palisade user conference october 25-26, 2007 making it happen: assessing volatility &

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Palisade User ConferenceOctober 25-26, 2007

Making It Happen: Assessing Volatility &Employing Simulation to Mitigate Risk

By

Roy NersesianMonmouth UniversityColumbia University

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Three Areas of Employing Simulation To Mitigate Risk:

1. Chartering Decision Optimization

2. Swap Optimization

3. Substituting Insurance for Swaps

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Typical Long-Term Rate ForecastType I

The market is presently at $10 per ton and will improve marginally over the next 5-10 years for the following reasons:

1.2.3.

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1 2 3 4 5 6 7 8 9 10Year

$0

$2

$4

$6

$8

$10

$12

$14

$16

$18

$20$/

Ton

The Nice Upward Linear Slope

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Typical Long-Term Rate ForecastType II

The market is presently at $10 per ton and will decline marginally over the next 5-10 years for the following reasons:

1.2.3.

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1 2 3 4 5 6 7 8 9 10Year

$0

$2

$4

$6

$8

$10

$12

$14

$16

$18

$20

$/To

nThe Nice Downward Linear Slope

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Typical Long-Term Rate ForecastType III

The market is presently at $10 per ton and will remain unchanged over the next 5-10 years for the following reasons:

1.2.3.

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1 2 3 4 5 6 7 8 9 10Year

$0

$2

$4

$6

$8

$10

$12

$14

$16

$18

$20$/

TonThe Nice Flat Slope

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1 2 3 4 5 6 7 8 9 10Year

$0

$2

$4

$6

$8

$10

$12

$14

$16

$18

$20$/

Ton

Take Your Pick!

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So Which Is Selected?

10% Fact X% What Client Wants to Hear Y% What Is in the Self-Interest of the Forecaster

X% + Y% = 90%

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Another Approach

Assume Economic Growth for Major Oil Consumers

Translate to Oil Import Demand

Identify Sources

Translate to Tanker Demand

Project Tanker Supply

Compare and Obtain Estimate of Surplus

Surplus Determines Rate Forecast

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Interesting Problem:

Future Tanker Supply Depends on NewbuildingOrders and Scrapping Activity

Both Dependent on the MarketHigh Market – Order Ships and Defer ScrappingLow Market – Scrap Ships and Defer Ordering

Must Know Result of Forecast in order toDetermine Future Vessel Supply

Supply Is Then Matched to DemandTo Obtain the Rate Forecast!

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1995 2000 2005 2010 20150%

5%

10%

15%

20%

25%

Actual Forecast

Degree of Fleet Surplus

Weak Market

Strong Market

Volatility Greatly Diminished in Forecast!

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General Nature of Macroeconomic Forecasts

Less Volatility

Outlook Poor for Next Few Years

Be Patient – Market Will Improve

The Infamous Check () Forecast

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1 2 3 4 5 6 7 8 9 10Year

$0

$2

$4

$6

$8

$10

$12

$14

$16

$18

$20

$/To

n

Forecast

At least this forecast is has a rationale notdependent on what the client wants to hear!But What’s Missing?

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1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 20060

50

100

150

200

250

300

350

WS

Rat

es

History of VLCC Rates(AG/East)

1980s Average W35 Post-1990 Average W71

Tanker Depression

AG ExportsIncreasng

GulfWar

PeaceDividend

Erika

AsianEconomies

Expand

AsianHiccup

DotcomBubbleBurst

Prestige

VenezuelaNigeriaJapan

IraqYukos

U.S.IndiaChina

The Irrationality of Life -The Wild Cards of Reality!

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A B C D E

Charter Period Minimum Most Likely MaximumSpot $10 $15 $20One-Year $13 $17 $21Two-Year $15 $19 $23Three-Year $18 $21 $24Five-Year $23 $25 $27

Weak Market

Why Not Just Go With the Flow?

