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### INTRODUCTIONTORISK MANAGEMENT

Defense Resources Management Institute

Naval Postgraduate School

Monterey, California

Arabic - Fortuitous and favorable.

Greek - Fortuitous and neither favorable nor unfavorable.

Latin (risicum) - the challenge that a barrier reef presents to a sailor.

French (risque) - mainly negative connotation, but sometimes positive.

Oxford Dictionary - “... the chance of hazard, bad consequences, loss, etc....”

DEFINITIONS IEconomic risk - the chance of loss due to ….

Business risk - the chance ofloss associated with …

Market risk - the chance that a portfolio of investments can lose money because…..

Inflation risk - the danger that a general increase in prices ...

Interest-rate risk - market risk due to interest rate fluctuations

Credit risk - the chance that of a default on a loan ...

Liquidity risk - the difficulty in selling a fixed asset ...

Derivative risk - the chance of financial loss due to increased volatility ….

Cultural risk - the chance of loss because of product market …..

DEFINITIONS IICHANCE

Random Occurrence

BAD CONSEQUENCE

Sense of Loss

Hirschey & Pappas, Fundamentals of Managerial Economics Dryden Press, 1998

PROBABILITY

- It’s a number – it’s JUST A NUMBER!
- It’s a number between 0 and 1 (0 ≤P≤1)
- It quantifies the likelihood of an event
- It’s a function of experience, judgment, subjective assessment, available data
- It’s uses all information you think is relevant to the determination of the likelihood of occurrence of an event

Probability Rules

- Probability = 0 if “never/impossible”
- Probability = 1 if “always/certain”
- If we are collectively exhaustiveand
- mutually exclusive then

the probabilities over the outocmes

SUM to 1.

If mutually exclusivethen :

P(A or B) = P(A) + P(B)

If independent :

P(A and B) = P(A) x P(B)

Probability RulesProbability from Data

- Given data we can always derive approximate probabilities using relative frequency.
- Relative frequency can be used as an estimate of the probability of the observed value
- Taken all together, these can represent the underlying PROBABILITY DISTRUBUTION FUNCTION

0.50

0.474

0.45

0.40

0.35

0.30

0.240

0.25

0.20

0.158

0.15

0.10

0.065

0.05

0.038

0.020

0.004

0.001

0.00

[1.5 - 2.5)

[2.5 - 3.5)

[3.5 - 4.5)

[4.5 - 5.5)

[5.5 - 6.5)

[6.5 - 7.5)

[7.5 - 8.5)

[8.5 - 9.5)

Prob. of an event = proportion of observations that corresponds to the event

= percent of observations that

corresponds to the event

= portion of area of histogram that

corresponds to the event

AN INVESTMENT DECISION

- Planning for retirement
- Two options for investment
- Each has a track record, the historical rates-of-return over a specified time period
- Each can be used to compute various statistics; e.g., average rate-of-return, etc.

?

r < 0

I don’t want a rate of

return < 0!

I want a rate

of return > 0!

What’s the likelihood of

?

r < 0

The relative frequency histogram over the outcomes contains allrelevantinformation.

This information allows us to quantify risk.

This is provides our most powerful tool for risk management.

THE FREQUENCY HISTOGRAM( The “KEY to it ALL’’ )A QUANTITATIVE DEFINITION OF RISK

Risk is a COMBINATION of the answers to three questions:

(1) “What can go wrong?”

(2) “How likely is it to go wrong?”

(3) “If it does go wrong, what are the consequences?”

Adapted from S. Kaplan and B. John Garrick, “On the Quantitative Definition of Risk”, Risk Analysis, Vol.1, no.1, 1981

EXAMPLE: Hinterland Illegal Immigration

recession;

depression;

economic collapse

What can go wrong?

chances are 1 in a 10;

a 10% chance;

PF = .10

How likely is it to go wrong?

large numbers of illegal

immigrants ;

increasing crime;

failing social services; social unrest;

If it does go wrong, what happens to Drmecia?

A QUANTITATIVE DEFINITION OF RISK

What can go wrong?

