148

Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

Embed Size (px)

Citation preview

Page 1: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132
Page 2: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

3Risk Analysis - Michèle Breton

Course Outline

Risk and the risk analysis processDeterministic models and sensitivity analysisBasic probabilities, expectation and decision criteriaProbabilistic models and Monte-Carlo simulationDecision trees, utility theory and real options

PESCE 2013

Page 3: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

Risk Analysis - Michèle Breton 4

INTRODUCTION

PESCE 2013

Page 4: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

5Risk Analysis - Michèle Breton

Geologists tell you that the chances of finding oil are 90% for a given prospect. You find a dry wellEconomists tell you that there is a 90% chance that the demand for electricity will exceed your capacity in the next 25 years. You build a power plant, but its capacity is under-used

PESCE 2013

What Is a Good Decision?

Page 5: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

6Risk Analysis - Michèle Breton

What Is a Good Decision?

Did you take the right decision?

How can you tell if your decision was right?

Were your experts wrong?

PESCE 2013

Page 6: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

Risk Analysis - Michèle Breton 7

Capabilities

Information processingComputationConsistency

StructureIntuitionAlternative generation

PESCE 2013

Page 7: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

Risk Analysis - Michèle Breton 8

Decision Problems

Unique

Complex

Uncertain

Subjective

Conceptual framework

Mathematical model

Probabilities

Analysis

PESCE 2013

Page 8: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

9Risk Analysis - Michèle Breton

Risk Analysis

Risk evaluation• Identify, quantify, characterize unwanted events

Risk management• Decision making, acceptable risks, communication,

risk mitigation and hedging

PESCE 2013

Page 9: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

10Risk Analysis - Michèle Breton

What Is Risk/Uncertainty?

Technical EconomicEnvironmentalPolitical…

PESCE 2013

Page 10: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

11Risk Analysis - Michèle Breton

Unpredictable events• Account for the risk of hazardous material spillage

Probability• Quantify the risk of a nuclear accident

Consequence• Evaluate the risk of a negligence

Menace• Consider the political risk

PESCE 2013

What Is Risk/Uncertainty?

Page 11: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

12Risk Analysis - Michèle Breton

Risk Definition

There is no precise definition – depends on the context and applicationMultidimensional concept

• Damages, consequences (values)• Uncertainty (probability)• Impact (decision maker’s circumstances)

There is no universally accepted measure

PESCE 2013

Page 12: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

13Risk Analysis - Michèle Breton

10 000 $

-10 000 $

0.99

0.01

10 000 Iranian Rials

-10 000 Iranian Rials

0.5

0.5

10 000 $

-10 000 $

0.5

0.5

10 000 $

50 000 $

0.5

0.5

Perception vs. Attitude

Different decision• Perception of risk• Risk preference

Examples10 000 $

-10 000 $

0.5

0.5

For Carlos Slim …

1 MXN = 1886.0989 IRR

PESCE 2013

Page 13: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

14Risk Analysis - Michèle Breton

Global Risk

Is a combination of many elementsIs related both to uncertainty and adverse consequencesDecreases with time, with increasing informationIs estimated subjectively – no single measure is universally accepted

PESCE 2013

Page 14: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

15Risk Analysis - Michèle Breton

The Risk Analysis Process

Structuring the problem• Alternatives, uncertainties, variables and parameters,

values, relations and dependencies

Deterministic modeling• Computation of results, preference measures,

sensitivity analysis

PESCE 2013

Page 15: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

16Risk Analysis - Michèle Breton

The Risk Analysis Process

Probabilistic modeling• Probability distributions, parameter estimation,

scenario forecasting, dependencies

Analysis• Risk profile, optimal strategy, value of information,

value of flexibility, sensitivity analysis

Results

PESCE 2013

Page 16: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

17Risk Analysis - Michèle Breton

Applications

Equipment replacement decisionsDetermination and revision of the probability of a discoveryProject evaluation and selectionDrilling, testing and development decisionsFarming-out, joint-ventures and abandonment decisionsEvaluation of reserves

PESCE 2013

Page 17: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

18Risk Analysis - Michèle Breton

Structuring Decision Problems

Parameters, futuresVariables, alternatives, plansAvailable information and uncertaintyDependenciesObjective and risk mitigation

