Bài giảng Tiếng Anh về Risk Analysis (phân tích rủi ro)

Bài giảng Tiếng Anh về Risk Analysis (phân tích rủi ro)

SECTION RISK ANALYSIS

RISK ANALYSIS

Risk introduction

Risk analysis tools

Risk reducing solutions

WHAT IS RISK?

Risk, in traditional terms, is viewed as a

‘negative’ Webster’s dictionary, for instance,

defines risk as “exposing to danger or hazard” The Chinese symbols for risk, reproduced below, give a much better description of risk

The first symbol is the symbol for “danger”,

while the second is the symbol for

“opportunity”, making risk a mix of danger and opportunity

WHAT IS RISK?

Risk is possibility of difference between actual outcome and expected outcome as planned

WHY RISK ANALYSIS ?

Future Certainty is Uncertainty

Project returns are spread over time

Most variables affecting NPV are subject to high level of uncertainty

Information and data needed for more accurate forecasts are costly to acquire

Need to reduce the likelihood to undertake a "bad" project while not failing to accept a "good" project

WHY RISK ANALYSIS ?

Business is associated with uncertainty

To deal with uncertainty:

to adapt to possible change

 Predict and limit uncertain elements

WHY RISK ANALYSIS ?

Decision making contexts

Business risk Financial risk Strategic risk

TYPES OF RISK

STRATEGIC RISK

Strategic risk relating fundamental changes in the economic and political environment

TYPES OF RISK

RISK ANALYSIS TOOLS

Sensitivity Analysis

Scenarios Analysis

Monte Carlo Risk Analysis

 Software: Crystal-Ball, @Risk

Sensitivity Analysis is the first step to risk analysis

Test the sensitivity of a project's outcome (NPV) to changes in one parameter value at a time

Basically "What if" analysis

Allows you to test which variables are important as a source of risk

A variable is important depending on:

 Its share of total benefits or costs

 Likely range of values

SENSITIVITY ANALYSIS

LIMITATIONS OF SENSITIVITY ANALYSIS

Range and probability distribution of variables

Sensitivity analysis doesn't focus on the realistic range

of values Sensitivity analysis doesn't represent the probabilities for each range Generally high probability of values close to mean and a small probability of being at the extremes.

Direction of effects

For most variables, the direction is obvious A) Revenue increases NPV increases B) Cost increases NPV decreases C) Inflation Not so obvious

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One-at-a-time testing is not realistic because of correlation among variables

A) If Quantity (Q) sold increases, costs will increase

Profits = Q (P - UC)

B) If inflation rate changes, all prices change C) If exchange rate changes, all tradable goods' prices and foreign liabilities change.

 One method of dealing with these combined or

correlated effects is scenario analysis

LIMITATIONS OF SENSITIVITY ANALYSIS

SCENARIO ANALYSIS

Scenario analysis recognizes that certain

variables are interrelated Thus a small number

of variables can be altered in a consistent

manner at the same time.

What is the set of circumstances that are likely

to combine to produce different "cases" or

"scenarios"?

A Worst case / Pessimistic case

B Expected case / Best estimate case

C Best case / Optimistic case

Note: Scenario analysis does not take into account the Probability of cases arising

SCENARIO ANALYSIS

Interpretation is easy when results are

robust:

A Accept project if NPV > 0 even in the worst case

B Reject project if NPV < 0 even in the best case

C If NPV is sometimes positive, sometimes negative, then results are not conclusive Unfortunately, this would be the most common case.