Future

scenario

F

How likely is it to go wrong?

PF

Probability

of F

If it does go wrong, what are the consequences?

Y

Result due

to F

THE ANSWER TO THE FIRST QUESTION

1. It all starts with the future scenario, F.

2. The F is uncertain so we need probability, PF.

3. F causes a result, an outcome of concern, Y.

4. Y is a function of F. We need to know this relation!

The relation between Y and F is uncertain!!!

F→ X → Y

F1

F2

F3

…

FK

Y1

Y2

Y3

…

YN

THE “SYSTEM”

X1 then X2 then….. XM

F1, F2,… → X1 thenX2 then… → Y1, Y2,…

=

EXAMPLE: Hinterland Illegal Immigration

Illegal immigration is proportional to the ratio of per capita GDP.

GDPD/popD

GDPH/popH

Y

illegal immigration =

G. H. Hanson (2009), “The Economics and Policy of Illegal Immigration in the U.S.”, Washington, D.C.: Migration Policy Institute

THE ANSWER TO THE SECOND QUESTION

PF

PY

THE “SYSTEM”

X1 then X2 then….. XM

Probability Distribution

for

Outcomes of Interest

Probability Distribution

for

Future Scenarios

→ Math Model→

SIMULATION

MODELING

THE ANSWER TO THE THIRD QUESTION

What number of illegal immigrants do you most want to avoid? 10000; 100000; 1000000; 10000000; 20000000.

HOW YOU FEEL

(about the possible Y)

=

PREFERENCE

What outcome do you most prefer to avoid: minor economic strain; substantial strain; or collapse of government social/educational services?

THE ANSWER TO THE THIRD QUESTION

1. It all starts with the future scenario, F.

2. The F is uncertain so we need probability, PF.

3. F causes a result, an outcome of concern, Y.

4. Y is a function of F. GivenPFwe can derivePY

5. How do you feel about the probable outcomes?

Do you prefer to avoid some Y more than other Y?

Preferences < = > value function< = > v(Y)

(1) v(Y) > 0 if Y is “good”

(2) v(Y) < 0 if Y is “bad”

Value Function Charcteristics

reference point [defining GAINS from LOSSES]

(2) loss aversion [losses MORE IMPORTANT than GAINS]

(3) decreasing marginal values

THE ANSWER TO THE THIRD QUESTION

A QUANTITATIVE DEFINITION OF RISK

1. It all starts with the future scenario, F.

2. The F is uncertain so we need probability, PF.

3. F causes a result, an outcome of concern, Y.

4. Y is a function of F. Given PF we can derivePY

5. Your preference info, v(Y), is the LAST PIECE!

defines the consequences!

F

g(F)

g(F)

PY

Y

v(Y)

Risk

Hinterland Economy Collapse

Prob. of Economic Collapse

Prob. Dist. Illegal

Immigrants

Number of Illegal

Immigrants

How does Drmecia “feel” about the Y?

v(Y)

Y

“I can’t bear the thought of experiencing loss! “

In the limit the weight we assign to all outcomes <=> a loss

tends to -∞.

In this case risk is very simple to quantify risk.

“Experiencing loss would be a catastrophe!”

ASSESSING THE RISK (SPECIAL CASE)

RISK = P{ Y correspond to loss }

RISK = P{ Y ≥ reference point }

RISK = P{ unacceptable Y }

RISK = P{ Y you prefer to avoid }

OVERALL C-RATING System for Readiness:

C-1 = MAE > 89% P{not capable} ≤ 0.11

C-2 = MAE 80-89% 0.11 ≤ P{not capable} ≤ 0.20

C-3 = MAE 70-79% 0.21 ≤ P{not capable} ≤ 0.30

C-4 = MAE 50-69% 0.31 ≤ P{not capable} ≤ 0.50

C-5 = MAE < 50% 0.50 ≤ P{not capable}

Senate Armed Services Committee, terminology used in arguments before the committee, Feb. 1997

AR 220 – 1 (2010), AFI 10-201 (2006), SORTS (US Department of Defense)

1950 B.C. – Code of Hamurabi – formalization of bottomry contracts containing a risk premium for chance of loss of ships and cargo.