PESCE 2013

Page 18: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

19Risk Analysis - Michèle Breton

Examples: deciding about

Size of a production facilityExploration for oilEnergy resource plan

PESCE 2013

Page 19: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

Risk Analysis - Michèle Breton 20

DETERMINISTIC MODELSEvaluation of a situation

PESCE 2013

Page 20: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

21Risk Analysis - Michèle Breton

Investment Opportunities

Most decisions under risk may be considered as investment opportunities

• Exploration for hydrocarbons in new regions• Expansion schedule for power plant's capacities• Development of new capacity, new energy sources• Reliability, quality, process, product improvement

programs• Long-term contracts

PESCE 2013

Page 21: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

22Risk Analysis - Michèle Breton

Modeling and Economic Analysis

The determination of the economic value of these investment opportunities must take into account many elements, some of which are uncertain:

• Development and operation costs• Demand, revenues• Price of energy

While others result from decisions:• Development plan• Production method• Pricing• Capacity

PESCE 2013

Page 22: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

23Risk Analysis - Michèle Breton

Deterministic Model:a Basic Tool

Choose the “best” optionEvaluate projectsAnalyze risk

PESCE 2013

Page 23: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

24Risk Analysis - Michèle Breton

Scenario Evaluation

Scenario: a given situation, for a given set of decisions and of values for the uncertain parametersDeterministic model: evaluation tool, generally in the form of a spreadsheet cash-flow model

PESCE 2013

Page 24: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

25Risk Analysis - Michèle Breton

Inputs

Model parameters are based on information gathered from various departments or experts:

• Investments & development planning• Operation costs• Demand• Oil price

The precision of this information varies. Usually, it increases during the life of the project

PESCE 2013

Page 25: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

26Risk Analysis - Michèle Breton

Base Scenario

The most probable values for all parameters make up what is called the base scenario

PESCE 2013

Page 26: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

27Risk Analysis - Michèle Breton

Outputs

Evolution of some interesting variables:• Revenues• Cash flows• Cumulated cash flows

Corresponding economic indicators:• Total discounted flows• Payback time• Maximum exposure• Surplus• Internal rate of return

PESCE 2013

Page 27: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

28Risk Analysis - Michèle Breton

Setting Up a Cash Flow

The following table presents the investment schedule for a nuclear plant project of 2000 MW capacity. Operation costs are expected to be $15 million per year plus $17 per megawatt produced, and capacity factor to be 90%. Operation costs are expected to increase by 6% per year after 20 years of operation. Abandonment cost is $500M.

PESCE 2013

Page 28: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

29Risk Analysis - Michèle Breton

Suppose that there is no inflation and that electricity price, presently at $34/MWh, will increase by 0.2% during the first 25 years, increase by 1.9% per year for the next 10 years, and by 0.6% per year afterwards.

Year 0 1 2 3 4 5 6 7 8 9 10 Investment ($ million)

10 10 15 15 15 95 600 1200 750 300 150

nucleardet

PESCE 2013

Page 29: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

30Risk Analysis - Michèle Breton

Cash-ins• Revenues (sales) • Salvage value of assets• Refunds of past expenses• Sales of services

PESCE 2013

Inputs of Cash Flow Models

Page 30: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

31Risk Analysis - Michèle Breton

Cash-outs• Technical costs (separated according to fiscal

treatment): • Capital expenditures• Operating costs (fixed or variable)

• Government take

PESCE 2013

Inputs of Cash Flow Models

Page 31: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

32Risk Analysis - Michèle Breton

Economic indicators “summarizing” the value of a project

• Time evolution of cash flows• Cumulated values• Net present value, return• Decomposition of cash flows

PESCE 2013

Outputs of cash-flow models

nucleardet

Page 32: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

33Risk Analysis - Michèle Breton

The cash flows generated by a project are divided between a Company (or a group of companies) and the State (possibly via a State Company)

• Royalties• Taxes (fiscal depreciation)• Advances and refunds

PESCE 2013

Dividing the Cash Flows

nucleardet

Page 33: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

34Risk Analysis - Michèle Breton

Investing in a Risky Project

Investing in a project irrevocably commits resources in the expectation of receiving future gainsTwo important factors have to be accounted for when evaluating an investment project:

• Return on investment in alternative investment opportunities (cost of capital)

• Risk associated with the project

PESCE 2013

Page 34: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

35Risk Analysis - Michèle Breton

Valuation of a Risk-free Project

Investing in a project prevents the use of capital in other opportunities, and particularly in "no risk" ventures with guaranteed rate of returnIn order for a project to be interesting, the return on investment should be at least as high as the best "no risk" alternative

