Palisade Risk Conference
November 4-5, 2010 Las Vegas
Determining Optimal Swaps
For Risk Mitigation
Roy Nersesian
Monmouth & Columbia Universities
A Random Walk Down Wall Street by Burton G. Malkiel
Fundamental knowledge is no help in selecting stocks – all is random motion
2
Proof: Two-thirds of portfolio managers cannot beat the S&P average performance
despite investing on basis of in-depth stock analysis and market timing
Investment portfolio management techniques assuming random walk:
1.
Buy S&P index funds
2.
Buy S&P index funds and
cash account – play broad
market
3.
Select attractive stock
group, but do not select
stocks – buy appropriate
ETFs
3
Yet in hindsight, stock movements can be explained:
In the 1970s, the Hunt brothers and their speculator-friends pushed
the price of silver from a buck or two to above $50 per ounce by
artificially holding back on supply, taking massive positions in silver
futures, and squeezing those who went short in silver
H.L. Hunt made the money his sons lost
4
What they did not anticipate were thousands upon thousands of
individuals selling their treasured silver plate dinnerware and
other family heirlooms to silver merchants not for the intrinsic
value of the craftsmanship, but for the intrinsic value of the metal
Melting down untold tons of family heirlooms inundated the silver
market all but wiping out one of America’s richest families and
their investment buddies
5
If you’re unable to forecast future prices because you can’t foresee
what forces will act on prices to drive them up or down, then perhaps
there is an appearance of randomness in day-to-day fluctuations
Perhaps investing is nothing more than throwing the dice
6
Purely random prices can be negative
So prices can’t be entirely random:
If too high – propensity to sell
If too low – propensity to buy
7
Trick is estimating what is too high and too low!
Caveat Emptor
Price limits and volatility based on an analysis of past data normally
do not relate well to future price patterns for extended periods of time
8
To evaluate swaps, must first model price
Need daily absolute price change
Jan
Jan
Jan
Jan
Jan
Jan
Jan
Jan
Jan
Jan
Jan
Jan
Jan
Jan
Jan
Jan
03,
04,
05,
06,
07,
10,
11,
12,
13,
14,
18,
19,
20,
21,
24,
25,
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
2005
$/Bbl
$42.16
$43.96
$43.41
$45.51
$45.32
$45.31
$45.66
$46.46
$48.11
$48.41
$48.46
$47.61
$47.01
$48.31
$48.61
$49.43
Daily
Change
Absolute
Change
$1.80
-$0.55
$2.10
-$0.19
-$0.01
$0.35
$0.80
$1.65
$0.30
$0.05
-$0.85
-$0.60
$1.30
$0.30
$0.82
$1.80
$0.55
$2.10
$0.19
$0.01
$0.35
$0.80
$1.65
$0.30
$0.05
$0.85
$0.60
$1.30
$0.30
$0.82
Most of the time from 1860-1973 oil was about $2-3 per barrel
9
Histogram of Daily Change in Oil Prices
Histogram
700
100%
90%
600
80%
500
Frequency
70%
Cumulative %
60%
400
50%
300
40%
200
30%
20%
100
10%
More
$19
$18
$17
$16
$15
$14
$13
$12
$11
$10
$9
$8
$7
$6
$5
$4
$3
0%
$2
0
$1
Frequency
$Change Frequency Cumulative %
$1
660
50.73%
$2
369
79.09%
$3
156
91.08%
$4
51
95.00%
$5
41
98.16%
$6
13
99.15%
$7
6
99.62%
$8
0
99.62%
$9
0
99.62%
$10
1
99.69%
$11
2
99.85%
$12
0
99.85%
$13
0
