nancy beneda 1

MANAGING AN ASSET MANAGEMENT FIRM’S

RISK PORTFOLIO

Nancy Beneda1

Vaaler Insurance Fellow

Associate Professor, Department of Finance, University of North Dakota,

Box 7096,

Grand Forks, ND 58202-7096, USA

1 University of North Dakota Box 7096 Grand Forks, ND 58201 (701) 777-4690 fax (701) 777-5099 [email protected]

MANAGING AN ASSET MANAGEMENT FIRM’S

RISK PORTFOLIO

1

mailto:[email protected]

Abstract:

This paper presents a simplified model for quantifiably measuring and managing

various types of risk, as a portfolio of risks. An asset management firm may face a

variety of risks due to the broad nature of various investments. The technique utilizes

computerized simulation and optimization modeling. The software used to administer

the simulations is Crystal Ball. The use of simulation allows risk managers to combine

various categories of risk, a firm faces, into one risk portfolio. These techniques will

enable risk managers to have the information needed to achieve the desired level of

overall firm risk and the expected cost of managing risk. The firm’s overall risk metric

selected for use in this paper is the standard deviation of after-tax operating earnings.

1. INTRODUCTION

A primary objective of risk management is to preserve the operating

effectiveness of the organization. The focus is to ensure that the organization is not pre-

vented from achieving its objectives of earning a profit and maximizing the wealth of the

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stockholders. In recent years, there has been considerable discussion about the potential

shift toward enterprise risk management, which would bring together the management of

all risks: financial, pure (traditionally insured hazards), operational, and strategic risks

into a single risk portfolio.

The use of enterprise risk management may be especially useful to asset

management firms. Innovation and growth are common characteristics of asset

management firms. Further, asset management firms may be involved in a broad

range of investing activities in various economic and business segments. Firms,

which are expanding either into new markets or new product areas may have a

higher degree of operational and strategic risks. Further these firms will want to

evaluate the effect of new investment projects on overall firm risk. Being able to

more accurately measure the total risk, which a firm faces, will result in a better

understanding of the extent to which the firm will be able to handle new speculative

projects. Further, if a firm is able to lessen the current risk it faces, it may have

greater latitude in the speculative risks it can undertake.


the overall risk of an asset management firm by using computerized simulation and

optimization modeling. The firm’s overall risk metric selected for use in this paper is the

standard deviation of after-tax operating earnings. The software used to administer the

simulations is Crystal Ball. The use of simulation allows risk managers to combine the

various categories of risk, a firm faces, into one risk portfolio. These techniques will

enable risk managers to have the information needed to achieve the desired level of

overall firm risk and the expected cost of managing risk.

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The rest of the paper is organized as follows. Section 2 includes a description of

the methodology. Section 3 provides a description of the hypothetical situation and

includes a description of the types of risk that the hypothetical asset management firm

faces. Section 4 provides the results of the simulation and optimization modeling and

reports the after-tax operating earnings and standard deviation of operating earnings

under various risk management decision scenarios. Section 5 provides concluding

remarks.

2. METHODOLOGY

Several techniques and concepts which are currently included in various

literature sources are combined in this paper, to develop a methodology of

measuring a firm’s overall risk. Some of these techniques include 1) risk

categorization (i.e. dividing firm risks into various components such as financial,

pure, strategic, and operational), 2) simulation modeling, 3) value-at-risk, and 4)

optimization modeling and portfolio theory.

In this paper the standard deviation of after-tax operating earnings is the firm’s

overall risk metric. Rather than calculating a unique value for after-tax operating

earnings, simulation modeling is used to create a probability distribution. Assumptions

regarding each of the four categories of risks (i.e. financial, pure, strategic, and

operational) are developed and incorporated into the model. Assumptions about model

inputs include type of probability distribution, range of possible occurrences, and/or

volatility of possible occurrences. The assumptions are used in the simulation to create

the possible outcomes of after-tax operating earnings and the probability distribution of

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outcomes. Simulation modeling is simply an advanced form of sensitivity analysis in

which a probability is attached to each possible outcome.