MONTE CARLO METHOD OF RISK ANALYSIS

A natural extension of sensitivity and scenario analysisSimultaneously takes into account different probability distributions and different ranges of possible values for key project variables

Allows for correlation (co-variation) between variablesGenerates a probability distribution of project

outcomes (Cash flows, NPV) instead of just a single

STEPS IN BUILDING

A MONTE CARLO SIMULATION

1 Mathematical model: project evaluation spreadsheet

2 Identify variables which are sensitive and uncertain

3 Define uncertainty

 Establish a range of options (minimum and maximum)

 Allocate probability distribution, most common distributions being: Normal distribution, Triangular distribution, Uniform distribution, Step distribution

4 Identify and define correlated variables

 Positive or negative correlation

 Strength of correlation

5 Simulation model: does a series of analysis for various

combinations of parameter values

6 Analysis of results

 Statistics

 Distributions

F3 F4 V6

V1 V2

V3 V4 V5

FORECASTING THE OUTCOME OF

x x x

Maximum

Minimum Observations

Minimum Maximum

Variable Value Probability

0.1

Minimum Maximum

Variable Value

0.3 0.5

0.1

Time

Now

The Single -Value Estimate

Variable Value Probability

x x

x

x x

x

x xx

The Deterministic Probability Distribution

1.0

FORECASTING THE OUTCOME OF

A FUTURE EVENT

DETERMINISTIC VS SIMULATION ANALYSIS

$

Simulation Analysis

Price Quantity

Revenue (V1 x V2) Materials

Salaries Expenses Operating Cost (V3+V4+V5) Fixed Cost

Total Costs (F2 + V6)

Profit/Loss (F1 - F3)

V1 V2 F1 V3 V4 V5 F2

F3 F4 V6

FOUNDATIONS OF RISK ANALYSIS PROBABILITY DISTRIBUTIONS

FOUNDATIONS OF RISK ANALYSIS PROBABILITY DISTRIBUTIONS

Non-Standard Flexible Distributions

SIMULATION RUNS USING COMPUTER PACKAGE

$

Results

Price Quantity Revenue (V1 x V2)

Materials Salaries Expenses Operating Cost (V3+V4+V5)

Fixed Cost

Total Costs (F2 + V6)

Profit/Loss (F1 - F3)

V1 V2 F1 V3 V4 V5 F2

F3 F4

y

y x

R1 R2 R3 R4

V6

Deterministic Analysis Simulation Analysis

CASE 1: PROBABILITY FOR NEGATIVE N.P.V = 0

Probability Cumulative Probability

-Decision: Accept

+

Note: Lower end of cumulative probability distribution is to the

right of zero N.P.V point

CASE 2: PROBABILITY FOR POSITIVE N.P.V = 0

Probability Cumulative Probability

-Decision: Reject

+

Note: Higher end of cumulative probability distribution is to

the left of zero N.P.V point

CASE 3: THE PROBABILITY FOR ZERO N.P.V IS GREATER THAN 0 BUT LESS THAN 1

Probability Cumulative Probability

CASE 4: MUTUALLY EXCLUSIVE PROJECTS

GIVEN THE SAME PROBABILITY, ONE PROJECT ALWAYS SHOWS A HIGHER RETURN

Probability Cumulative Probability

Case 5: Mutually Exclusive Projects - High Return versus Low Loss

Probability Cumulative Probability

Need to know attitude toward risk:

A If risk neutral, then uncertain which is best.

B If risk averse, then B preferred to A.

C If risk lover, then A may be preferred to B.

SIMPLE EXAMPLE

PROJECT: OIL SPECULATION

Buy a barrel of oil today and sell it in a year's time

Steps:

1) What is the RANGE of possible values?

 Minimum value: Zero probability of being below $10

 Maximum value: Zero probability of being higher than $60

2) What is the PROBABILITY of finding values

between these extremes?

RELATIVE PROBABILITY DISTRIBUTION FOR PRICE OF OIL NEXT YEAR

Price of Oil ($/barrel)

10 15 20 25 30 40 50 60

SINGLE - VALUED OR DETERMINISTIC MODEL

Based on BEST estimate or expected values

= $27.75 NPV = -20 + 27.75/1.1 = 5.23

Result: Therefore, undertake the project

MONTE CARLO SIMULATION OF MODEL

Repeatedly (500 times, for example) pick price values from

distribution at random This is done by picking a random

number between 0 and 100% and looking up the corresponding price value from the cumulative probability distribution For each simulation, calculate value of NPV After 500 simulation runs,

500 values of NPV are obtained for which expected NPV and

other characteristics of NPV distribution can be found.