99.85%
$14
0
99.85%
$15
1
99.92%
$16
0
99.92%
$17
0
99.92%
$18
0
99.92%
$19
1
100.00%
More
0
100.00%
Bin
10
Plot of price change vs cumulative probability
$10
$9
$8
$7
$/bbl
$6
$5
$4
$3
$2
$1
$0
0%
20%
40%
60%
80%
100%
Cumulative Probability
Large probability of a small change in price; and conversely,
a small probability of a large change in price
Cumulative probability will be changed to random number
to use the above curve for a random price generator
11
Price change can be modeled by the formula:
Ax - A
X = BY
Y=C*RAND()
A, B, C unknown variables
If A=B18, B=B19 and C=B20
=$B$18^($B$19^($B$20*RAND()))-$B$18
When random number = 0, above = 0
12
Modeling Price
Starts with Future Max/Min Price Assessments
Start Oil Price
$80
Highest
$180
Upper
$170
Lower
$50
Lowest
$40
Bias Factor
2
This is a wide range of possibilities exceeding historic
high of $147/bbl and a lower limit that will probably
never be seen again
13
Below $50 the propensity to sell falls from 50 to 10%
meaning that the propensity to buy increases to 90%
Above $170 the propensity to sell increases from 50 to 90%
meaning that the propensity to buy falls to 10%
14
A Factor
1.000
50% Cum
$1.00
B Factor
1.000
Objective1
-$1.00
C Factor
1.000
100% Cum
$10.00
Objective2
-$10.00
Objective
$11.00
The A, B, and C Factors are unknown, but we know:
The 50% cumulative probability will pass through $1/Bbl and
the 100% cumulative probability will pass through $10/Bbl
15
At 50% cumulative probability,
the change is $1/Bbl
At 100% cumulative probability,
the change is $10/Bbl
$10
$9
$8
$7
$/bbl
$6
$5
$4
$3
$2
$1
$0
0%
20%
40%
60%
80%
100%
Cumulative Probability
16
Can use either RiskOptimizer or Evolver
If RiskOptimizer, under Runtime, select Iterations and enter “1”
17
RiskOptimizer or Evolver menu would be the same
18
A Factor
1.334
50% Cum
$1.00
B Factor
9.593
Objective1
-$0.03
C Factor
0.942
100% Cum
$10.00
Objective2
-$0.02
Objective
$0.04
Objective 1 – 50% cum prob has a value of $1
=$B$18^($B$19^($B$20*0.5))-$B$18-E18
Objective 2 – 100% cum prob has a value of $10
=$B$18^($B$19^($B$20*1))-$B$18-E20
Objective – minimize absolute value of above
=ABS(E19)+ABS(E21)
19
Daily Oil Change Generator
12.00
10.00
$1.00
Incremental Change
Cumulative Daily
Probability Oil Price
Distribution Change
0
0.00
0.1
0.09
0.2
0.22
0.3
0.39
0.4
0.63
0.5
0.97
0.6
1.48
0.7
2.27
0.8
3.54
0.9
5.77
1
9.98
8.00
6.00
4.00
2.00
$10.00
0.00
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Random Number
20
What is your view of the future – it’s covered!
21
The trading range of oil is quite wide because of the
selected min/max range of $40 to $180 on an annual basis!
Year 1
Year 2
Year 3
Year 4
Year 5
Average Minimum Maximum
$98.84
$73.30 $123.25
$74.20
$41.88 $115.80
$74.62
$36.27 $108.37
$59.73
$42.42
$79.01
$123.22
$55.92 $178.07
5-Yr Period
Average
Range Values $70.94
Range
$49.95
$73.92
$72.10
$36.59
$122.15
Minimum Maximum
$36.59
$122.15
22
The distribution of tomorrow’s price being today’s price plus a
randomly determined increment flattens out the probability
distribution
Maybe the normal distribution is not as normal as we think!