PESCE 2013

Page 35: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

36Risk Analysis - Michèle Breton

Discounting

Discounting allows comparison of non risky amounts received at different time and of different streams of amounts

• Present value for a given rate is the amount which is equivalent to the stream of cash flows generated by the project

• Internal rate of return is a rate such that the NPV of a stream of cash flows is 0

nucleardet

PESCE 2013

Page 36: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

37Risk Analysis - Michèle Breton

Discount Rate

Discount rates for projects must be chiefly based on rates of return* of alternative investment opportunities. These may vary in time, but may also vary according to the available capital The long term cost of capital is generally a lower bound when evaluating investment projects

* May include anticipated inflation

PESCE 2013

Page 37: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

38Risk Analysis - Michèle Breton

Use of Index Numbers

The computations in a cash-flow model must be done in money of the day (e.g. taxes, agreements, depreciation, refunds)When setting up the model, parameters are estimates in estimate date money

PESCE 2013

Page 38: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

39Risk Analysis - Michèle Breton

Use of Index Numbers

Cost and price data is obtained in estimate date moneyThis data is adjusted using an acceleration index - adjustment rates may differ (nominal or money of the day data)If desired, the cash-flows can be deflated to obtain constant money data Discounting is applied to account for time value. If it is applied on constant money data, if must not contain anticipated inflation PESCE 2013

Page 39: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

40Risk Analysis - Michèle Breton

Risk Premium

The previous argument is based on the assumption that cash flows are risk-free amounts. The investor will prefer a "risk-free" investment to an uncertain project with a null net present valueThe risk premium is the amount the investor will require of a risky project in excess of the present value of a risk-free project

PESCE 2013

Page 40: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

41Risk Analysis - Michèle Breton

Risk Preference

This risk premium depends on the investor (risk aversion) and on the magnitude of the risked amounts. It is usually difficult to ascertainExamples

• Insurance• Higher return from speculative stock• Higher price for reputable product• Price of flexibility

PESCE 2013

Page 41: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

42Risk Analysis - Michèle Breton

Accounting for the risk premium by increasing the discount rate is a common practice – but cannot be used in the context of risk analysis. Using a “risky” discount rate supposes that there exist comparable risky investment for which comparable amounts are required.The alternative is the use of risk analysis, sensitivity analysis or Monte-Carlo simulation in order to evaluate the risk premium directly

PESCE 2013

Estimating the Risk Premium

Page 42: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

43Risk Analysis - Michèle Breton

Examples

Valuation of capital investment (nuclear plant Texas Gulf Coast)Development of an oil fieldIntegrated resource plan

PESCE 2013

Page 43: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

Risk Analysis - Michèle Breton 44

SENSITIVITY ANALYSISIllustration of the effects of risk

PESCE 2013

Page 44: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

45Risk Analysis - Michèle Breton

The Base Case

Most probable realization for the uncertain parameter and corresponding decisionsIs often used for decision making (e.g. npv analysis)However, the probability of the realization of the base case may be very small

PESCE 2013

Page 45: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

46Risk Analysis - Michèle Breton

Steps of a Sensitivity Analysis

Identification of the various risk factorsEstimation of the range of possible values Computation of the (economic) effectAnalysis (risk management)

PESCE 2013

Page 46: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

47Risk Analysis - Michèle Breton

Sensitivity Analysis

In a sensitivity analysis, input parameters are varied one by one around their base case value in order to judge the impact of these variations on the profitability indicatorsThis provides the answers to "what if" type questions

PESCE 2013

Page 47: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

48Risk Analysis - Michèle Breton

Example

In the nuclear plant valuation example, the experts who estimated the data point out that it may vary. Thus:

• The forecast of long range electricity prices could be lower (no increase in real term price) or higher (environmental legislation)

PESCE 2013

Page 48: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

49Risk Analysis - Michèle Breton

Example

• Increase in variable operating costs could go from 4% to 7%

• Plant performance could be between 80% and 92% • Construction costs could vary by 200$ per nominal

KW, more or less• Fixed operating costs could be between 13 and 16 M$

per year.