Three Markets: Weak, Strong, and In-Between

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0 1 2 3 4 5

Charter Period in Years

$0

$10

$20

$30

MaximumMost LikelyMinimum

Weak Market

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3456789

F G H I


Transition Market

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0 1 2 3 4 5


$0

$10

$20

$30

$40

$50


Transition Market

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J K L M


Strong Market

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0 1 2 3 4 5


$0

$20

$40

$60

$80

$100

$120


Strong Market

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1 2 3 4 5 6Market 1 1 1 0 0 0Spot $21 $23 $26 $17 $14 $13One-Year $29 $22 $27 $17 $16 $15Two-Year $25 $25 $24 $24 $18 $18Three-Year $35 $35 $35 $21 $21 $21Five-Year $40 $40 $40 $40 $40 $25Ownership $42 $42 $42 $42 $42 $42

0 – 70% Chance Weak Market1 – 20% Chance Transition Market2 – 10% Chance Strong Market

Market Conditions

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Number 20-YearVessels Daily Hire

Spot 0 $618One-Year 1 $492Two-Year 1 $501Three-Year 1 $642Five-Year 1 $612Ownership 0 $576

Total Hire $2,247

For a Fleet of Four VesselsSelect Type of Charters

Run @RISK Simulation



Total Hire $2,624



Total Hire $2,576

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Mean 1,817 Risk 2.13%

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Mean 2,276 Risk 1.73%

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Mean 2,031 Risk 0.15%

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Mean 2,335 Risk 19.6%

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Reward vs Risk

0

1,000

2,000

3,000

0 5 10 15 20 25% Risk

Rew

ard

Premium to Reduce Risk

Risk Reward (Cost)Spot 2.13 1,8175-Yr Non-Staggered 19.6 2,3355-Yr Staggered 1.73 2,276Diversified 0.15 2,031

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Oil Company Reaction

One Big Yawn

1. Have Given up on Discrete Forecasts2. Admit to Failure Because of Wild Cards3. Believe in a Diversified Portfolio of Charters4. Very Focused on Today’s Deals (Overriding

Consideration in Diversification

Nevertheless This is a Methodology of AnalysisFor Billions of Dollars of Shipping Expense

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Oil Company Reaction to Today’s Market

1. Today’s Market Is Strong, But How Long?

2. As Long as China Keeps Growing at 10%/Year

3. But For How Long? Who Knows!

4. So Why Bother? Simple Solution: Stay Diversified and Let Market Deals DetermineDiversification, Not a Computer Simulation!

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Swap Optimization

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“We Advise Our Clients to Cover 20-30% of Their Exposure With Swaps”

Where Does That Come From?

Heuristic Advice(Sounds Good)

Is There Another Way?

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Before Anything Can Occur, Have to be AbleTo Simulate Future Prices

Can Always Explain Past Price Patterns

But The Future Has All the Appearance of Randomness

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What are the Minimum Inputs RequiredTo Forecast the Future Price?

Not-So Random Walk Price Generator

Desired Range $30Start Price $50

Highest $80Upper $70Lower $40Lowest $30

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Bias Factor vs Stock Price

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60 70 80 90 100

Stock Price

Bia

s

Price over $70: Propensity to SellPrice over $80: 90% Chance of a –1 (Down Market)

Price below $40: Propensity to BuyPrice below $30: 90% Chance of a +1 (Up Market)

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Avg Price Minimum Maximum RangeYear 1 $45.97 $35.31 $54.99 $19.68Year 2 $39.97 $29.43 $50.28 $20.84Year 3 $50.03 $35.33 $65.44 $30.12Year 4 $43.09 $31.43 $59.30 $27.87Year 5 $53.38 $35.68 $76.29 $40.61

Avg RangeA Factor 15.551 $27.82B Factor 0.337

Objective-$2.18

AeBx - C

Average5-YearRange

Objective:Desired Rangeof $30 LessAverage RangeClose to 0

RangeFor Each of5 Years

Use RISKOptimizerTo Determine TheseFactors

In Order forThis EquationTo Generate anObjective ValueClose to Zero

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Price Change vs Cumulative Probability

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cumulative Probability

Pri

ce C

han

ge

What We Would Like: Large Probability of Small Incremental Change

Small Probability of Large Incremental Change

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Weekly Stock Price Change Generator

$0

$1

$2

$3$4

$5

$6

$7

0% 20% 40% 60% 80% 100%


Not Too Concave!Implies a Linear Relationship Between

Probability of Price Change and Degree of Change(Can Incorporate a Maximum Change)

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Head and Shoulders?

