Palisade User Conference
October 25-26, 2007
Making It Happen: Assessing Volatility &
Employing Simulation to Mitigate Risk
By
Roy Nersesian
Monmouth University
Columbia University
1
Three Areas of Employing Simulation
To Mitigate Risk:
1. Chartering Decision Optimization
2. Swap Optimization
3. Substituting Insurance for Swaps
2
Charter Rates for Varying Charter Periods
In Strong and Weak Markets
$100
Short Term Rates High
$/Day in $000
$80
$60
Long Term Rates
Determined by
Charterers Ability
To Build and Own
$40
$20
Long Term Rates
Determined by
Owner's Need to
Cover Cash Outlays
Short Term Rates Low
$0
Spot
1-Year
3-Year
5-Year
10-Year
3
Typical Long-Term Rate Forecast
Type 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.
4
The Nice Upward Linear Slope
$20
$18
$16
$14
$/Ton
$12
$10
$8
$6
$4
$2
$0
1
2
3
4
5
6
7
8
9
10
Year
5
Typical Long-Term Rate Forecast
Type 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.
6
The Nice Downward Linear Slope
$20
$18
$16
$14
$/Ton
$12
$10
$8
$6
$4
$2
$0
1
2
3
4
5
6
7
8
9
10
Year
7
Typical Long-Term Rate Forecast
Type 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.
8
The Nice Flat Slope
$20
$18
$16
$14
$/Ton
$12
$10
$8
$6
$4
$2
$0
1
2
3
4
5
6
7
8
9
10
Year
9
Take Your Pick!
$20
$18
$16
$14
$/Ton
$12
$10
$8
$6
$4
$2
$0
1
2
3
4
5
6
7
8
9
10
Year
10
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%
11
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
12
Interesting Problem:
Future Tanker Supply Depends on Newbuilding
Orders and Scrapping Activity
Both Dependent on the Market
High Market – Order Ships and Defer Scrapping
Low Market – Scrap Ships and Defer Ordering
Must Know Result of Forecast in order to
Determine Future Vessel Supply
Supply Is Then Matched to Demand
To Obtain the Rate Forecast!
13
Degree of Fleet Surplus
25%
Actual
Forecast
20%
15%
Weak
Market
10%
Strong
Market
5%
0%
1995
2000
2005
2010
2015
Volatility Greatly Diminished in Forecast!
14
General Nature of Macroeconomic Forecasts
Less Volatility
Outlook Poor for Next Few Years
Be Patient – Market Will Improve
The Infamous Check () Forecast
15
 Forecast
$20
$18
$16
$14
$/Ton
$12
$10
$8
$6
$4
$2
$0
1
2
3
4
5
6
7
8
9
10
Year
At least this forecast is has a rationale not
dependent on what the client wants to hear!
But What’s Missing?
16
The Irrationality of Life -The Wild Cards of Reality!
History of VLCC Rates
(AG/East)
350
Venezuela
Nigeria
Japan
Iraq
Yukos
300
WS Rates
250
Gulf
War
200
Asian
Economies
Expand
AG Exports
Increasng
150
Tanker
Depression
100
Peace
Dividend
Dotcom
Bubble
Burst
Erika
Asian
Hiccup
Prestige
U.S.
India
China
50
1980s Average W35
Post-1990 Average W71
0
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006
17
Why Not Just Go With the Flow?