PESCE 2013

Page 49: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

50Risk Analysis - Michèle Breton

Sensitivity TableElectricity price high 2785 815.61

probable 2223 -53.45low 1904 -362.56

Variable costs high 1759 -96.81probable 1576 -53.45low 1293 79.69

Plant efficiency high 92% -8.51probable 90% -53.45low 80% -278.12

Construction costs high 1.7 -296.52probable 1.5 -53.45low 1.3 189.63

fixed costs high 16 -60.54probable 15 -53.45low 13 -39.27

PESCE 2013

Page 50: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

51Risk Analysis - Michèle Breton

Spider Diagram

PESCE 2013

Page 51: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

52Risk Analysis - Michèle Breton

Tornado Diagram

PESCE 2013

Page 52: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

53Risk Analysis - Michèle Breton

Sensitivity Analysis

Is easy to do and easy to understandDetermines the range of probable values Illustrates extreme casesAnswers what if and what should questionsPoints out critical parametersPoints out the range of acceptable situationsIndicates trade-offs and allow risk management

nuclearsens

PESCE 2013

Page 53: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

54Risk Analysis - Michèle Breton

Sensitivity Analysis

Considers only independent variations of parametersDoes not take probabilities into accountDoes not account for correlations in parameter values

PESCE 2013

Page 54: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

55Risk Analysis - Michèle Breton

Uses

Sensitivity analysis can be used to evaluate the risk of an investment projectIt can also help in choosing among many possible projectsExample: BED

PESCE 2013

Page 55: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

Risk Analysis - Michèle Breton 56

PROBABILITIESMeasure of uncertainty

PESCE 2013

Page 56: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

57Risk Analysis - Michèle Breton

What Is a Probability

A probability is a measure of an uncertain eventThis measure is applied to the “likelihood” of the eventAn event which is more likely to happen than another has a higher probabilityBy convention, probabilities are between 0 and 1

PESCE 2013

Page 57: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

58Risk Analysis - Michèle Breton

Three Kinds of Probability

Geometric probability

Honest dice

PESCE 2013

Page 58: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

59Risk Analysis - Michèle Breton

Three Kinds of Probability

Limit of frequencies

Statistical data

PESCE 2013

Page 59: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

60Risk Analysis - Michèle Breton

Three Kinds of Probability

Subjective probability

Personal firm belief of the decision maker

PESCE 2013

Page 60: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

61Risk Analysis - Michèle BretonPESCE 2013

A Probability Tree

high

low

Price

medium

10%

70%

20%

A probability tree is the representation of a state of mind

Page 61: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

62Risk Analysis - Michèle BretonPESCE 2013

Dependent and Independent Events

0,1

B

NB A

NA

0,8

0,2

0,9

B

NB

0,3

0,7

0,6

B

NB A

NA

0,8

0,2

0,4

B

NB

0,4

0,6

Page 62: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

63Risk Analysis - Michèle Breton

Notation

: Probability that B is realized, given that A is realized: Probability that both A and B are realized: Probability that either A or B is realized

PESCE 2013

Page 63: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

64Risk Analysis - Michèle Breton

when new informationbecomes available

PESCE 2013

Change of Probability

A1 A2 A3 A4 A5

B

Bayes

Page 64: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

65Risk Analysis - Michèle Breton

Example

In a region, the probability of drilling a dry well is 90%. When there is no oil, a test gives positive results 40% of the time. When there is oil, the test gives a positive result 80% of the time. Suppose that the test in some prospect is negative, what is the probability of this prospect containing oil?

PESCE 2013

Page 65: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

66Risk Analysis - Michèle Breton

Random Variables

X: number of points on the dieProbability distribution:

PESCE 2013

x 1 2 3 4 5 6

P(X=x)

1/6 1/6 1/6 1/6 1/6 1/6

Page 66: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

67Risk Analysis - Michèle Breton

Random Variables

X: construction costProbability density:

Construction costs ($/KW)

PESCE 2013

Page 67: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

68Risk Analysis - Michèle Breton

Probability Distribution/Density

b

abxa i dxxfxXPbXaP

i)()()(

PESCE 2013

Page 68: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

69Risk Analysis - Michèle Breton

Understanding a distribution

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 190

0.05

0.1

0.15

0.2

0.25

PESCE 2013

Page 69: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

70Risk Analysis - Michèle Breton

Definitions

ModeMedianMeanRangeStandard deviationVaRTVaR

95% VaR=7,5

TVaR95=9

PESCE 2013

Page 70: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

71Risk Analysis - Michèle BretonPESCE 2013

Mathematical Expectation Decision Criterion

Page 71: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

72Risk Analysis - Michèle Breton

Preventive maintenance, equipment backupAsymmetrical distributionsExploration wellsResearch and developmentExpected Net Present Value where

• p: probability of a success• V: net present value if success• C: sunk cost if failure

