1 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
2
Three Areas of Employing Simulation To Mitigate Risk:
1. Chartering Decision Optimization
2. Swap Optimization
3. Substituting Insurance for Swaps
4
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
6
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
8
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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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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3456789
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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F G H I
Charter Period Minimum Most Likely MaximumSpot $16 $30 $34One-Year $18 $30 $36Two-Year $20 $30 $38Three-Year $22 $30 $40Five-Year $26 $30 $42
Transition Market
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0 1 2 3 4 5
Charter Period in Years
$0
$10
$20
$30
$40
$50
MaximumMost LikelyMinimum
Transition Market
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J K L M
Charter Period Minimum Most Likely MaximumSpot $30 $50 $120One-Year $32 $48 $60Two-Year $34 $46 $50Three-Year $36 $43 $45Five-Year $38 $40 $42
Strong Market
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0 1 2 3 4 5
Charter Period in Years
$0
$20
$40
$60
$80
$100
$120
MaximumMost LikelyMinimum
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
Number 20-YearVessels Daily Hire
Spot 4 $656One-Year 0 $548Two-Year 0 $593Three-Year 0 $563Five-Year 0 $599Ownership 0 $576
Total Hire $2,624
Number 20-YearVessels Daily Hire
Spot 0 $561One-Year 0 $530Two-Year 0 $521Three-Year 0 $506Five-Year 4 $644Ownership 0 $576
Total Hire $2,576
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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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“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%
Cumulative Probability
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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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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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
$120
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Cumulative Probability
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1011121314151617181920
A B C D E F G HNot-So Random Walk Price Generator for 100 X GBP/$
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%
Cumulative Probability
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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23456789
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
57
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
63
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
64
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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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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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)
79
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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