of 1 Risk-Bearing
Chapter 10 Contents • 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 • 10. 9 Standard Deviation as a Measure of Risk 2
10. 1 What is Risk? • Uncertainty – 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 me • Before unsealing, my bid is uncertain to you • After unsealing, my bid is known to you 3
Uncertainty that matters • Risk is uncertainty that “matters” to the observer – You manage “The Intergalactic Herrings” and have a choice between two contracts for the concert hall • 1 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) 4
Contractual Outcomes • “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 1 • if sales are in fact lower than N*, it pays more if it selected choice 2 5
Strategies for Controlling Risk • Herring’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, …) 6
Naming the Strategies: Research • The 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 7
Naming the Strategies: Insurance or Option • The 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 option 8
Naming the Strategies: Hedging • The 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 9
What is Risk? Risk Aversion • Herring’s ultimate contracting strategy will depend upon its level of risk aversion • Risk aversion – A measure of an individual’s willingness to pay for a reduction in exposure to risk 10
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” • Upside: favorable outcome • Downside : unfavorable outcome 11
What is Risk? Both Upside and Downside • Some 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 unfavorable 12
What is Risk? 20/20 Hindsight • The appropriateness of a riskmanagement 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 decision • But. . . 13
What is Risk? Preserving your Options • 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” 14
What is Risk? Knowing when to Purchase Information • But … – a decision that was based on timely and carefully purchased information characterizes a well-made decision • “Know when to buy a vowel” 15
What is Risk? Tailor the Contract • 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 risks 16
What is Risk? Looking Back • 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 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) 17
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 exposure 18
What is Risk? Risk-Controlling Tools • Many 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: – moral hazard – lack of a legitimate economic purpose) 19
10. 2 Risk and Economic Decisions • Risk exposure of households: – Sickness, disability, & death risks – Unemployment risk – Consumer-durable asset risk – Liability risk – Financial asset risk 20
Risk exposure of firms • Input/output channels strike, boycott, embargo, war, safety, supply/ demand • Loss of production facilities fire, legislation, civil action, strike, nationalization, war • Liability risk customer, employee, community , environment • Price risks input, output, foreign exchange, interest • Competitor risk 21 technology, intellectual property, economic
Government: – Major calamities • weather, forest fires, riots – Guarantees • exports, small business loans, mortgages, and student loans, crop prices – Interventions • bank failures, strategic firm failures, crop failures, medical coverage 22
10. 3 The Risk Management Process • Risk identification • Risk assessment • Selection of risk-management techniques • Implementation • Review 23
Risk identification • Some risks are commonly underidentified, and so are not hedged – disability coverage is often too low • Some risks that do not exist are ‘hedged’ – life insurance is often over-prescribed • Some risks offset each other – liability of a car within a fleet; price/quantity 24
Risk assessment • The quantification of the identified risks – quantification of exposure to risk requires specialized skills • Actuaries • Investment counselors 25
Selection of risk-management techniques • Risk avoidance • Loss prevention and control • Risk retention • Risk transfer 26
Implementation • Risk 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) • Futures shed both down- and up-side risks 27
Implementation • Some 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 28
Review • Management 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 change – Term life insurance with an annual renewable term is more flexible than policies without this clause 29
10. 4 The Three Dimensions of Risk Transfer • Hedging • Insuring • Diversifying 30
Hedging • A 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”) 31
Insuring • Insuring is the payment of a premium to avoid losses • Insurance 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 32
Diversifying • Diversification 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 m = 0. 15, a standard deviation s = 0. 20, and are correlated with each other with rho = 0. 9 33
s = 0. 2000 s = 0. 1421 s* = 0. 1342 Theoretical Minimum 34
Observation • Most 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 correlation • Progressively adding one more new stock has a diminishing affect on risk 35
Equation for Homogeneous Diversification with n Stocks 36
10. 5 Risk Transfer and Economic Efficiency • Institutional 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 37
10. 6 Institutions for Risk Management • A complete market for allocating risk would permit the separation of productive activity and risk-bearing – While technology is driving the risk marketplace towards completeness, this will not be achieved because: • transaction costs • incentive costs 38
10. 7 Portfolio Theory: Quantitative Analysis for Optimal Risk Management • Portfolio theory – quantitative analysis for optimal risk management • Portfolio theory selects from a set of (usually divisible) risks by optimizing risk-return • Consumption and risk preferences are exogenous • It is sometimes possible to devise a strategy that reduces the risk of all contracting parties 39
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 table 40
Returns on GENCO & RISCO 41
• Probability Distributions of Returns of GENCO and RISCO • 0. 6 • 0. 5 • 0. 4 • Probability • 0. 3 • 0. 2 • 0. 1 • 0 • 50% • GENCO • 30% • RISCO • 10% • -10% • Return 42 • -30%
Observation • Both companies have the same expected return, but there is considerably more risk associated with RISCO 43
10. 9 Equations: Mean 44
Equations: Standard Deviation 45
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’s • However, we would expect share prices to follow a continuous distribution, rather than the discrete distribution illustrated 46
Continuous Distributions • 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 47
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Two New Distributions of Return • The 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 VOLCO 49
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Caveat • The 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 number 51
Caveat • The distribution of ODDCO’s returns follow a Cauchy Distribution • The 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 SD 52
Caveat • As we progress, we will assume that stock returns do have a mean and a standard deviation, but this is a key assumption 53
Another Caveat • You 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 54
Another Caveat: Resolution • The 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 cetera 55
Another Caveat: Resolution • One 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) 56
Yet Another Caveat • Recall 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 problem 57
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 returns 58
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