PESCE 2013

Examples

reliability

Page 72: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

73Risk Analysis - Michèle Breton

Best Strategy

expnpv

PESCE 2013

Page 73: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

74Risk Analysis - Michèle Breton

Risk Measures

Variance, standard deviation

Percentiles (VaR)Conditional expectations (TVaR)

PESCE 2013

Page 74: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

75Risk Analysis - Michèle Breton

Risk-return Trade-off: the Efficient Frontier

Maximise return for a given level of riskMinimise risk for a given returnLagrangean interpretation, risk tolerance

PESCE 2013

Page 75: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

76Risk Analysis - Michèle Breton

Expected Value Adjusted for Risk

where R is the risk tolerance (order of the total amount that one is willing to risk)

PESCE 2013

Page 76: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

Risk Analysis - Michèle Breton 77

MONTE-CARLO SIMULATIONRisk evaluation in a complex model

PESCE 2013

Page 77: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

78Risk Analysis - Michèle Breton

Monte-Carlo Simulation

Allows simultaneous variations of parametersUses probability distributionsAccounts for correlation

PESCE 2013

Page 78: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

79Risk Analysis - Michèle Breton

Steps in a Monte-Carlo Simulation

1. Stochastic modeling: obtain probability distributions for the uncertain input parameters (statistical information or analysis)

2. Select a combination of input parameters from these distributions using random numbers

3. Compute economic indicators (outputs) for this combination of parameters

PESCE 2013

Page 79: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

80Risk Analysis - Michèle Breton

Steps in a Monte-Carlo Simulation

4. Repeat steps 2 and 3 many times5. Present results in the form of a probability

distribution

PESCE 2013

Page 80: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

81Risk Analysis - Michèle Breton

Number of equipment failures in a week: Poisson distribution of mean 2

PESCE 2013

Page 81: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

82Risk Analysis - Michèle Breton

Number of producing wells in100: Binomial (100,0.9)

PESCE 2013

Page 82: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

83Risk Analysis - Michèle Breton

Net pay: triangular of minimum 20m, probable 30m and maximum 60m

PESCE 2013

Page 83: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

84Risk Analysis - Michèle Breton

Reserves: Lognormal with mean of 150 BCF and standard deviation of 150 BCF

PESCE 2013

Page 84: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

85Risk Analysis - Michèle Breton

Variable opex: Normal with mean of $10 per MW and standard deviation of $2 per MW

PESCE 2013

Page 85: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

86Risk Analysis - Michèle Breton

Delay: Uniform between 0 minutes and 5 minutes

PESCE 2013

Page 86: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

87Risk Analysis - Michèle Breton

Random Valuesrandom

PESCE 2013

Page 87: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

Risk Analysis - Michèle Breton 88

Sampling

Electricity price: highVariable costs increase: 5.65%Plant efficiency: 85%Construction costs: 1.42$/WFixed costs: 13.7M$/yrAbandonment cost: 475M$

Porosity: 0.17Water saturation: 0.30Net pay: 9mArea: 32 haRecovery factor: 30%

PESCE 2013

A “trial” corresponds to the generation of random values for all parameters

Page 88: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

89Risk Analysis - Michèle Breton

Results

For each specific trial, a “result” is computed using the deterministic model. This result is recorded and will be used to produce the distribution of results of all trials

PESCE 2013

Page 89: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

90Risk Analysis - Michèle Breton

Example

Compute recoverable reserves according to pessimistic and optimistic scenariosEvaluate nuclear plant project according to pessimistic and optimistic scenariosCompare with Monte-Carlo simulation.

RESERVNuclearsimul

PESCE 2013

Page 90: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

91Risk Analysis - Michèle Breton

Distribution of Results

PESCE 2013

Page 91: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

92Risk Analysis - Michèle Breton

Trend Chart

PESCE 2013

Page 92: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

93Risk Analysis - Michèle Breton

Examples

Exploration for oilCorrelated reserves

Drill BitOilsim

Multizone

Oil field

PESCE 2013

Page 93: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

94Risk Analysis - Michèle Breton

Monte-Carlo Simulation

Illustrates possible consequences of a decision or a strategy, but cannot choose best strategy (specifically in sequential problems)Often the only possible solution when stochastic model is complexCan be used along with an optimizer – the objective is then a summary statistic

PESCE 2013

Page 94: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

Risk Analysis - Michèle Breton 95

DECISION TREESSequential decision processes

PESCE 2013

Page 95: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

96Risk Analysis - Michèle Breton

What Is a Tree?