Three Markets: Weak, Strong, and In-Between
A
3
4
5
6
7
8
9
Charter Period
Spot
One-Year
Two-Year
Three-Year
Five-Year
B
C
D
E
Weak Market
Minimum Most Likely Maximum
$10
$15
$20
$13
$17
$21
$15
$19
$23
$18
$21
$24
$23
$25
$27
18
Weak Market
$30
$20
Maximum
Most Likely
Minimum
$10
$0
0
1
2
3
4
5
Charter Period in Years
19
F
3
4
5
6
7
8
9
Charter Period
Spot
One-Year
Two-Year
Three-Year
Five-Year
G
H
I
Transition Market
Minimum Most Likely Maximum
$16
$30
$34
$18
$30
$36
$20
$30
$38
$22
$30
$40
$26
$30
$42
20
Transition Market
$50
$40
$30
$20
Maximum
Most Likely
Minimum
$10
$0
0
1
2
3
Charter Period in Years
4
5
21
J
3
4
5
6
7
8
9
Charter Period
Spot
One-Year
Two-Year
Three-Year
Five-Year
K
L
M
Strong Market
Minimum Most Likely Maximum
$30
$50
$120
$32
$48
$60
$34
$46
$50
$36
$43
$45
$38
$40
$42
22
Strong Market
$120
$100
Maximum
Most Likely
Minimum
$80
$60
$40
$20
$0
0
1
2
3
4
5
Charter Period in Years
23
Market
Spot
One-Year
Two-Year
Three-Year
Five-Year
Ownership
1
1
$21
$29
$25
$35
$40
$42
2
1
$23
$22
$25
$35
$40
$42
3
1
$26
$27
$24
$35
$40
$42
4
0
$17
$17
$24
$21
$40
$42
5
0
$14
$16
$18
$21
$40
$42
6
0
$13
$15
$18
$21
$25
$42
Market Conditions
0 – 70% Chance Weak Market
1 – 20% Chance Transition Market
2 – 10% Chance Strong Market
24
Spot
One-Year
Two-Year
Three-Year
Five-Year
Ownership
Number
Vessels
4
0
0
0
0
0
Total Hire
$2,624
Spot
One-Year
Two-Year
Three-Year
Five-Year
Ownership
Number
Vessels
0
0
0
0
4
0
Total Hire
$2,576
20-Year
Daily Hire
$561
$530
$521
$506
$644
$576
20-Year
Daily Hire
$656
$548
$593
$563
$599
$576
Spot
One-Year
Two-Year
Three-Year
Five-Year
Ownership
Number
Vessels
0
1
1
1
1
0
Total Hire
$2,247
20-Year
Daily Hire
$618
$492
$501
$642
$612
$576
For a Fleet of Four Vessels
Select Type of Charters
Run @RISK Simulation
25
Mean 1,817
Risk 2.13%
26
Mean 2,276
Risk 1.73%
27
Mean 2,031 Risk 0.15%
28
Mean 2,335 Risk 19.6%
29
Spot
5-Yr Non-Staggered
5-Yr Staggered
Diversified
Risk
2.13
19.6
1.73
0.15
Reward (Cost)
1,817
2,335
2,276
2,031
Rew ard vs Risk
Reward
3,000
2,000
1,000
Prem ium to Reduce Risk
0
0
5
10
15
20
25
% Risk
30
Oil Company Reaction
One Big Yawn
1.
2.
3.
4.
Have Given up on Discrete Forecasts
Admit to Failure Because of Wild Cards
Believe in a Diversified Portfolio of Charters
Very Focused on Today’s Deals (Overriding
Consideration in Diversification
Nevertheless This is a Methodology of Analysis
For Billions of Dollars of Shipping Expense
31
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 Determine
Diversification, Not a Computer Simulation!
32
Swap Optimization
33
“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?
34
Before Anything Can Occur, Have to be Able
To Simulate Future Prices
Can Always Explain Past Price Patterns
But The Future Has All the Appearance of Randomness
35
What are the Minimum Inputs Required
To Forecast the Future Price?