23
Hedging an Oil Project with Swaps
Nominal
Monthly
Month
Working
Revenue
Nominal
Nominal
Capital
Initial:
Oil
Volume
$thousand
Debt &
Net Cash
Price
000 bpd
No Swaps
OPEX
Flow
$1,000,000
Nominal
Dividends
1
$100.00
102
$306,704
$330,000
($23,296)
$976,704
$0
2
$115.33
103
$354,862
$330,000
$24,862
$1,001,566
$1,566
3
$130.91
103
$406,029
$330,000
$76,029
$1,076,029
$76,029
4
$134.18
102
$410,004
$330,000
$80,004
$1,080,004
$80,004
5
$134.95
105
$425,272
$330,000
$95,272
$1,095,272
$95,272
6
$133.95
102
$409,660
$330,000
$79,660
$1,079,660
$79,660
7
$159.76
104
$500,029
$330,000
$170,029
$1,170,029
$170,029
8
$159.32
107
$509,383
$330,000
$179,383
$1,179,383
$179,383
Oil price – price every 30 days
Volume – slowly expanding RiskTriang distribution
Revenue – 30 days of price X volume
Debt & operating expenses – held constant
Dividends – can only be paid on excess working capital
24
Nominal
Net Cash
Flow
($23,000)
$17,070
$85,983
$91,132
$118,287
$716
($38,365)
($34,318)
($41,027)
$3,483
($7,681)
Working
Capital
Initial:
$1,000,000
$977,000
$994,070
$1,080,052
$1,091,132
$1,118,287
$1,000,716
$961,635
$927,317
$886,290
$889,773
$882,091
Nominal
Dividends
$0
$0
$80,052
$91,132
$118,287
$716
$0
$0
$0
$0
$0
Working
Nominal
Capital
Net Cash
Initial:
Nominal
Flow
$1,000,000 Dividends
($23,000)
$977,000
$0
($30,235)
$946,765
$0
($63,233)
$883,532
$0
($58,903)
$824,628
$0
($105,035)
$719,593
$0
($119,313)
$600,281
$0
($103,184)
$497,097
$0
($156,767)
$340,330
$0
($168,004)
$172,326
$0
($110,798)
$61,528
$0
($159,039)
($97,511)
$0
Nominal
Negative
Working
Capital
Evaluation
Count
of Months
Negative
Working
Capital
0
Maximum
Negative
Working
Capital
$0
Reward
Negative cash flows
insufficient to wipe out
out working capital (WC)
$5.1 mm in dividends
Total
Dividends
$5,077,049
Nominal
Negative
Working
Capital
Evaluation
Count
of Months
Negative
Working
Capital
50
($97,511)
Risk
Negative cash flows
sufficient to wipe out WC
Total
Dividends
$0
Maximum
Negative
Working
Capital
$2,642,944
Max negative WC $2.6 mm
50 months of negative WC
$0 dividends in five years
25
Measure of Reward
19% chance of not making a dime
Average dividend payout – $4.5 mm
26
Measures of Risk
58% chance of at least
1 month of neg WC with
a mean of 17 months
58% chance of neg WC
with an average of $1 mm
27
Risk Mitigation with Swaps
If market price is > swap price, then monthly payment is
based on 30 days X 1,000 bpd X difference between
market and swap prices
If market price is < swap price, then monthly payment
is based on 30 days X 1,000 bpd X difference between
swap and market prices
28
Swap cap:
Swap floor:
Swap
volume:
$100
$100 Monthly
50 Revenue Nominal Nominal
Max 100 $thousand Debt & Net Cash
With
Swaps
OPEX
Flow
$307,000
$330,000 ($23,000)
$327,492
$330,000 ($2,508)
$362,734
$330,000 $32,734
$365,367
$330,000 $35,367
$380,672
$330,000 $50,672
$320,174
$330,000 ($9,826)
$301,874
$330,000 ($28,126)
$304,432
$330,000 ($25,568)
$301,802
$330,000 ($28,198)
$325,684
$330,000 ($4,316)
$321,232
$330,000 ($8,768)
$341,965
$330,000 $11,965
Nominal
Working
Nominal
Capital
Initial:
Negative
Nominal Working Evaluation
Dividend
$1,000,000
s
Capital
$977,000
$0
Count
$974,492
$0
of Months Maximum
$1,007,225 $7,225
Negative Negative
$1,035,367 $35,367
Working Working
$1,050,672 $50,672
Capital
$990,174
$0
0
$0
$962,048
$0
$936,481
$0
$908,283
$0
Total
$903,966
$0
Dividends
$895,198
$0
$3,864,131
$907,163
$0