Stock Price

$30

$50

$70

$90

0 26 52 78 104 130 156 182 208 234 260

Week

Nevertheless Can Create Any Chart Pattern Imaginable!

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Nice Breakout

Stock Price

$30

$50

$70

$90

0 26 52 78 104 130 156 182 208 234 260

Week

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The Dog

Just Keep Hitting the F9 Key to Create a SlewOf Price Patterns

Stock Price

$30

$50

$70

$90

0 26 52 78 104 130 156 182 208 234 260

Week

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Problem:A Copper Mining CompanyRisk: Low Price of Copper

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Revenue in U.S. $ and Debt in British £sRisk: Adverse Change in Exchange Rates

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1234567891011121314151617181920

A B C D E F G HNot-So Random Walk Price Generator for Copper

Avg Price Minimum Maximum RangeDesired Range $400 Year 1 $1,565.71 $1,425.62 $1,685.36 $259.74Start Price $1,500.00 Year 2 $1,725.41 $1,571.12 $1,907.66 $336.54

Year 3 $1,449.42 $1,204.18 $1,818.50 $614.32Highest 2,200$ Year 4 $1,334.99 $1,196.78 $1,451.94 $255.16Upper 2,100$ Year 5 $1,743.06 $1,399.48 $1,963.10 $563.62Lower 1,300$ Lowest 1,200$ Avg Range

A Factor 7.261 $405.88Bias Factor 2 B Factor 2.759

Objective$5.88

StartWeek Weekly Price Month

0 Up/Down Change $1,500.001 0.50 1 $3.70 $1,503.702 0.50 -1 $14.00 $1,489.703 0.50 -1 $18.29 $1,471.404 0.50 1 $63.54 $1,534.94 1

Inputs

Outputs

Modeling Future Copper Price(Based on Past Prices)

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A Nice Concave Shape!

The Probability of a Small Incremental Change Higher Than Probability of A Large Incremental Change

1112131415161718192021222324

I J K L M N O PCumulative WeeklyProbability PriceDistribution Changes

0.0001 $0.000.1 $2.310.2 $5.350.3 $9.350.4 $14.630.5 $21.580.6 $30.750.7 $42.820.8 $58.730.9 $79.70

1 $107.32

Weekly Copper Price Change Generator

$0

$20

$40

$60

$80

$100

$120

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%


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1011121314151617181920

A B C D E F G HNot-So Random Walk Price Generator for 100 X GBP/$

Avg Price Minimum Maximum RangeDesired Range 5 Year 1 71.46 70.12 72.56 2.44Start Price 70 Year 2 72.70 70.51 74.63 4.12

Year 3 69.63 67.59 71.43 3.84Highest 80 Year 4 70.52 68.34 72.98 4.64Upper 75 Year 5 68.63 67.02 71.26 4.24Lower 65Lowest 60 Avg Range

A Factor 1.472 3.85Bias Factor 2 B Factor 0.493

Objective-1.15

StartWeek Weekly Price Month

0 Up/Down Change 70.001 0.50 1 0.12 70.122 0.50 1 0.54 70.663 0.50 1 0.69 71.354 0.50 -1 0.26 71.09 1

Modeling Future GBP/$ Conversion Rate(Based on Past Conversion Rates)

Inputs

Outputs

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1112131415161718192021222324

I J K L M N O PCumulative WeeklyProbability PriceDistribution Changes

0.00 0.000.1 0.070.2 0.150.3 0.230.4 0.320.5 0.410.6 0.510.7 0.610.8 0.710.9 0.82

1 0.94

Weekly 100 X GBP/$ Price Change Generator

0.00.10.20.30.40.50.60.70.80.91.0

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%


Not As Concave as Desired

Probability of Any Incremental Change AboutThe Same (Linear Relationship)

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56789

1011

L M N O P Q R

Copper MiningMinimum Most Maximum Actual Price Revenue

Month Production Likely Production Production $/Ton $MM1 1000 1100 1300 1133 1,397$ 1,583$ 2 1000 1110 1310 1140 1,402$ 1,599$ 3 1000 1120 1320 1147 1,424$ 1,633$