Not-So Random Walk Price Generator
Desired Range
Start Price
$30
$50
Highest
Upper
Lower
Lowest
$80
$70
$40
$30
36
Bias Factor vs Stock Price
1.0
Bias
0.8
0.6
0.4
0.2
0.0
0
10
20
30
40
50
60
70
80
90
100
Stock Price
Price over $70: Propensity to Sell
Price over $80: 90% Chance of a –1 (Down Market)
Price below $40: Propensity to Buy
Price below $30: 90% Chance of a +1 (Up Market)
37
Year 1
Year 2
Year 3
Year 4
Year 5
A Factor
B Factor
Avg Price Minimum
$45.97
$35.31
$39.97
$29.43
$50.03
$35.33
$43.09
$31.43
$53.38
$35.68
Maximum
$54.99
$50.28
$65.44
$59.30
$76.29
Use RISKOptimizer
15.551
To Determine These
0.337
Factors
AeBx - C
Range
$19.68
$20.84
$30.12
$27.87
$40.61
Avg Range
$27.82
Range
For Each of
5 Years
Average
5-Year
Range
Objective
-$2.18 Objective:
Desired Range
of $30 Less
In Order for
Average Range
This Equation
Close to 0
To Generate an
Objective Value
Close to Zero
38
39
Price Change vs Cum ulative Probability
Price Change
6
5
4
3
2
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cum ulative Probability
What We Would Like:
Large Probability of Small Incremental Change
Small Probability of Large Incremental Change
40
Weekly Stock Price Change Generator
$7
$6
$5
$4
$3
$2
$1
$0
0%
20%
40%
60%
Cum ulative Probability
80%
100%
Not Too Concave!
Implies a Linear Relationship Between
Probability of Price Change and Degree of Change
(Can Incorporate a Maximum Change)
41
Nevertheless Can Create Any Chart Pattern Imaginable!
Head and Shoulders?
Stock Price
$90
$70
$50
$30
0
26
52
78
104
130
156
182
208
234
260
Week
42
Nice Breakout
Stock Price
$90
$70
$50
$30
0
26
52
78
104
130
156
182
208
234
260
Week
43
The Dog
Stock Price
$90
$70
$50
$30
0
26
52
78
104
130
156
182
208
234
260
Week
Just Keep Hitting the F9 Key to Create a Slew
Of Price Patterns
44
Problem:
A Copper Mining Company
Risk: Low Price of Copper
45
Revenue in U.S. $ and Debt in British £s
Risk: Adverse Change in Exchange Rates
46
Inputs
A
B
C
D
1 Not-So Random Walk Price Generator for Copper
2
3 Desired Range
$400
Year 1
4 Start Price
$1,500.00
Year 2
5
Year 3
6 Highest
$ 2,200
Year 4
7 Upper
$ 2,100
Year 5
8 Lower
$ 1,300
9 Lowest
$ 1,200
10
A Factor
11 Bias Factor
2
B Factor
12
13
14
15
Week
Weekly
16
0
Up/Down Change
17
1
0.50
1
$3.70
18
2
0.50
-1
$14.00
19
3
0.50
-1
$18.29
20
4
0.50
1
$63.54
E
F
G
Avg Price
$1,565.71
$1,725.41
$1,449.42
$1,334.99
$1,743.06
Minimum
$1,425.62
$1,571.12
$1,204.18
$1,196.78
$1,399.48
Maximum
$1,685.36
$1,907.66
$1,818.50
$1,451.94
$1,963.10
7.261
2.759
Outputs
H
Range
$259.74
$336.54
$614.32
$255.16
$563.62
Avg Range
$405.88
Objective
$5.88
Start
Price
$1,500.00
$1,503.70
$1,489.70
$1,471.40
$1,534.94
Month
1
Modeling Future Copper Price
(Based on Past Prices)
47
A Nice Concave Shape!