=30*IF(I6>$T$1,$T$1*$T$3+I6*(J6-$T$3),IF(I6<$T$2,$T$2*$T$3+I6*(J6-$T$3),I6*J6))
If the end-of-month price in I6 is greater than the swap cap, then revenue is the
cap price X the swap volume plus the market price for the volume in J6 not
covered by the swap volume
If this condition is not true and if the market price is below the swap floor, then
revenue is the floor price X the swap volume plus the market price for the
volume not covered by the swap
If both conditions are not true, which can only happen when the market price is
between the floor and the cap, then revenue is simply market price times volume
29
Measure of Reward with 50 Swaps – 50% Coverage
83% of receiving dividends vs 58% without swaps
Average dividend $3.2 mm vs $4.5 mm
Cost of swap - $1.3 mm in reduced dividend payout
30
Measure of Risk with Swaps
36% chance of at least 1 month of neg WC with a mean of 9 months
vs unprotected 58% chance with 17 months of neg WC
31
35% chance of neg WC with an average of $0.25 mm with swaps
vs unprotected 58% chance of neg WC with an average of $1 mm
32
Expanding the Model to Hedge Floating Interest Rate Risk
Absolute
3-month
Monthly
LIBOR
Change
Bin
Jan-90
8.63
Feb-90
8.69
0.0630
Mar-90
8.94
0.2500
Apr-90
9.38
0.4370
May-90
8.75
0.6250
Jun-90
8.50
0.2500
Jul-90
8.11
0.3910
Aug-90
8.31
0.2040
Sep-90
8.50
0.1870
Oct-90
8.06
0.4370
Monthly change is converted to a histogram
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
Frequency Cumulative %
11
4.58%
54
27.08%
28
38.75%
27
50.00%
36
65.00%
22
74.17%
10
78.33%
11
82.92%
10
87.08%
8
90.42%
5
92.50%
2
93.33%
2
94.17%
6
96.67%
2
97.50%
0
97.50%
0
97.50%
1
97.92%
2
98.75%
1
99.17%
0
99.17%
0
99.17%
33
Histogram of Monthly Changes in Interest Rates
Histogram
60
100%
90%
50
Frequency
40
80%
70%
Frequency
30
Cumulative %
60%
50%
40%
20
30%
20%
10
10%
0
0%
Bin
34
RiskOptimizer/Evolver Decision Model
35
Simulating Floating Interest Rates
A Factor
6.472
50% Cum
15.00
B Factor
7.184
Objective1
0.13
C Factor
0.505
100% Cum
150.00
Objective2
0.52
Objective
0.65
Cumulative
Monthly
Probability
Int Rate
Monthly Interest % Change Generator
1.60
Distribution
Change
0
0.00
0.1
0.01
0.2
0.03
0.3
0.06
0.4
0.10
0.5
0.15
0.6
0.23
0.7
0.36
0.20
0.8
0.57
0.00
0.9
0.91
1
1.51
Incremental Change
1.40
1.20
1.00
0.80
0.60
0.40
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Random Number
36
Every iteration of a simulation
creates a new interest rate
scenario
37
Aggregate cost broken down to operating cost, debt repayment
and interest rate expense
Swap cap:
Swap floor:
Swap volume:
(Max 100)
$100
$100
50
Monthly
Revenue
$thousand
With Swaps
$337,227
$347,070
Swap cap:
$100,000
Swap floor:
$100,000
Nom % Debt:
50%
Nominal
Debt
OPEX
Repayment
Interest
$100,000
$150,000
$90,000
$100,000
$150,000
$91,623
With No Swaps:
The mean is 26 months of negative working capital with a 24% chance
of no negative working capital and a 14% chance of negative working capital
exceeding 50 months
With Above Swaps:
The mean declined to 21 months with a 35% chance of no negative working
capital with a 2% chance of negative working capital exceeding 50 months
38
Risk Mitigation and Its Cost
The two swaps reduced the risk as represented by the maximum
negative working capital from $2.8 billion to $1.2 billion or $1.6 billion
(a 57% reduction)
The cost to mitigate risk in reducing the maximum negative working
capital by $1.6 billion for the case of 50 oil swaps and 50% coverage