Copper Production Varies Between Min and Max WithOverall Growth With Time

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1011

R S T U V WMiningCosts Cash

Mining Without Debt Debt FlowRevenue Debt Charges Charges w/o

$MM Charges GBP GBP/$ $MM Swap1,583$ 1,108$ 500 0.702 $712 -$2371,599$ 1,112$ 500 0.694 $721 -$2341,633$ 1,115$ 500 0.707 $708 -$189

Mining Costs Are For OperationsDebt Charges in £ Translated to $

Cash Flow is Revenue Net of OperationalAnd Financial Costs

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1011121314151617181920212223

W X Y ZLowest

Desired BalanceWorking Working TotalCapital Capital Dividends

Cash $3,000 -$89 $24,231Floww/o Working

Swap Capital Dividends-$194 $2,806-$170 $2,636 $0-$287 $2,350 $0-$209 $2,141 $0-$306 $1,835 $0-$242 $1,593 $0-$265 $1,328 $0-$336 $992 $0-$320 $672 $0-$143 $529 $0-$326 $203 $0-$132 $71 $0-$160 -$89 $0$24 -$64 $0

Working CapitalDrained from NegativeCash Flows

Risk is Defined as theLowest Negative BalanceIn Working Capital Account

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293031323334353637383940414243

W X Y$461 $1,755 $0$272 $2,027 $0$370 $2,397 $0$426 $2,823 $0$249 $3,072 $0$350 $3,350 $72$513 $3,513 $350$542 $3,542 $513$412 $3,412 $542$239 $3,239 $412$275 $3,275 $239$427 $3,427 $275$372 $3,372 $427$572 $3,572 $372$538 $3,538 $572

When Cash Flow Is Positive (Column W), the Working Capital Account (Column X)Accumulates Funds

When Working Capital ExceedsMinimum Amount ($3,000),Excess Is Paid Out as a Dividend(Column Y)

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Producer and Consumer ConductBusiness As Usual

If Price Above Swap Price: Producer Pays Consumer The Difference Between Market Price and Swap Price Multiplied by the Swap Volume

If Price Below Swap Price: Consumer Pays Producer The Difference Between Market Price and Swap Price Multiplied by the Swap Volume

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Swap Benefit and Cost Analysis

Viewpoint of Producer:

Benefit:When Prices are Low, Swap InflowAdds to Revenue Reducing Risk of Loss

Cost:When Prices are High, Swap OutflowDecreases Revenue Reducing Profitability

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Swap Benefit and Cost Analysis

Viewpoint of Consumer:

Benefit:When Prices are High, Swap InflowReduces Loss From Buying High

Cost:When Prices are Low, Swap OutflowReduces Savings From Buying Low

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Swap Collar

If Price is Above the Cap, Producer PaysConsumer the Difference Multiplied by the

Swap Volume

If Price is Below the Floor, Consumer PaysProducer the Difference Multiplied by the

Swap Volume

If Price is Between the Floor and CapNo Exchange of Funds

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10111213

AA AB AC AD AE AF AGSwap cap $1,500 $0.72Swap floor $1,500 $0.72 LowestSwap volume 500 0 Desired Balance

Working Working TotalDebt Capital Capital Dividends

Revenue Charges Cash $3,000 $264 $13,393with with Flow

Copper Currency with both WorkingSwap Swap Swaps Capital Dividends$1,563 $721 -$266 $2,734$1,514 $718 -$316 $2,418 $0$1,563 $725 -$277 $2,141 $0$1,616 $716 -$217 $1,924 $0

Revenue Adjusted for Copper Swap &Debt Charges Adjusted for Currency Swap

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Reward versus Risk

The Cost of Risk Reduction is Less ProfitabilityYour Choice?