11
12
13
14
15
16
17
18
19
20
21
22
23
24
I
J
Cumulative Weekly
Probability
Price
Distribution Changes
0.0001
$0.00
0.1
$2.31
0.2
$5.35
0.3
$9.35
0.4
$14.63
0.5
$21.58
0.6
$30.75
0.7
$42.82
0.8
$58.73
0.9
$79.70
1 $107.32
K
L
M
N
O
P
Weekly Copper Price Change Generator
$120
$100
$80
$60
$40
$20
$0
0%
10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Cumulative Probability
The Probability of a Small Incremental Change
Higher Than Probability of A Large Incremental Change
48
Inputs
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
A
B
C
D
E
F
G
H
Not-So Random Walk Price Generator for 100 X GBP/$
Avg Price Minimum Maximum
Range
Desired Range
5
Year 1
71.46
70.12
72.56
2.44
Start Price
70
Year 2
72.70
70.51
74.63
4.12
Year 3
69.63
67.59
71.43
3.84
Highest
80
Year 4
70.52
68.34
72.98
4.64
Upper
75
Year 5
68.63
67.02
71.26
4.24
Lower
65
Lowest
60
Avg Range
A Factor
1.472
3.85
Bias Factor
2
B Factor
0.493
Objective
Outputs
-1.15
Start
Week
Weekly
Price
Month
0
Up/Down Change
70.00
1
0.50
1
0.12
70.12
2
0.50
1
0.54
70.66
3
0.50
1
0.69
71.35
4
0.50
-1
0.26
71.09
1
Modeling Future GBP/$ Conversion Rate
(Based on Past Conversion Rates)
49
Not As Concave as Desired
11
12
13
14
15
16
17
18
19
20
21
22
23
24
I
J
Cumulative Weekly
Probability
Price
Distribution Changes
0.00
0.00
0.1
0.07
0.2
0.15
0.3
0.23
0.4
0.32
0.5
0.41
0.6
0.51
0.7
0.61
0.8
0.71
0.9
0.82
1
0.94
K
L
M
N
O
P
Weekly 100 X GBP/$ Price Change Generator
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0%
10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Cumulative Probability
Probability of Any Incremental Change About
The Same (Linear Relationship)
50
Copper Production Varies Between Min and Max With
Overall Growth With Time
L
5
6
7
8
9
10
11
Month
1
2
3
M
Minimum
Production
1000
1000
1000
N
Most
Likely
1100
1110
1120
O
P
Q
Copper
Maximum
Actual
Price
Production Production
$/Ton
1300
1133
$
1,397
1310
1140
$
1,402
1320
1147
$
1,424
R
Mining
Revenue
$MM
$
1,583
$
1,599
$
1,633
51
Mining Costs Are For Operations
Debt Charges in £ Translated to $
Cash Flow is Revenue Net of Operational
And Financial Costs
R
4
5
6
Mining
7
Revenue
8
$MM
9 $
1,583
10 $
1,599
11 $
1,633
S
Mining
Costs
Without
Debt
Charges
$
1,108
$
1,112
$
1,115
T
Debt
Charges
GBP
500
500
500
U
GBP/$
0.702
0.694
0.707
V
W
Debt
Charges
$MM
$712
$721
$708
Cash
Flow
w/o
Swap
-$237
-$234
-$189
52
W
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Cash
Flow
w/o
Swap
-$194
-$170
-$287
-$209
-$306
-$242
-$265
-$336
-$320
-$143
-$326
-$132
-$160
$24
X
Desired
Working
Capital
$3,000
Working
Capital
$2,806
$2,636
$2,350
$2,141
$1,835
$1,593
$1,328
$992
$672
$529
$203
$71
-$89
-$64
Y
Lowest
Balance
Working
Capital
-$89
Dividends
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
Z
Total
Dividends
$24,231
Working Capital
Drained from Negative
Cash Flows
Risk is Defined as the
Lowest Negative Balance
In Working Capital
Account
53
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
W
$461
$272
$370
$426
$249
$350
$513
$542
$412
$239
$275
$427
$372
$572
$538
X
$1,755
$2,027
$2,397
$2,823
$3,072
$3,350
$3,513
$3,542
$3,412
$3,239
$3,275
$3,427
$3,372
$3,572
$3,538
Y
$0
$0
$0
$0
$0
$72
$350
$513
$542
$412
$239
$275
$427
$372
$572
When Cash Flow Is Positive
(Column W), the Working