Risk Categorization and Components of Overall Risk

Generally the major risks a firm faces can be categorized into one of the following risk categories (Vaughan and Vaughan, 2003; Harrington and Niehaus, 2004):

1. Financial risk – controllable 2. Pure risk - controllable 3. Operational – uncontrollable 4. Strategic – uncontrollable

Generally, financial risks and pure risks are considered to be manageable in the sense

that loss financing techniques can be used to mitigate them. Examples of financial risk

include interest rate risk, commodities risk, and foreign currency exchange risk and

generally are managed by using futures or options contracts. Pure risk generally

includes loss of property or a required payment of cash due to different types of

liabilities. These types of hazards are generally managed through the purchase of

insurance. Risk reduction techniques may also be used to manage financial and pure

risks. For example sprinkler systems might be installed to reduce the severity of damage

caused by fire. Another example is the installation of safety regulations to prevent

worker injuries.

Examples of strategic risks include product obsolescence and increased competition.

Examples of operational risks include increasing cost of operations or input shortages.

Generally loss financing techniques, such as futures, options, and insurance are not

commonly used for managing strategic and operational risks. Operational and strategic

risk reduction may be achieved from making appropriate choices about which products to

produce and which markets to enter.

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In this paper it is illustrated how overall firm risk can be reduced by using loss

financing techniques to manage financial risk and pure risk. An asset management firm

with a high degree of operational and strategic risk will want to reduce financial risk and

pure risk to a greater degree than one with low operating and strategic risk. The

techniques presented in this paper illustrate how risk managers can quantifiably measure

overall risk and risk reduction from loss financing.

Simulation modeling and probability distributions

Simulation is the process of building a mathematical or logical model of a system

or a decision problem, and experimenting with the model to assist in solving the decision

problem (Powell and Baker, 2004; Evans and Olson, 2002). Simulation modeling is an

alternative to deterministic modeling. With deterministic models, input and output

variables are fixed. No uncertainty can be built into a deterministic model.

If a risk analyst is able to make assumptions concerning the shape of the

distributions, of the revenue and expense items, which are affected by various types of

risks, computer simulation can be employed to estimate the probability distribution of

total operating earnings. Under such assumptions the model outputs will not have a

unique value, but rather will be characterized by a probability distribution. Knowing the

probability distribution of outputs provides insights into the risks involved in making

decisions about purchasing futures contracts or purchasing insurance.

The technique of simulation modeling is especially useful when the probability

distributions of the input variables are not “normal.” Many input variables do not follow

a normal distribution. For example, a Poisson distribution is used in many cases to

represent the distribution of expected frequency of losses during a given period. The

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Poisson distribution describes the number of times an event occurs in a given interval,

such as the number of telephone calls per minute or the number of errors per page in a

document (Powell and Baker, 2004). The Poisson distribution is used in this paper to

represent frequency of customer liability lawsuits.

A lognormal distribution is used to represent the distribution of expected average

loss severity. The lognormal distribution is widely used in situations where values are

positively skewed or where most of the values occur near the minimum value (Powell

and Baker, 2004). This type of distribution is common for security valuation or in

estimating accident severity, in which the value cannot fall below ‘zero.’ In this paper

the lognormal distribution is used to describe the possible outcomes for lawsuit severity.

The ability to make model assumptions about the probability distribution of an

uncertain input variable (i.e. unit price or expected foreign currency exchange rate) is the

essence of simulation modeling. Unless a large number of exposures are present, the

true distribution of total losses will likely exhibit positive skewness and the difference

from the “normal” distribution could be substantial. In this case the normal distribution

will tend to understate the probability of large losses. As a consequence the firm will

underestimate the likelihood of large potentially disruptive losses.

The software used to administer the simulations is Crystal Ball. The type of

simulation modeling used is Monte Carlo simulation, which is a sampling experiment

whose purpose is to estimate the distribution of an outcome variable that depends on

several probabilistic input variables. Thus, it is not necessary to rely on the assumption

that total earnings are normally distributed.

Value-at-Risk

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It is useful to apply the concept of value-at-risk, when evaluating the overall

risk of an enterprise (Vaughan and Vaughan, 2003; Harrington and Niehaus, 2004).

Value-at-risk is simply an alternative technique used to describe a probability

distribution for the value or earnings (losses) of a firm (or portfolio). Value-at-risk

is used in addition to developing an average for an outcome and the associated

probability distribution.