Desired Working Capital $3 Million

Swap Volume Probability of

Working Capital Being Copper Currency

Total

Dividends < $0 <-$1 MM <-$2MM 0 0 $15.6 mm 41.5% 30.0% 20.0%

500 0 $11.3 mm 24.8% 11.9% 4.8% 700 0 $9.7 mm 15.8% 5.0% 1.0% 500 200 $11.8 mm 20.6% 8.0% 2.3% 500 500 $12.3 mm 15.5% 3.9% 0.5%

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Desired Working Capital $4.5 Million

Swap Volume Probability of

Working Capital Being Copper Currency

Total

Dividends < $0 <-$1 MM <-$2MM 0 0 $15.6 mm 25.1% 16.4% 10.0%

500 0 $11.5 mm 7.6% 2.8% 0.6% 700 0 $9.7 mm 2.4% 0.4% - % 500 200 $11.7 mm 4.0% 0.9% 0.1% 500 500 $12.3 mm 1.5% 0.1% - %

Working Capital as a Means of Risk Mitigation

Your Choice Now?

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Has Financial Community Embraced Simulation as a Means to Mitigate Risk?

Inherent Problem is Assessing the HighestAnd Lowest Projected Price

Since 2002 Copper Prices Have More ThanDoubled (China’s Drawing Down of World Resources)

Any Long Term Swap Entered Into by ProducerAn Unmitigated Disaster & a Financial WindfallFor the Consumer

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Producer May Have Been Forced to EnterCopper Futures Market to Counter Swap as a Condition for a Loan or to Insure Against FallingPrices Leading to a Bankruptcy

Short-Term Swaps Provide No Protection for aLong-Term Loan

Unfortunately Swaps Are Entered Into on Basis That Each Counterparty Will Profit!

Companies Rejoice When There Is a Cash InflowCompanies Do Not Philosophize Over Cash Outflows Yet One Counterparty Will Be Proven Wrong

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Can Take Financial Measures to Counter a Costly Swap – e.g. Futures

Great for Financial Intermediaries!

But What If Copper Prices Had Fallen?

Copper Producer Could Have Gone BankruptOr Perhaps Not Obtained Bank Support for Loan

Prices Are 100% Explainable in Hindsight, ButIf the Doubling of Copper Prices Should Have BeenForeseen, Then What Is Your Projection of theFuture Price of Copper as of Now?

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Tens of Trillions of Swaps Outstanding

Futures Far, Far Exceed Physical Trading Volume

Are These Linked?

Some Feeling that Oil Futures Affecting Oil Prices

Is There an Alternative Where One FinancialDerivative Does Not Create Another?

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Insuring a Business Risk

Problem Was Expanded to Include Interest Rate Risk

Rather than Introduce Another Layer of Swaps:

What If a Company Proposed to Insure AgainstCombinations of Low Copper Prices, Adverse CurrencyExchange Rates, and High Interest Rates?

A Claim Is in Terms of Negative Cash Flows WhenWorking Capital Is Negative

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1011121314

AH AI AJ AK ALDesiredWorkingCapital$6,000

Cash Working TotalFlow Capital Dividends Claim Claims-$149 $5,851 $5,284-$62 $5,788 $0 $0

-$150 $5,638 $0 $0-$252 $5,386 $0 $0-$364 $5,022 $0 $0-$320 $4,702 $0 $0

Format of Problem Includes Interest Rate RiskPlus Claim to Insurance Company

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32333435363738394041424344

AH AI AJ AK-$191 $613 $0 $0-$250 $363 $0 $0-$76 $287 $0 $0

-$170 $117 $0 $0-$249 -$132 $0 $132-$202 -$334 $0 $334-$69 -$403 $0 $403$551 $148 $0 $0-$259 -$111 $0 $111-$142 -$252 $0 $252-$140 -$392 $0 $392$124 -$268 $0 $268-$143 -$411 $0 $411

Column AI Is WorkingCapital Account and Column AJ Is Dividends

A Claim Can Be MadeWhen Negative Cash Flow Exhausts Working Capital Account in Column AI

A Claim Made in Column AK Compensates for a Negative Balance in Working Capital Account and Flows Through CashFlow Column AH in Following Year

Basis of Insurance Claim

Cash Working Dividends ClaimsFlow Capital Paid Made

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Total Claims Cell Designed as Output=RiskOutput() + SUM(AK10:AK68)