of interest expense is a $0.8 billion decrease in the dividend payout
Cost of mitigation is high, but so is the reduction in concomitant risk
39
Histogram
14
100%
90%
12
80%
10
70%
60%
8
Frequency
6
50%
Cumulative %
40%
30%
4
20%
2
10%
0.1100
0.1050
0.1000
0.0950
0.0900
0.0850
0.0800
0.0750
0.0700
0.0650
0.0600
0.0550
0.0500
0.0450
0.0400
0.0350
0.0300
0.0250
0.0200
0.0150
0%
0.0100
0
0.0050
Bin
Frequency Cumulative %
0.0000
0
0.00%
0.0025
12
9.68%
0.0050
2
11.29%
0.0075
10
19.35%
0.0100
7
25.00%
0.0125
9
32.26%
0.0150
9
39.52%
0.0175
7
45.16%
0.0200
6
50.00%
0.0225
6
54.84%
0.0250
7
60.48%
0.0275
7
66.13%
0.0300
6
70.97%
0.0325
4
74.19%
0.0350
4
77.42%
0.0375
1
78.23%
0.0400
6
83.06%
0.0425
3
85.48%
0.0450
2
87.10%
0.0475
2
88.71%
0.0500
1
89.52%
0.0525
1
90.32%
0.0550
2
91.94%
Adding More Risk
Currency Exchange Rate Between Euro and U.S. Dollar
0.0000
0.0000
0.0025
0.0050
0.0075
0.0100
0.0125
0.0150
0.0175
0.0200
0.0225
0.0250
0.0275
0.0300
0.0325
0.0350
0.0375
0.0400
0.0425
0.0450
0.0475
0.0500
0.0525
0.0550
0.0286
0.0182
0.0192
0.0382
0.0410
0.0091
0.0348
0.0333
0.0171
0.0011
0.0462
0.0392
Frequency
Jan-00
Feb-00
Mar-00
Apr-00
May-00
Jun-00
Jul-00
Aug-00
Sep-00
Oct-00
Nov-00
Dec-00
Jan-01
$/euro
1.01252
0.98396
0.96576
0.94656
0.9084
0.94941
0.94031
0.90549
0.87219
0.85511
0.85396
0.9002
0.93938
Absolute
Monthly
Change
Bin
40
A Factor
B Factor
C Factor
2.834
18.847
0.294
50% Cum
Objective1
100% Cum
Objective2
X 100
2.00
0.14
9.00
-0.03
Objective
0.17
Monthly $/Euro Change Generator
$0.10
$0.09
$0.08
0.02
Incremental Change
Cumulative Monthly
Probability $/Euro
Distribution Change
0
0.000
0.1
0.003
0.2
0.006
0.3
0.010
0.4
0.015
0.5
0.021
0.6
0.029
0.7
0.039
0.8
0.051
0.9
0.068
1
0.090
$0.07
$0.06
$0.05
$0.04
$0.03
$0.02
0.09
$0.01
$0.00
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Random Number
41
Swap cap:
Swap floor:
Swap volume:
$100
$100
Monthly
50 Revenue
Max 100 $thousand Nominal
With Swaps OPEX
$311,412
$100,000
$323,268
$100,000
$352,318
$100,000
$349,184
$100,000
$384,226
$100,000
$362,967
$100,000
$354,939
$100,000
$368,460
$100,000
$376,561
$100,000
$383,445
$100,000
$393,132
$100,000
$416,571
$100,000
Swap cap:
$100,000
$1.30
Swap floor: $100,000
$1.30
Nom % Debt:
50%
$100,000
Nominal
Debt
Max 100% Max $200 K Net Cash
Repayment Interest
Flow
$150,000
$90,000
$240,000
($28,588)
$150,000
$88,875
$229,804
($6,536)
$150,000
$89,320
$234,512
$17,805
$150,000
$105,547
$247,560
$1,623
$150,000
$87,629
$228,754
$55,472
$150,000
$94,909
$233,772
$29,196
$150,000
$91,771
$230,474
$24,465
$150,000
$90,225
$227,894
$40,567
$150,000
$109,165
$244,579
$31,982
$150,000
$98,054
$241,309
$42,136
$150,000
$115,989
$259,293
$33,839
$150,000
$96,245
$247,049
$69,521
Nominal
Working
Nominal
Capital
Negative
Initial:
Nominal Working
$2,000,000 Dividends Capital
$1,971,412
$0
$1,964,876
$0
$1,982,681
$0
$1,984,304
$0
$2,039,776 $39,776
$2,029,196 $29,196
$2,024,465 $24,465
$2,040,567 $40,567
$2,031,982 $31,982
$2,042,136 $42,136
$2,033,839 $33,839
$2,069,521 $69,521
Evaluation
Count
of Months
Negative
Working
Capital
0
Maximum
Negative
Working
Capital
$0
Total
Dividends
$1,130,121
Use the same methodology to measure risk reduction and
cost of risk mitigation
42
Nominal Value of Swaps
1993: $7 trillion
2010: $60+ trillion
Global GDP: $70 trillion
Nominal value of swaps
overwhelm global GDP
by a factor of nearly
ten
Yet at one time world operated with no swaps!