750 B.C. – Greece – the use of bottomry contracts.

1285 A.D. – King Edward - forbids use of soft coal in kilns to manage air pollution in London.

1583 A.D. – 1st life insurance policy issued in England.

19th and 20th century – water and garbage sanitation, building codes, fire codes, boiler inspections, railroads, steamboats, autos.

1959 A.D. – H. Markowitz, stock portfolio diversification.

The History of Risk ManagementWhat can go wrong F?

What is F and PF?

Identify

Risks

Assess Risks

What are the outcomes [Y, and PY]?

What are the consequences, v(Y)?

What is the risk [quantified]?

Prevent

Mitigate

Negotiate

Implement

Monitor

Management Action

Definition depends on a reference point.

National policy often specifies a reference point.

Not everyone has the same reference point.

THE RISK CURVE

Why not plot P{ Y ≥ y* } versus y*, for any y* ?

theoretical derivation

direct assessment

simulation

Determining theOutcomeDistributionGenerating your own data

earthquakes

Size of

earthquake

Earthquake cost

VARIABLE

Cost per

Total cost

earthquake

Program Cost

FIXED

Earthquake

policy

EARTHQUAKES

ACCEPTABLE RISK

“The perennial question free people ask with regard to defense is:

‘How much is enough?’ To this there can be no precise answer.

A country’s security is a function of the DEGREE OF RISK A

COUNTRY IS WILLING TO ACCEPT.”

Hitch & McKean, The Economics of Defense in the Nuclear Age, Atheneum, 1986

Ultimately, policy makers must decide how much the United States is willing to pay to lower the risks associated with de-ploying forces abroad. But some might argue that defense planners occasionally focus on absolute requirements – the minimum number of forces that they believe will meet

DoD’s military needs – without fully weighing the

relative risks and costs of alternative levels.

Moving U.S. Forces: Options for Strategic Mobility

Congressional Budget Office, Feb. 1997

“Our armed forces remain capable, within an acceptable level of risk, of meeting the demands of our strategy.”

Maj. Gen. John J. Maher,

Vice Director for Operations, Joint Staff:

testimony before House National Security readiness subcommittee,

Feb. 1997

“Computer security is basically risk management.”

“…. Managers have to decide what they are trying to protect and how much they are willing to spend, both in cost and convenience, to defend it.”

Stephen H. Wildstrom,

review of the book “Secrets and Lies by Bruce Schneier,

Businessweek

Sept. 2000

“…we continue to believe the federal government can benefit from risk management.”

“…. An effective risk management approach includes a threat assessment, a vulnerability assessment and a criticality assessment ...”

Raymond J. Decker,

Director, Defense Capabilities and Management, GAO,

Testimony before the Senate Committee on Governmental Affairs

Oct. 2001

Error

P(uncorrected) = 0.1

Reconciliation Check

P(corrected) = 0.9

P = .18

P(error) = 0.2

Correct

Data Entry

P(correct) = 0.8

P = .80

Correct

SECNAV M-5200.35 March 2007

Define Needs,

prepare Purchase

Requisition Form

Forward

to ASA

Direct or

Indirect/Reimb.?

End User

INDIR.

Forward

to SPFA

NO

YES

ASA reviews PR,

confirms funds, obtains approval

Admin.

Support

Funds

Available, etc.?

YES

SPFA assigns

PR number and form to PA

Sponsored

Program

Funds

Available, etc.?

SPFA

Reviews PR

NO

Purchase

Agent

with end user

End User

ASA /OA will

Assign req., number and

task Purchaser

Admin.

Support

Buy from

mandatory source or

go open market?

Sponsored

Program

NO

All required info.

present and adequate to

make procurement?

Screen request for mandatory sources of supply, prohibited or special items, and authority to buy

YES

Purchaser reviews for

completeness of

documentation

Purchase

Agent

Receive ordered items and sign acknowledging

STOP

End User

Admin.

Support

Sponsored

Program

YES

Order complete

and accurate?