A tree is a graph made up of nodes and arcs such that there exists a unique path from one specific node (called the root) to all the other nodes

PESCE 2013

Page 96: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

97Risk Analysis - Michèle BretonPESCE 2013

A Decision Tree

Construction0,20

environmental legislation 1044,56 920,691

0,00 920,69stop

permit 0,00 -123,87

-104,52 85,0435802Construction

0,800,55 no legislation -65,85 -189,72

high efficiency 21 0,00 -123,87

0,00 85,04 stop

0,00 -123,87

stop

0,00 -19,35

feasibility study Construction0,20

-19,35 49,9137894 environmental legislation 654,23 530,361

0,00 530,36stop

permit 0,00 -123,87

-104,52 6,97737843Construction

0,800,45 no legislation -312,14 -436,01

1 low efficiency 249,91 1 0,00 -123,87

0,00 6,98 stop

0,00 -123,87

stop

0,00 -19,35

no go

0,00 0,00

Page 97: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

98Risk Analysis - Michèle Breton

Decision and Event Nodes

Decision nodes (represented by squares) model a choice in a limited number of possible actions

Event nodes (represented by circles) model uncertainty

Decision 1outcome 1

cost 11

Decision 2outcome 2

cost 2

prob 1Event 1

outcome 1gain 1

prob 2Event 2

outcome 2gain 2

PESCE 2013

Page 98: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

99Risk Analysis - Michèle Breton

Drawing a Decision Tree

Identify the horizon and the evaluation dateIdentify all alternatives, present and future; do not forget “wait”, “stop” and “seek more information” options

PESCE 2013

Page 99: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

100Risk Analysis - Michèle Breton

Drawing a Decision Tree

Identify all uncertain events that can affect the consequences of decisions, or that can give useful information for future decisions. Make sure that all uncertain events at a given node form partitions

PESCE 2013

Page 100: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

101Risk Analysis - Michèle Breton

Drawing a Decision Tree

Draw the tree in chronological order - retard decisions as much as possibleEvaluate consequences at terminal nodes (leaves) using a deterministic modelEvaluate probability of uncertain events (subjective probabilities)

PESCE 2013

Page 101: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

102Risk Analysis - Michèle Breton

Possible, probable, a working possibility, betting chanceVery possible, reasonably certain, without doubtNot probable, impossible, a small chance, need to be very lucky, doubtful, highly improbable, almost impossible...

PESCE 2013

Evaluating a Subjective Probability

Page 102: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

103Risk Analysis - Michèle Breton

A way to quantify a subjective probability is to offer a choice between the event and a reference lottery

PESCE 2013

Evaluating a Subjective Probability

wet

white

black

dry

Page 103: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

104Risk Analysis - Michèle Breton

Which event is more probable?One adjusts the proportion of black balls in the box until the decision maker feels that both events are equally probable

PESCE 2013

Evaluating a Subjective Probability

wet

white

black

dry

Page 104: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

105Risk Analysis - Michèle Breton

Solving Simple Trees

100

500

~ ?

A Decision Node Is Replaced by the Best Option

500500

500

500

PESCE 2013

Page 105: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

106Risk Analysis - Michèle Breton

Solving Simple Trees

100

500

~ ?

0.5

0.5

An Event Node Is Replaced by its Certainty Equivalent

200200

PESCE 2013

Page 106: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

107Risk Analysis - Michèle Breton

Certainty Equivalent

The decision maker is indifferent between the lottery and the certainty equivalentFor a risk neutral decision maker, the certainty equivalent is equal to the expected value of the lotteryUtility theory provides a mechanism to find certainty equivalent for risk averse or risk seeking decision makers

PESCE 2013

Page 107: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

108Risk Analysis - Michèle Breton

Solving Complex Trees

All trees are simple trees at the end of the horizonTo solve a complex tree, simply “roll back” the horizon

PESCE 2013

Page 108: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

109Risk Analysis - Michèle Breton

Using a Software

Nucleartree

drilling

PESCE 2013

Page 109: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

110Risk Analysis - Michèle Breton

Optimal Strategy and Risk Profile0.20

environmental legislation Construction0.55 1 920.69

high efficiency permit 0.00 920.69 920.691

0.00 111.037979 -104.52 111.037979 0.80no legislation Construction

1 -91.38feasibility study 0.00 -91.38 -91.38

164.2106148 -19.35 64.2106148 0.20

environmental legislation Construction0.45 1 530.36

low efficiency permit 0.00 530.36 530.361

0.00 6.97717017 -104.52 6.97717017 0.80no legislation stop

2 -123.870.00 -123.87 0.00 -123.87

nuclearstrategy

PESCE 2013

Page 110: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

111Risk Analysis - Michèle Breton

Sensitivity

PESCE 2013

Page 111: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

112Risk Analysis - Michèle Breton

Value of Information

The expected value of information is the maximum price that the decision maker is willing to pay to obtain additional informationIt is equal to the additional gain the decision maker expects if this information is obtained