Why so many swaps?
Visit to shipping company –
6 people fixing real, existing ships on various charters
6 people playing with derivatives on virtual ships to
hedge physical ships
A Real Ship
44
For instance, suppose existing ships are on various
charters for up to 2-3 months and the assessment
on the future market is that it will weaken at end
of 2- 3 months
Charter the virtual fleet for 6-12 months with shipping
derivatives (swaps)
A Virtual Ship
45
Example of a Swap
This is what you can pay for a floating rate loan from
a few days to 12 month maturity in 2005
46
Alternatively, you can swap the floating rate loan and
pay the fixed indicated rate from 1 – 30 years
This swap would have been a disaster considering that floating
rates fell to near-zero!
So what are you going to do?
47
Charterer of virtual fleet must report to CFO on all
derivative positions as to whether money if flowing
in or out of the firm
Flowing in – fine
Flowing out – “What are you doing to stem the flood?”
Hence, charterer of virtual fleet must enter into other
derivative positions to neutralize those positions that
are a cash drain
Derivative positions pile up one on top of the other
to neutralize previous positions that turned out wrong
Forget about cash outflow being treated as the insurance
premium for obtaining a hedge against a potential loss
Cash outflow is a hemorrhaging of corporate blood that must
be stopped!
48
Investment Banker
“All we want is for a company to enter into its first swap…”
49
Alternative to Swaps
Business Risk Insurance
Nominal
Net Cash
Flow
($23,000)
($58,425)
($106,277)
($105,807)
($100,218)
($145,107)
($229,880)
($225,896)
($186,157)
($222,671)
($228,404)
($219,684)
($247,933)
($123,656)
($27,852)
$7,364
$23,505
($4,795)
($31,274)
$11,381
($43,393)
($21,678)
$45,629
($13,866)
$3,502
($895)
($51,258)
$34,468
Nominal
Working
Capital
Initial:
Nominal
$2,000,000 Dividends
$1,977,000
$0
$1,918,575
$0
$1,812,299
$0
$1,706,492
$0
$1,606,274
$0
$1,461,168
$0
$1,231,288
$0
$1,005,392
$0
$819,235
$0
$596,564
$0
$368,160
$0
$148,476
$0
($99,458)
$0
($223,114)
$0
($250,965)
$0
($243,601)
$0
($220,096)
$0
($224,891)
$0
($256,165)
$0
($244,784)
$0
($288,177)
$0
($309,855)
$0
($264,226)
$0
($278,092)
$0
($274,591)
$0
($275,486)
$0
($326,744)
$0
($292,275)
$0
Nominal
Negative
Working
Capital
($99,458)
($223,114)
($250,965)
($243,601)
($220,096)
($224,891)
($256,165)
($244,784)
($288,177)
($309,855)
($264,226)
($278,092)
($274,591)
($275,486)
($326,744)
($292,275)
Claim
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$99,458
$223,114
$250,965
$243,601
$220,096
$224,891
$256,165
$244,784
$288,177
$309,855
$264,226
$278,092
$274,591
$275,486
$326,744
$292,275
Once working capital is exhausted,
claim based on negative working
capital
Nominal net cash flow reflects
any claim from previous month
50
Emergency Prem
High Premium
Base Premium
Low Premium
$145,000
$95,000
$70,000
$20,000
Initial Reserves
Upper Trigger
Lower Trigger
$2,000,000
$2,000,000
$1,500,000
Earnings Rate
Borrowing Rate
6%
8%
Avg Ins Premium
Objective
$99,583
($1,573,229)
50
25
70
Monthly
Insurance
Premium
$20,000
$20,000
$20,000
$20,000
$20,000
$20,000
$20,000
$20,000
$20,000
$20,000