@RISK Simulation RunTo Collect Data on Claims

Zero Claims Eliminated

@RISK Best Fit Used to Obtain Probability Distribution

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@RISK Best FitProbability Distribution for Claims

Output Fit Between Actual & Prob Dist

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Comparison of Probabilities of OccurrenceBetween Actual Data and Probability Distribution

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10

A B CDetermining an Insurance Premium

Base Insurance Premium $90High Premium $120Low Premium $60Start reserves $100,000Upper Trigger $120,000Lower Trigger $80,000

Objective: $642

Base Insurance PremiumDetermined by RISKOptimizer

Objective:To Keep Difference BetweenStarting and Ending Reserves (30 Years Later) Close to Zero

Breakeven Insurance Premium

Starting Reserves Arbitrarily Selected

Base Premium of $90,000 Applies As Long As Reserves Are Between $80,000& $120,000

Above $120,000 in Reserves, Premium Cut to $60,000

Below $80,000 in Reserves, Premium Stepped Up to $120,000

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13141516171819202122232425

A B C D E F GReserves

Annual Earnings Reserves EndingYear Premium Rate Reserves Income Claims Reserves

1 $90 6.0% 100,000$ $0 $0 $100,0902 $90 6.0% 100,090$ $5 $0 $100,1853 $90 6.0% 100,185$ $11 $0 $100,2874 $90 6.0% 100,287$ $17 $0 $100,3945 $90 6.0% 100,394$ $24 $0 $100,5076 $90 6.0% 100,507$ $30 $0 $100,6287 $90 6.0% 100,628$ $38 $274 $100,4828 $90 6.0% 100,482$ $29 $1,936 $98,6659 $90 6.0% 98,665$ -$107 $0 $98,648

10 $90 6.0% 98,648$ -$108 $0 $98,630

Annual Premium Added To ReservesIncome only on Amount Over Reserves of $100,000Earnings on $100,000 Belong to Pension or Other Insurance FundClaims in Excess of Reserves of $100,000 Charged 8% by Insurance Fund

This is the Inducement for Insurance Fund to Act as Reserves

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@RISK Formula in Claims (Column F)

=RiskDiscrete({1,0},{0.1549,0.8451})*RiskBetaGeneral(0.9754, 5.5733, 0.12384, 17220, RiskTruncate(, 13200))/5

Claims Formula Reflects No Claims 84.5% of Time

Claims Occur 15.5% of Time Whose AmountDetermined by @RISK Best Fit Distribution Probability

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Distribution of Ending Reserves

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Probability of $100,000 in Initial ReservesFalling Below $75,000 is Only 0.12%(This Is $25,000 Below $100,000)

Hence Initial Reserves Can Be Reduced to $25,000With Only a 0.12% of Exhausting Reserves

Can Be Rerun With Different Working CapitalTo Obtain an Alternative Insurance Premium

Determining Required Reserves

77

Reviewing What Happened, Copper Prices Rose To a Level That Would Have Reduced Premium toZero To Keep From Accumulating Excess Reserves

Had Copper Prices Fallen, Reserves Would Have Been Drawn Down Necessitating Hikes in the InsurancePremium – Subsequent Rise in the Copper Price WouldBe Necessary to Replenish Reserves

If Copper Prices Never Came Back, Then InsuranceReserves Would Have Been Exhausted (Risk of BeingAn Underwriter!)

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It Has Been Demonstrated That:

Simulation Can Be Used to Mitigate Riskto

Determine the Optimal Chartering Policy

Determine Optimal Swap Positions(As Good As Ability to Foresee Max & Min Limits)

Determine an Insurance Premium to CoverBusiness Risk Rather Than Relying on Swaps

(Again As Good As the Inputs)

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These Methodologies Do Depend on Assessing Market Limits. But Who Does Know the Future?

&

If Someone Did Know the FutureWould He or She Be Here?

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Questions & Answers (Maybe!)

Excel spreadsheets available in:@RISK Bank Credit and Financial Analysis

(Available from Palisade)

Also discussed in:Corporate Financial Risk Management

(Available from Praeger Press)

palisade user conference october 25-26, 2007 making it happen: assessing volatility &

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