PESCE 2013

Page 112: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

113Risk Analysis - Michèle Breton

Expected Value of Perfect Information

Sequential decision problems are hard because the decision maker has to commit resources before knowing the realization of uncertain eventsIf uncertainty were resolved, the decision maker would have perfect information

PESCE 2013

Page 113: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

114Risk Analysis - Michèle Breton

No Information

200

-1025

+50

-4035

35

PESCE 2013

Page 114: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

115Risk Analysis - Michèle Breton

Perfect Information

200

+50

-40

-10

200

50

75

PESCE 2013

Page 115: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

116Risk Analysis - Michèle Breton

Expected Value of Perfect Information

: 40

200

-1025

+50

-4035

35

200

+50

-40

-10

200

50

75

PESCE 2013

Page 116: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

117Risk Analysis - Michèle Breton

Expected Value of Imperfect Information

Imperfect information allows the decision maker to revise probabilitiesValuable information has an impact on the decisionPrice of the information should not exceed its expected value

PESCE 2013

Page 117: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

118Risk Analysis - Michèle Breton

Example

A consulting firm is offering to analyze the situation for environmental legislationPast performances of this consulting firm indicate a 75% predicting accuracy when legislation is passed, 50% when it is not What is the maximum amount you should pay for this analysis?

nucleartest

PESCE 2013

Page 118: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

119Risk Analysis - Michèle Breton

Decision Tree

Clearly lays out the problem so that all options can be challenged Allows to analyze fully the possible consequences of a decisionModels adaptive strategiesHelps to choose the best strategy and evaluates the strategic value in a project (real options) Provides a framework to quantify the values of outcomes and the probabilities of achieving them

PESCE 2013

Page 119: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

120Risk Analysis - Michèle Breton

Examples

Bidding for a contractBuy or lease decisionOil exploration

PESCE 2013

Page 120: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

121Risk Analysis - Michèle Breton

The Real Option Approach

Useful when a predominant source of uncertainty can be monitored continuously (e.g. electricity prices)A simple decision tree with an underlying asset processVarious solution approaches, the most general is dynamic programmingReal option: flexibility value

PESCE 2013

Page 121: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

122Risk Analysis - Michèle Breton

Stochastic optimization

Taking the best decision under uncertaintyWhen uncertainty is revealed progressively, choosing the best strategy (tree)Monte-Carlo simulation can be used to assess strategies Simulation can also be coupled with search heuristics Decision trees are stochastic dynamic programs – curse of dimensionality Oil field

PESCE 2013

Page 122: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

Risk Analysis - Michèle Breton 123

UTILITY THEORYModeling attitude to risk

PESCE 2013

Page 123: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

124Risk Analysis - Michèle Breton

Attitudes to Risk

0

100

~ 50

0.5

0.5Risk neutral

0.5100

0~ 75

0.5

Risk seeker

~ 25

Risk averse

100

0

0.5

0.5

PESCE 2013

Page 124: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

125Risk Analysis - Michèle Breton

Risk Premium

The risk premium is the difference between the expected value and the certainty equivalentThe amount of the risk premium indicates the attitude to risk of the decision makerAttitude to risk may differ according to the consequences

PESCE 2013

Page 125: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

126Risk Analysis - Michèle Breton

Attitude to Risk

The certainty equivalent reflects the preferences of the decision makerThere is no “correct” attitude

PESCE 2013

Page 126: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

127Risk Analysis - Michèle Breton

Amount at Risk

0

50

100

150

200

250

300

350

400

450

500

0 200 400 600 800 1000

expected value certainty equivalent

riskpremium

PESCE 2013

Page 127: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

128Risk Analysis - Michèle Breton

Uncertainty

0102030405060708090

100

0 0.2 0.4 0.6 0.8 1

expected value certainty equivalent

risk premium

PESCE 2013

Page 128: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

129Risk Analysis - Michèle Breton

Gains vs. Losses

0

4000

< 32000.8

0.2Risk averse

0

-4000

>-32000.8

0.2Risk seeker

PESCE 2013

Page 129: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

130Risk Analysis - Michèle Breton

Consistent Risk Attitude

Finding the certain equivalent for each event is difficult and time consumingConsistency problemDecentralization problem