Place order with source, direct delivery point, and provide estimated delivery date

NO

Receive order (if delivery point)

Reconcile with vendor

Purchase

Agent

What can go wrong?

NO

ERROR

0.9

How likely is it to go wrong?

Receipt

Review

ERROR

P = .1

0.1

0.9

0.1

P = .0729

ERROR

ASA

Screen

Request

0.9

0.9

0.1

P = .081

Reimburse

Or

Direct Funds

ERROR

Purchaser

0.9

0.1

P = .09

ERROR

SPFA

P = .3439

P = .1

0.1

ERROR

NO

ERROR

0.9

Receipt

Review

ERROR

P = .05

0.05

0.9

0.1

P = .07695

ERROR

ASA

Screen

Request

0.9

0.95

0.1

P = .0855

Reimburse

Or

Direct Funds

ERROR

Purchaser

0.95

0.1

P = .095

ERROR

SPFA

P = .30745

0.05

P = .05

ERROR

NO

ERROR

0.95

Receipt

Review

ERROR

P = .05

0.05

0.95

0.05

P = .04287

ERROR

ASA

Screen

Request

0.95

0.95

0.05

Reimburse

Or

Direct Funds

P = .0451

ERROR

Purchaser

0.95

0.05

P = .0475

ERROR

SPFA

P = .1855

0.05

P = .05

ERROR

NO

ERROR

0.95

P = .01

Receipt

Review

ERROR

0.01

0.99

0.01

P = .009703

ERROR

ASA

Screen

Request

0.99

0.99

0.01

Reimburse

Or

Direct Funds

ERROR

P = .009801

Purchaser

0.99

0.01

ERROR

P = .0099

SPFA

P = .0394

0.01

P = .01

ERROR

ESTIMATING SHIPBOARD HELICOPTER O&M COSTS

Life-cycle cost estimates for the helicopter are needed. The cost analysis staff is organized into four groups, one each for the four main components of the life-cycle cost: (1) R&D; (2) Procurement; (3) Operations and Maintenance; and (4) Salvage/Residual. As leader of the O&M cost estimating group you have decided to use a factor cost estimates since:

Relevant O&M cost data produce reliable CERs for the three components of the O&M cost [POL, Parts, and “Other”] as functions of the procurement cost.

The helicopter is a recently developed model and procurement cost is expected to be $3.7 million (+/- 3%).

Why not just use an O&M cost factor approach: annual O&M cost = 10% of acquisition cost?

POL[$/hr] = 112.84 + 30.16 × ACQ + error

Parts[$/hr] = -84.96 + 57.21 × ACQ + error

Other[$/hr] = 45.21 + 10.12 × ACQ + error

PROBABILISTIC COST ESTIMATING

Future explanatory variable is not always known with

certainty

Cost estimate

is a RANDOM

VARIABLE

There always is the model residual error

Intercept is

subject to

estimation

error

Slope coefficient is

subject to estimation error

y = a + b x + e

What is the resulting distribution

function?

PROBABILISTIC COST ESTIMATINGWhat is the most appropriate distribution function?

y = a + b x + e

What is the most appropriate distribution function?

What is the most appropriate distribution function?

What is the most appropriate distribution function?

cParts= a2 + b2×ACQ + e2

cOther = a3 + b3×ACQ + e3

CO,M&S = [cPOL + cParts + cother]×H

FACILITIES FOR THE FLIGHT SIMULATOR DEPARTMENT(ACTIVITIES, TIME ESTIMATES, AND DEPENDENCIES)

RISK is a factor in every decision with significant uncertainty

RISK is a combination of the answers to 3 questions

what can go wrong?

how likely is it to go wrong?

if it does go wrong, what are the conse-quences?

SUMMARYRISK is quantified using PROBABILITY.

use it to express the riskiness an alternative.

use it to find the least risky alternative.

THINK about the RISK vs COST tradeoff curve.

SUMMARYMANAGING RISK requires the information provided by the tradeoff curve!

THINK about where you want to be on the curve.

THINK about changing the tradeoff curve!

USE THE MODEL to help find how to change things!

SUMMARY
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