A risk manager might be interested in determining the probability of certain

critical events occurring, such as the probability of negative profits. For example,

suppose a probability distribution exists for a random variable, such as a firm’s

after-tax operating earnings. One might describe the probability distribution as

“the value-at-risk for this year’s earnings is $10 million at the 5 percent level.” This

statement could be interpreted to mean that the probability that the firm will have a

loss greater than $10 million is 5 percent”. Simulation modeling is used in this

paper to determine values-at -risk for different risk levels. This information is also

helpful to risk managers in making decisions about how much risk financing to

incur.

Optimization Modeling and Portfolio Theory

Optimization is a technique which attempts to maximize or minimize an objective

function, by changing the values of the decision variables, which are subject to one or

more constraints. The technique is similar to achieving an optimal portfolio (Bodie, et

al. 2002). Portfolio theory suggests that optimal allocations of a pool of money exist

which maximizes the targeted expected return, given a specified portfolio variance. In

the example selected for this paper, the objective is to maximize the after-tax operating

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income given a specified level of standard deviation of after-tax operating income, for a

hypothetical enterprise.

Obtaining optimal values generally requires that you search in an iterative or ad

hoc fashion. This involves running a simulation for an initial set of values, analyzing the

results, changing one or more values, re-running the simulation, and repeating the process

until you find a satisfactory (optimal) solution. This process can be very tedious and time

consuming and it is often not clear how to adjust the values from one simulation to the

next.

Computerized optimization overcomes the limitations of the ad hoc and the

enumerative methods by intelligently searching for optimal solutions to optimization

problems. Once an optimization problem is described (by selecting decision variables,

identifying the objective, and imposing constraints and requirements), the computer-

generated optimization and simulation software is invoked to evaluate the simulation

model for different sets of decision variable values. This is an iterative process that

successively generates new sets of decision variable values, until an optimal solution is

found.

3. HYPOTHETICAL SITUATION

A hypothetical asset management firm is used to illustrate the procedure. In

this example, the overall after-tax operating income is used for measuring the value-

at-risk for all of the various investments. In this simplified illustration it is assumed

that the firm has two investment activities and has risk in all four of the specified

categories: financial, operational, strategic and pure risks. The assumptions (i.e.

type of distribution, range, and/or standard deviation) for each of the uncertain

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variables in the model are presented in Schedule 1.

The month of January, 2004 is arbitrarily selected as the reporting month. It

is further assumed that the firm is located in the US, reports all of its revenues and

expenses in US dollars, and pays only US taxes at a tax rate of 35%.

Investment Activity A - Financial Risk (Foreign Currency Exchange Risk) and operating risk

The financial risk the hypothetical company faces is foreign exchange risk.

The expected annual sales for the upcoming month are 20,000 units, which are sold

to a company located in Canada. All the units sold to the Canadian firm are

contracted in Canadian dollars on the transaction date of December 15, 2003.

However the Canadian dollars will not be received by the hypothetical asset

management firm until January 31, 2004. In other words the amount of Canadian

dollars is determined on December 15, 2003 and deliverable on January 31.

Foreign exchange risk results because it is not known what the exchange rate will be

on January 31, 2004. The company may however choose to hedge the foreign

currency risk with futures contracts.

There are two uncertain variables which describe the foreign currency risk

this company faces. If the company does not hedge, the uncertain variable is the

expected price per Canadian dollar on January 31, 2004. If the company hedges

with futures contracts, the uncertain variable of concern is the expected basis on

January 31, 2004. Schedule 1, Panel A presents the assumptions concerning

expected price per franc and expected basis.

These assumptions were developed based on an analysis of foreign exchange

rates and bases, obtained from the Wall Street Journal, over the period, January

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1990 through December 2003. In this example a March 2004 futures contract is

entered on December 15, 2003 and closed out two months early on January 31,

2004. Thus the historical data to evaluate basis risk, included the futures price and

exchange rate, which occur two months prior to each of the four contract maturities

of March, June, September, and December. Schedule 1 also shows the

computation of the price per Canadian dollar when futures contracts are used. This

calculation incorporates the futures basis.

Another source of risk related to Investment activity A is operating risk,

which reflects the volatility of its Cost of Goods Sold (COGS) and operating

expenses. See Schedule 1, Panel A. It is assumed that the probability distribution

which best represents the outcomes for operating costs is the normal distribution

with a standard deviation of $192,500.