Capital Account (Column X)
Accumulates Funds
When Working Capital Exceeds
Minimum Amount ($3,000),
Excess Is Paid Out as a Dividend
(Column Y)
54
Producer and Consumer Conduct
Business 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
55
Swap Benefit and Cost Analysis
Viewpoint of Producer:
Benefit:
When Prices are Low, Swap Inflow
Adds to Revenue Reducing Risk of Loss
Cost:
When Prices are High, Swap Outflow
Decreases Revenue Reducing Profitability
56
Swap Benefit and Cost Analysis
Viewpoint of Consumer:
Benefit:
When Prices are High, Swap Inflow
Reduces Loss From Buying High
Cost:
When Prices are Low, Swap Outflow
Reduces Savings From Buying Low
57
Swap Collar
If Price is Above the Cap, Producer Pays
Consumer the Difference Multiplied by the
Swap Volume
If Price is Below the Floor, Consumer Pays
Producer the Difference Multiplied by the
Swap Volume
If Price is Between the Floor and Cap
No Exchange of Funds
58
Revenue Adjusted for Copper Swap &
Debt Charges Adjusted for Currency Swap
AA
1 Swap cap
2 Swap floor
3 Swap volume
4
5
6
7
8
9
10
11
12
13
AB
$1,500
$1,500
500
Revenue
with
Copper
Swap
$1,563
$1,514
$1,563
$1,616
AC
$0.72
$0.72
0
Debt
Charges
with
Currency
Swap
$721
$718
$725
$716
AD
Cash
Flow
with both
Swaps
-$266
-$316
-$277
-$217
AE
AF
AG
Desired
Working
Capital
$3,000
Lowest
Balance
Working
Capital
$264
Total
Dividends
$13,393
Working
Capital
$2,734
$2,418
$2,141
$1,924
Dividends
$0
$0
$0
59
Reward versus Risk
Desired Working Capital $3 Million
Probability of
Swap Volume
Total
Working Capital Being
Copper
Currency 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%
The Cost of Risk Reduction is Less Profitability
Your Choice?
60
Working Capital as a Means of Risk Mitigation
Desired Working Capital $4.5 Million
Probability of
Swap Volume
Total
Working Capital Being
Copper
Currency 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%
- %
Your Choice Now?
61
Has Financial Community Embraced
Simulation as a Means to Mitigate Risk?
Inherent Problem is Assessing the Highest
And Lowest Projected Price
Since 2002 Copper Prices Have More Than
Doubled (China’s Drawing Down of World Resources)
Any Long Term Swap Entered Into by Producer
An Unmitigated Disaster & a Financial Windfall
For the Consumer
62
Producer May Have Been Forced to Enter
Copper Futures Market to Counter Swap as a
Condition for a Loan or to Insure Against Falling
Prices Leading to a Bankruptcy
Short-Term Swaps Provide No Protection for a
Long-Term Loan
Unfortunately Swaps Are Entered Into on Basis
That Each Counterparty Will Profit!
Companies Rejoice When There Is a Cash Inflow
Companies Do Not Philosophize Over Cash Outflows
Yet One Counterparty Will Be Proven Wrong
63
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 Bankrupt
Or Perhaps Not Obtained Bank Support for Loan
Prices Are 100% Explainable in Hindsight, But
If the Doubling of Copper Prices Should Have Been
Foreseen, Then What Is Your Projection of the
Future Price of Copper as of Now?
64
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 Financial
Derivative Does Not Create Another?
65
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 Against
Combinations of Low Copper Prices, Adverse Currency
Exchange Rates, and High Interest Rates?