OIL SPECULATION PROJECT: BASE CASE

Assumptions: -P0 = $20

-r = 0.10 Step Rectangular Distribution

Range for Next year’s Oil Price $10 to $60

Assumptions: -P0 = $20

-r = 0.10

• Step Rectangular Distribution

• Range for Next Year’s Oil Price $10 to $60

•500 Model Runs

-15 -10 -5 0 5 10 15 20 25 30 35 Expected Value (NPV) = 5.29 Standard Deviation = 9.24

Let next year’s oil price range be as follows:

Base Case with Uniform Distribution

100% Probability of result falling below corresponding value

Cumulative NPV Distribution

Base Case with Normal Distribution

100% Probability of result falling below corresponding value

Normal Distribution with Range ($10, $45.50)

100% Probability of result falling below corresponding

SUMMARY OF RESULTS FOR OIL SPECULATION PROJECT

A Base Case

B Base Case with Narrower Oil Price

Range ($10 to $30)

C Base Case with Uniform Distribution

D Base Case with Normal Distribution

E Base Case with Normal Distribution

HOW TO REDUCE THE COST OF RISK

Use Capital and Futures Markets

 Use forward, futures, and option markets to hedge specific project risks

 Use the capital market to diversify the risk to equity

owners; ideally, diversification will eliminate unique or unsystematic risk and reduce the cost of equity capital

 If there is no well-developed capital market then risks can

be reduced by spreading them over more investors

Use Contractual Arrangements to Reallocate Risks

and Returns

 Risk Shifting

 Risk Management

CONTRACTING CRITERIA

Contract with lowest cost (highest return if

investment occurs) not necessarily best contract

Efficient contracts may provide:

 better risk shifting - better distribution of cost across

ZERO SUM VERSUS POSITIVE SUM PERSPECTIVES

Cost focus is implicitly a zero sum perspective

What one party gains the other loses

Efficiency perspective is explicitly a positive sum

perspective With right contract one party can gain substantially without corresponding cost to other party

RISK SHIFTING

The following options are available:

Contracts that limit the range of values of a particular cash flow item,

or of net cash flow.

For example, a buyer may agree to purchase a minimum quantity

or to pay a minimum price in order to be sure of delivery; these

measures would put a lower bound on the sales revenue.

Similar measures would include:

a limited product price range

•a fixed price growth path

•an undertaking to pay a long-run average price

•specific price escalator clauses that would maintain the

competitiveness of the product, e.g indexing price to the price of a close substitute

Re: Quickfix Project

contract that specifies that unit costs (co)

will not rise above $12

0.1 0.3 0.5 0.7 0.9

Expected value of NPV = - $0.74 Srd Deviation = $44.41

Expected loss from accepting = 18.28 Expected loss from rejecting = 17.54

Risk-sharing contracts that reduce the risk borne by investors by increasing the correlation between sales revenue and some cost items

e.g., - profit sharing contract with labor

bonds with interest rates indexed to the product’s sales price

Risk-sharing contracts that decrease the correlation between benefit items or alternatively between cost items

CONTRACT THAT RESTRUCTURE INTRA-PROJECT CORRELATIONS

- The benefits from restructuring correlations are based on the formula

for the variance of the sum of two random variables (x and y)

For example, let:

x = revenues (R)

y = costs (C)

a = 1, b = -1v(net profit) = v(R-C) = v(R) + V(C) - 2 cov(R,C)

- any measure that will increase the positive correlation between R and C will increase cov (R,C) and reduce the variance of the net profit