Investment Activity B Pure Risk (Customer Liability Lawsuits) and Strategic Risk

Another major risk the company faces is potential customer liability lawsuits.

Generally, in a situation in which there is a significant number of losses per period, the

expected loss can be calculated as:

1) Expected loss = expected frequency of losses * expected average loss severity

In this formula, as long as the distributions of both expected frequency of losses and

expected average loss severity are ‘normal,’ the formula works accurately in estimating

an expected loss in a static scenario. However, typically neither one of the distributions

for these variables exhibit characteristics of a normal distribution. Further it is difficult to

estimate a probability distribution of the expected losses without simulation modeling.

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In this paper a Poisson distribution is used to represent the distribution of expected

frequency of losses and a lognormal distribution is used to represent expected average

loss severity. Historical data on frequency and severity can help a company estimate

future losses. In this hypothetical example, the expected frequency of customer liability

lawsuits is two and the expected severity per lawsuit is $320,000. Thus, using a

deterministic model, the total expected losses from customer liability lawsuits for January

2004 is $640,000. However, as will be shown, simulation modeling produces quite

different results. See Schedule 1, Panel B for a description of these uncertain variables.

The other two sources of risk for Investment Activity B are strategic and

operating risk. The strategic risk represents the volatility of selling price and the Uniform

distribution is used is used to represent the probability of occurrences. See Schedule 1,

Panel B. The operating risk reflects the volatility of operating expenses, including

COGS. It is assumed that the probability distribution which best represents the outcomes

for operating costs is the normal distribution with a standard deviation of $127,500

4. RESULTS

Deterministic Model

A model in which the inputs are fixed is referred to as a deterministic model.

Deterministic modeling precludes simulation modeling and the development of

probability distributions. Schedule 2 presents a schedule of the deterministic

computation of the expected after-tax operating income for Investment activities A and

B, and overall. In addition to being deterministic, the computation of after-tax operating

income also assumes that no loss financing is being used to manage risk. In other words,

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in Schedule 2, it is assumed that no insurance is purchased and no futures contracts are

used to hedge the foreign currency risk.

Investment Activity A includes foreign revenues in Canadian dollars and

operating expenses. The current price of the Canadian dollar on December 15, 2003 is

$0.8121. Thus, the Canadian dollars (CD) to be received on January 31, 2004 from the

December transaction are fixed in the amount of 2,462,750.89 CD. This is calculated as

revenues in dollars divided by the current exchange rate:

$2,000,000 / $0.8121 = 2,462,750.89 CD

Since the expected exchange rate, on January 31, 2004, is 0.8139, if the position is

left open the foreign revenues are projected to be $2,004,433. This is calculated as the

fixed number of Canadian dollars times the expected exchange rate:

2,462,750.89 CD * $0.8139 = $2,004,432.95

Also included in Investment Activity A is expected cost of goods sold (COGS) and other

operating expenses of $1,925,000.

Investment Activity B includes local revenues in US dollars, operating expenses

and losses from customer lawsuits. Operating expenses for Investment B are estimated

to be $1,275,000. The expected losses from liability lawsuits is $640,000 (deterministic

outcome), which is the expected frequency (two) times the expected severity per lawsuit

($320,000).

Simulation Modeling

Simulation Modeling is used to produce a more accurate reflection of after-tax

operating income. The uncertain parameter information and probability distributions

(presented in Schedule 1) are incorporated into the simulated model. The uncertain input

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variables include price per unit in US dollars, expected Canadian exchange rate, expected

futures basis, operating expenses, expected frequency of lawsuits, and expected severity

of lawsuits. The computerized simulation program then creates a probability distribution

for the output variable, the after-tax operating income (see Schedule 3).

The results presented in Schedule 3 represent a quantifiable measure of risk,

assuming the hypothetical firm uses no loss financing (i.e. no futures contracts and no

insurance). The probability distribution for after-tax operating income can be presented

in several ways. Schedule 3 presents the statistics (Panel A), the frequency chart (Panel

B), the percentile ranges (Panel C), and several percent levels for values-at risk (Panel

D). Schedule 3, Panel A presents the mean, median, standard deviation and skewness.