A Claim Is in Terms of Negative Cash Flows When
Working Capital Is Negative
66
Format of Problem Includes Interest Rate Risk
Plus Claim to Insurance Company
2
3
4
5
6
7
8
9
10
11
12
13
14
AH
AI
Desired
Working
Capital
$6,000
Cash
Flow
-$149
-$62
-$150
-$252
-$364
-$320
Working
Capital
$5,851
$5,788
$5,638
$5,386
$5,022
$4,702
AJ
AK
AL
Dividends
Claim
Total
Claims
$5,284
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
67
Basis of Insurance Claim
32
33
34
35
36
37
38
39
40
41
42
43
44
Cash
Flow
Working
Capital
Dividends
Paid
AH
-$191
-$250
-$76
-$170
-$249
-$202
-$69
$551
-$259
-$142
-$140
$124
-$143
AI
$613
$363
$287
$117
-$132
-$334
-$403
$148
-$111
-$252
-$392
-$268
-$411
AJ
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
Claims
Made
AK
$0
$0
$0
$0
$132
$334
$403
$0
$111
$252
$392
$268
$411
Column AI Is Working
Capital Account and
Column AJ Is Dividends
A Claim Can Be Made
When 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 Cash
Flow Column AH in
Following Year
68
Total Claims Cell Designed as Output
=RiskOutput() + SUM(AK10:AK68)
@RISK Simulation Run
To Collect Data on Claims
Zero Claims Eliminated
@RISK Best Fit
Used to Obtain Probability Distribution
69
@RISK Best Fit
Probability Distribution for Claims
Output
Fit Between Actual & Prob Dist
70
Comparison of Probabilities of Occurrence
Between Actual Data and Probability Distribution
71
A
B
C
1 Determining an Insurance Premium
2
3 Base Insurance Premium
$90
4 High Premium
$120
5 Low Premium
$60
6 Start reserves
$100,000
7 Upper Trigger
$120,000
8 Lower Trigger
$80,000
9
10 Objective:
$642
Base Insurance Premium
Determined by RISKOptimizer
Objective:
To Keep Difference Between
Starting 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
72
13
14
15
16
17
18
19
20
21
22
23
24
25
A
B
Year
1
2
3
4
5
6
7
8
9
10
Annual
Premium
$90
$90
$90
$90
$90
$90
$90
$90
$90
$90
C
Reserves
Earnings
Rate
6.0%
6.0%
6.0%
6.0%
6.0%
6.0%
6.0%
6.0%
6.0%
6.0%
D
E
Reserves
$ 100,000
$ 100,090
$ 100,185
$ 100,287
$ 100,394
$ 100,507
$ 100,628
$ 100,482
$
98,665
$
98,648
Reserves
Income
$0
$5
$11
$17
$24
$30
$38
$29
-$107
-$108
F
G
Claims
$0
$0
$0
$0
$0
$0
$274
$1,936
$0
$0
Ending
Reserves
$100,090
$100,185
$100,287
$100,394
$100,507
$100,628
$100,482
$98,665
$98,648
$98,630
Annual Premium Added To Reserves
Income only on Amount Over Reserves of $100,000
Earnings on $100,000 Belong to Pension or Other Insurance Fund
Claims in Excess of Reserves of $100,000 Charged 8% by Insurance Fund
This is the Inducement for Insurance Fund to Act as Reserves
73
@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 Amount
Determined by @RISK Best Fit Distribution Probability
74
Distribution of Ending Reserves
75
Determining Required Reserves
Probability of $100,000 in Initial Reserves
Falling Below $75,000 is Only 0.12%
(This Is $25,000 Below $100,000)
Hence Initial Reserves Can Be Reduced to $25,000
With Only a 0.12% of Exhausting Reserves
Can Be Rerun With Different Working Capital
To Obtain an Alternative Insurance Premium
76
Reviewing What Happened, Copper Prices Rose
To a Level That Would Have Reduced Premium to
Zero To Keep From Accumulating Excess Reserves
Had Copper Prices Fallen, Reserves Would Have
Been Drawn Down Necessitating Hikes in the Insurance
Premium – Subsequent Rise in the Copper Price Would
Be Necessary to Replenish Reserves
If Copper Prices Never Came Back, Then Insurance
Reserves Would Have Been Exhausted (Risk of Being
An Underwriter!)
77
It Has Been Demonstrated That:
Simulation Can Be Used to Mitigate Risk
to
Determine the Optimal Chartering Policy
Determine Optimal Swap Positions
(As Good As Ability to Foresee Max & Min Limits)
Determine an Insurance Premium to Cover
Business Risk Rather Than Relying on Swaps
(Again As Good As the Inputs)
78
These Methodologies Do Depend on Assessing Market Limits.
But Who Does Know the Future?
&
If Someone Did Know the Future
Would He or She Be Here?
79
Excel spreadsheets available in:
@RISK Bank Credit and Financial Analysis
(Available from Palisade)
Also discussed in:
Corporate Financial Risk Management
(Available from Praeger Press)
Questions & Answers (Maybe!)
80