PESCE 2013

Page 130: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

131Risk Analysis - Michèle Breton

Using a Utility Function

Accept the behavioral axiomsFind the utility function describing attitude towards risk takingUse the utility function to find certain equivalents

PESCE 2013

Page 131: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

132Risk Analysis - Michèle Breton

Behavioral Axioms

> Indicates preference of outcomesA>B: outcome A is preferred to B~ Indicates indifference of outcomesA~B: the decision maker is indifferent between A and B

PESCE 2013

Page 132: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

133Risk Analysis - Michèle Breton

If A>B and B>C, then A>C

PESCE 2013

Transitivity

Page 133: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

134Risk Analysis - Michèle Breton

If A>B>C, then there exists a probability p such that

PESCE 2013

Existence

A

C

p

1-p~ B

Page 134: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

135Risk Analysis - Michèle Breton

If

Then B can be substituted to the lottery without changing preferences

PESCE 2013

Substitution

A

C

p

1-p~ B

Page 135: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

136Risk Analysis - Michèle Breton

If A>B and p is greater than q, then

PESCE 2013

Preference

A

B

p

1-p

A

B

q

1-q>

Page 136: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

137Risk Analysis - Michèle Breton

Probability (No Fun in Gambling)

A

B

B

p

q

1-p

1-q

A

B

pq

1-pq

~

PESCE 2013

Page 137: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

138Risk Analysis - Michèle Breton

Existence of a Utility Function

Acceptation of these axioms leads to the existence of a utility function that can be used for any uncertain ventureUtility function can treat any variables and multiple attributesUtility is a scale measuring preferences for outcomes. Conventionally, it takes values from 0 to 1

PESCE 2013

Page 138: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

139Risk Analysis - Michèle Breton

Building a Utility Function

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2000 4000 6000 8000 10000

utilit

y

amount

PESCE 2013

Page 139: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

140Risk Analysis - Michèle Breton

Building a Utility Function

-2000$

+8000$0.5

0.5

PESCE 2013

Page 140: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

141Risk Analysis - Michèle Breton

Using a Utility Function0

10.5

0.5

0.5

0.5

0.5

PESCE 2013

Page 141: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

142Risk Analysis - Michèle Breton

Value of Information

With non-linear utility, expected utility of information cannot be computed directlyOne has to find iteratively the cost which would make the decision maker indifferent between obtaining the information or not

PESCE 2013

Page 142: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

143Risk Analysis - Michèle Breton

The Exponential Utility Function

Within a reasonable range of values, many utility curves can be fit by an exponential function

R is the risk tolerance (in the units of x)Rules of thumb: net income or 20% market value or 15% of equity

utility

PESCE 2013

Page 143: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

144Risk Analysis - Michèle Breton

Expected Value Adjusted for Risk

Taylor expansion of the utility function shows that the certain equivalent of a risky amount X is approximately equal to

PESCE 2013

Page 144: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

145Risk Analysis - Michèle Breton

Market for Risk and Side Bets

Shifting the risk to less risk-averse party increases the utility of both partiesRisk transferring or risk sharing instruments

• Joint ventures• Insurance• Derivatives• …

PESCE 2013

Page 145: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

146Risk Analysis - Michèle Breton

Allais' paradox

50 M

0

10 M

0

0.10

0.90

0.11

0.89

D

C

10 M

0

50 M

10 M

0.10

0.89

0.01

A

B

PESCE 2013

Page 146: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

147Risk Analysis - Michèle Breton

Failure? of Utility Theory

EmotionsComprehension

• Probability• Consequences• Complexity

PESCE 2013

Page 147: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

148Risk Analysis - Michèle Breton

Conclusion

Utility theory and certainty equivalent approach accounts for risk explicitly with the risk penalty or risk tolerance, and for time considerations with a risk-free discount rate to evaluate streams of payoff Monte-Carlo simulation directly illustrates the effect of risk and allows one to choose, between various alternatives, the preferred risk/return profile

PESCE 2013

Page 148: Programa Ejecutivo de Capacitación en el Sector Energía Risk Analysis Michèle Breton, November 2013 Risk Analysis - Michèle BretonPESCE 20132

Risk Analysis - Michèle Breton 149

Thank you for your attention

PESCE 2013