The standard deviation of $859,983 is quite large, almost 6 times the expected after-tax

operating earnings of $146,575. Notice that the simulation results in an expected after-

tax operating income which is different from the result obtained from the deterministic

model. This results from the variation of probability distributions of the input variables.

Panel B of Schedule 3 presents a frequency chart, which is simply a picture of the

frequency of the outcomes. Panel C of Schedule 3 presents the ranges of outcomes by

quartile. Panel D presents various values at risk. For example the value at risk at the

5% level is $1,400,000. In other words there is a 5% probability that the firm will have a

loss greater than $1,400,000.

Simulation Modeling and the affects of Loss Financing

A simulation similar to that reported in Schedule 3 was run, in which the

hypothetical losses are completely financed. See Schedule 4. In this simulation the

foreign currency risk is completely hedged using futures contracts and the customer

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liability lawsuits are fully insured. In this scenario basis risk replaces foreign

currency risk. Using futures contracts the expected price of the Canadian Dollar on

January 31, 2004 is $0.8125, calculated as shown in Schedule 1 Panel A.

The results of this simulation indicated a much lower standard deviation of

$306,721. However the lower risk is not without cost. The expected after-tax

operating income was lower as well, $93,196 under this scenario. The ranges also

tightened up substantially. The maximum loss drops from $11.4 million to $4.6

million. Further, under this scenario, the value-at risk at the 5% level is only

$370,000 versus $1,400,000 under no loss financing..

Simulation Modeling and Optimal Risk Financing

Schedule 5 illustrates the results of utilizing optimization software (i.e.

Crystal Ball OptQuest) to determine how much hedging and insurance should be

utilized to achieve a specified standard deviation. If a firm has an idea of how

much risk can be incurred by the firm, a risk level can be specified. Assume that

management feels that a standard deviation of after-tax operating income of

$400,000 could be tolerated if profits were sufficient. The firm would like to know

what level of after-tax operating income could be achieved given a standard

deviation equal to $400,000.

The decision variables are how many Canadian dollars to hedge and how

much insurance to purchase. At the specified level of risk (i.e. standard deviation =

$400,000), Crystal Ball OptQuest identifies the optimal number of futures contracts

as eleven. This results in 1,375,000 Canadian dollars being hedged, calculated as

11 * 125,000 (contract size). The optimal amount of insurance identified by

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OptQuest is $580,162.

Running a new simulation under these assumptions yields the results as

shown in Schedule 5. The after-tax operating income, of $125,234 is only a little

higher than that when full loss financing is utilized, but less than when none is used.

The maximum loss of $6.9 million, and the value-at risk at 5%, of $0.9 million, are

also mid-range values.

5. CONCLUSION


the overall risk of a firm as a risk portfolio, using computerized simulation and

optimization modeling. The software used to administer the simulations is Crystal Ball.

The use of simulation allows risk managers to analyze the impact of risk management

decisions on overall firm risk. These techniques will enable risk managers to have the

information needed to achieve the desired level of overall firm risk and the expected cost

of managing risk.

Enterprise risk management brings together the management of all risks:

financial, pure (traditionally insured hazards), operational, and strategic risks into a

single risk portfolio. The use of enterprise risk management is especially useful to firms

which are highly innovative. Firms, which are expanding either into new markets or new

product areas may have a higher degree of operational and strategic risks. If a firm is

able to lessen the current risk it faces, it may have greater latitude in the speculative risks it

can undertake.

REFERENCES

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Bodie, Zvi, Alex Kane, and Alan Marcus; 2002, Investments, McGraw Hill, New York, New York.

Evans, James R. and David L. Olson; 2002, Simulation and Risk Analysis, Prentice Hall, Upper Saddles River, New Jersey.

Harrington, Scott E. and Gregory R. Niehaus; 2004, Risk Management and Insurance, McGraw Hill Irwin, New York, New York.

Powell, Stephen G. and Kenneth R. Baker; 2004, The Art of Modeling with Spreadsheets, John Wiley & Sons, Inc., New York, New York.

Vaughan, Emmett J. and Therese Vaughan; 2003, Fundamentasl of Risk and Insurance, John Wiley & Sons, Inc., New York, New York.