$20,000
$20,000
$20,000
$20,000
$70,000
$70,000
$70,000
$95,000
$95,000
$95,000
$95,000
$95,000
$95,000
$95,000
$95,000
$95,000
$145,000
$145,000
Reserves
Ending
Reserves
Income
Claims
Reserves
$Thousands $Thousands $Thousands $Thousands
$2,000,000
$0
$0 $2,020,000
$2,020,000
$100
$0 $2,040,100
$2,040,100
$201
$0 $2,060,301
$2,060,301
$302
$0 $2,080,602
$2,080,602
$403
$0 $2,101,005
$2,101,005
$505
$0 $2,121,510
$2,121,510
$608
$0 $2,142,118
$2,142,118
$711
$0 $2,162,828
$2,162,828
$814
$0 $2,183,642
$2,183,642
$918
$0 $2,204,561
$2,204,561
$1,023
$0 $2,225,583
$2,225,583
$1,128
$0 $2,246,711
$2,246,711
$1,234
$99,458 $2,168,487
$2,168,487
$842
$223,114 $1,966,215
$1,966,215
($225)
$250,965 $1,785,025
$1,785,025
($1,433)
$243,601 $1,609,990
$1,609,990
($2,600)
$220,096 $1,457,294
$1,457,294
($3,618)
$224,891 $1,323,785
$1,323,785
($4,508)
$256,165 $1,158,112
$1,158,112
($5,613)
$244,784 $1,002,716
$1,002,716
($6,649)
$288,177
$802,890
$802,890
($7,981)
$309,855
$580,055
$580,055
($9,466)
$264,226
$401,363
$401,363
($10,658)
$278,092
$207,613
$207,613
($11,949)
$274,591
$16,073
$16,073
($13,226)
$275,486
($177,639)
($177,639)
($14,518)
$326,744
($373,901)
($373,901)
($15,826)
$292,275
($537,002)
Evolver/RiskOptimizer determines Base Premium rate only – other
incremental rates are selected as is initial reserves
Objective is to have same beginning and ending reserves
51
Initial reserves $2 billion inadequate – 12.6% chance of exhausting
reserves
Increasing to $10 billion reduces chance to 0.3%
52
Combining interest and currency exchange rate swaps
with no oil swap exposure significantly reduced the
business risk premium from $70,000 to $12,000
Emergency Prem
High Premium
Base Premium
Low Premium
$87,000
$37,000
$12,000
$10,000
Initial Reserves
Upper Trigger
Lower Trigger
$2,000,000
$2,000,000
$1,500,000
Earnings Rate
Borrowing Rate
6%
8%
Avg Ins Premium
$10,000
Objective
$684,279
50
25
70
53
Current Research
The Search for the Algorithm to Forecast Chaos
Chaos is the S&P500
Algorithm takes into account:
1.
2.
3.
4.
Opening/High/Low/Closing Price
Volume Adjusted Price
Velocity and Acceleration of Volume Adjusted Price
Superimposed Sinusoidal Wave Patterns
54
1st Buy
2nd Buy
3rd Buy
4th Buy
5th Buy
6th Buy
7th Buy
8th Buy
9th Buy
10th Buy
11th Buy
12th Buy
Total
Profit
$124
$92
$87
$48
$61
$52
$24
$24
$0
$0
$0
$0
$511
Objective
% Gains % Losses
100%
0%
100%
0%
100%
0%
100%
0%
100%
0%
100%
0%
100%
0%
100%
0%
0%
0%
0%
0%
0%
0%
0%
0%
$/Trans
$25
$31
$29
$24
$31
$26
$24
$24
$0
$0
$0
$0
# Trans
5
3
3
2
2
2
1
1
0
0
0
0
19
8.19
Objective of Evolver is to determine constants in algorithm
to maximize % Gains – 2* % Losses + Number Transactions/100
55
Based on previous 90 days, algorithm generated above buy signals
56
Selling short similarly constructed
57
Model rerun daily after close to see if buy or sell signal
Stock bought or sold next day at average high/low price
Performance
Month
# Buys
# Profit
# Loss
# Shorts
June
1
1
July
5
August
September
# Profit
# Loss
4
1
1
4
3
1
7
6
1
6
6
0
0
0
0
1
19 buy signals
• 17 wins
• 2 losses
8 short signals
• 6 wins
• 2 losses
58
www.nerses.com
Click on left link for explanation and right link for results
59
Q&A
60