CONTRACT THAT RESTRUCTURE INTRA-PROJECT CORRELATIONS

0.1 0.3 0.5 0.7 0.9

Re: Quickfix Project

- contract with supplier that establishes a cost ceiling of $12

- correlated initial selling price (po) and unit cost (Co) such that 18<Po<20 and correlation between Co & Po = +0.6

0.1 0.3 0.5 0.7 0.9

Re: Quickfix Project

- cost ceiling of $12 -contract for selling price linked to initial costs (Co)

If Co < 9, Po = 16; otherwise Po = 20

P(NPV<0) = 3%

0.1 0.3 0.5 0.7 0.9

Re: Quickfix Project

- cost ceiling of $12 -Revised contract for selling price

If Co < 9, Po = $16

9 < Co < 11, Po = $19; otherwise Po = $20

0.1 0.3 0.5 0.7 0.9

Re: Quickfix Project

- cost ceiling of $12 -Revised contract for selling price

If Co < 9, Po = $16.50

9 < Co < 11, Po = $18.50; otherwise Po = $19.50

Similarly, adding another product line will decrease the

variance of revenues provided that the revenues form the new

V(R o + R n ) = V(R o ) + V(R n ) + 2cov(R o , R n )

Also, any measure that reduces the positive correlation of costs will reduce the variance of total cost, which should also have the effect of reducing the variance of net profit

RESTRUCTURE INTRA-PROJECT CORRELATIONS

DIVERSIFICATION REDUCES RISK

Example A:

 An island economy trying to develop its tourist industry

 The chief source of uncertainty is the weather

Rate of return from manufacturing activities Weather Probability Suntan Lotion Umbrellas

Portfolio consisting of 50% suntan lotion shares and 50% umbrella shares

Note that in this case the Partial correlation

coefficient = -1

DIVERSIFICATION REDUCES RISK

RISK POOLING REDUCES RISK

Let yi = possible returns from a risky project

Assume that there are many such projects and that their returns are independently and identically distributed.

 Without Pooling (i.e investing in only one project)

Expected Value: E(yi) = y (mean return)

Variance: V(yi) = V(y)

 With Pooling (e.g buying shares in a number (n) if similar

projects) Let ai = proportion of total investment in each project = 1/n

Expected Value: aiE[y1+y2+ +yn]=ny/n=y

Variance: V[ai(y1+y2+ +yn)]

= V[y1/n+y2/n+ +yn/n]

= nV[y/n] = nV[y]/n 2 = V[y]/n lim V[y]/n = 0

EXAMPLE OF OIL EXPLORATION

Assume there are 100 firms in the oil exploration business

Each has $1 million invested and each drills one

well, which is independent of the others

Outcomes Probability Profit Rates of Return

If an investor puts all his/her money in the shares of one company, then the risk would be very high

However, if an investor constructs a portfolio

consisting of one share of each of the 100 companies, the riskiness of this portfolio will equal:

V[R] = 1.44 [R] / n = 12%

Question: Which risk should be included in the rate

of return that determines a project’s value (NPV)?

EXAMPLE OF OIL EXPLORATION

RISK MANAGEMENT

Problem:

 Many projects have

 large investment outlays

 long periods of project payout

 incomplete sharing of information and technology especially with foreign investors

 differences in the ability of the parties to bear risks

 unstable contracts

 Projects may be attractive in aggregate but are

unattractive to one or more parties due to uncertainties about sharing risks and returns

The result is that attractive projects are not being undertaken

CONTRACTING RISKS

Potential unilateral departures from contract terms

by one party that jeopardizes the other party’s

position

Examples

 Downside Risks

 Contractor walks away from project

 Government defaults on agreement if the share (of a smaller pie) going to the contractor is perceived to be too large

TAKING ACCOUNT OF CONTRACTING RISKS

IN ESTIMATING EXPECTED CASH FLOWS

Effect of contracting risk on total contractor returns.

- The contractor may not be permitted to share in the upside returns

- Hence, the contractor should evaluate the project using a “realistic”

probability distribution that reflects any contracting risks.