Schedule 1 Information about four types of risk:

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Panel A. Investment Activity A

Financial Risk (foreign exchange risk) uncertain variablesExpected basis -0.0024 Uniform distribution; max = -0.004; min = -0.008Expect price per CD 1/31/2004 0.8139 Normal distribution; standard deviation = 0.13139

Computation of expected price of CD under futures contractsMarch futures price on Dec 15, 2003Expected basis (St –Ft) on January 31, 2004Expected price of CD under futures contract

0.8149-0.00240.8125

KnownUncertain

N/A

Operational Risk (Volatility of operating costs and expenses)Other operating expenses $1.925mil Normal distribution; std dev = $192,500

Panel B. Investment Activity B

Strategic Risk (expected volatility of unit price)Unit price of product $100 Uniform distribution; max = $110; min = $90

Pure Risk (customer liability lawsuits)Expected frequency of lawsuits 2 Poisson distribution; std dev = 1; min = 0Expected severity per lawsuit $320,000 Lognormal distribution; standard dev = $700,000

Operational Risk (Volatility of operating costs and expenses)Other operating expenses $1.275mil Normal distribution; std dev = $127,500

Schedule 2 Deterministic modeling of expected after-tax operating income

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Investment Activity A

Price per unit in US dollars $100.001

Units sold to Canadian firm 20,000Current (December 15) price of unit in CD $0.8121 Fixed number of Canadian dollars to be received January 31, 2004 2,462,750.89Expected exchange rate (January 31) 0.81391

Revenues (position open) $2,004,432.95

COGS and Other Operating Expenses -$1,925,000.001

Operating Income (A) $79,432.95

Investment Activity B

Price per unit in US dollars $100.00Units sold locally 20,000Revenues $2,000,000.00

COGS and Operating Expenses -$1,275,000.001

Expected frequency of lawsuits next month 21

Expected severity per lawsuit -$320,000.001

Expected Losses from Customer Lawsuits -$640,000.00

Operating Income (B) $85,000.00

Total Operating Income (A and B)

Operating Income $164,432.95Taxes -$57,551.53After-tax Operating Income $106,881.42

1 Variables in model which are uncertain

Schedule 3 Simulation modeling of after-tax operating income;

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no risk controls in placeForecast: After-tax Operating Income

Panel AStatistics

Trials 500Mean $146,575 Median $287,534 Standard Deviation $859,983 Skewness -2.79

Panel BFrequency Chart

Panel C Percentiles for after-tax operating income

Percentile Range

0% to 25%($11,440,002) to

($42,788) 25%

to 50% ($42,788) to $287,53350% to 75% $287,533 to $596,187

75% to 100% $596,187 to 1,596,476

Panel D Values at Risk

Probability Value at risk1

5% ($1,400,000)10% ($500,000)15% ($260,000)

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Frequency Chart

dollars

.000

.011

.022

.033

.044

0

5.5

11

16.5

22

($1,768,605.88) ($953,652.00) ($138,698.12) $676,255.76 $1,491,209.63

500 Trials 481 Displayed

Forecast: After-tax Operating Income

1 indicates that the after-tax operating loss will be greater than the indicated amount at the indicated probability

Schedule 4 Simulation modeling of after-tax operating income Hedging in place and full insurance coverage

Panel A Statistics


Panel B Frequency Chart

Frequency Chart

dollars

.000

.008

.015

.023

.030

0

3.75

7.5

11.25

15

($644,959.70) ($300,947.98) $43,063.75 $387,075.48 $731,087.21

500 Trials 496 Displayed

Forecast: After-tax Operating Income

Panel C Percentiles for after-tax operating incomePercentile Range0% to 25% ($4,581,327) to ($108,459)25% to 50% ($105,900) to $102,48050% to 75% $102,480 to $287,743 75% to 100% $287,743 to $972,952



5% ($370,000)10% ($270,000)15% ($200,000)


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Schedule 5 Simulation modeling of after-tax operating incomeOptimal hedging in place and optimal insurance purchased and SD <= $400,000

Panel A Statistics


Panel B Percentiles for after-tax operating income

Percentile dollars 0% to

25% ($6,921,728) to ($77,099) 25% to 50% ($77,099 to $135,859 50% to

75% $135,859 to 343,257 75% to

100% $343,257 to $1,134,372



5% ($905,000)10% ($380,000)15% ($230,000)


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