Notes on Monte Carlo Simulation Techniques

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Notes on Monte Carlo Simulation Techniques
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Uncertainty, Risk and Traditional Financial
Modeling

• Financial decisions are made in an environment of
  uncertainty about future outcomes
• Uncertainty involves variables that are
  constantly changing
• E.g., the closing trading price of a stock on a
  particular day or the sales of a firm in a
  particular quarter
• In such an environment, all decision-makers are
  faced with the same level of uncertainty
• In making financial decisions, we evaluate each
  outcome from a risk-return standpoint

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Uncertainty, Risk and Traditional Financial
Modeling

• Risk involves only the uncertain outcomes that
  affect us in a direct way
• Simply because we are faced with uncertainty does
  not imply that we are also faced with risk
• For example, a financial analyst in a
  multinational firm is faced with the uncertainty
  of the future value of the yen-dollar rate
• However, only if this exchange rate affects this
  firms bottom-line profits is the firm faced with
  risk

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Uncertainty, Risk and Traditional Financial
Modeling

• In traditional spreadsheet financial modeling, it
  is common to approach risk by performing scenario
  and sensitivity analysis
• Scenario analysis implies altering key
  assumptions (drivers) of the model to capture
  certain assumed scenarios
• For example, in the DCF valuation model, we could
  alter the assumption about the growth rate of
  sales during the forecast period to capture the
  following three scenarios
• High growth 15
• Average growth 10
• Low growth 5

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Uncertainty, Risk and Traditional Financial
Modeling

• Sensitivity analysis involves making unit changes
  of key assumptions (drivers) of the model and
  examining the impact on outcome variables
• This is captured through the inclusion of
  sensitivity tables in the spreadsheet model
• However, a major drawback of traditional
  financial modeling is that it suffers from the
  absence of any probabilities attached to the
  values of key drivers in the model

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What is Monte Carlo Simulation?

• Monte Carlo simulation techniques add two major
  improvements to traditional financial modeling
• The uncertainty of the values of the models
  drivers is addressed by assigning predefined
  probability distributions to those variables
• The model is simulated thousands of times, given
  different values of the drivers drawn from the
  predefined probability distributions, to produce
  associated results
• The outcomes of the Monte Carlo simulation are
  then tabulated into probability distributions
  that allow us to evaluate the probabilities of
  various outcomes in the model

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Steps in Monte Carlo Simulation Process

• Step 1 Create the model (include the assumptions
  (drivers) of the model and link the models
  variables)
• Step 2 Identify the probability distributions of
  the models drivers
• Step 3 Simulate the model (either use the
  default number of trials and other preferences or
  change these values before you run the
  simulation)
• Step 4 Interpret and evaluate the results of the
  simulation

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Identifying Probability Distributions of the
Models Drivers

• To identify the probability distribution(s) of
  the models driver(s), it is proper to use
  historical data for the particular variable
• Having obtained historical data, the goal is to
  match a probability distribution to the data
• Exploring various distributions, we evaluate the
  fit of the distribution based on some commonly
  used goodness-of-fit tests, such as
• Kolmogorov-Smirnov Test
• Anderson-Darling Test
• Chi-Square Test

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Identifying Probability Distributions of the
Models Drivers

• Each goodness-of-fit test has its advantages and
  disadvantages
• However, a commonly used test is the Chi-Square
  because it can be applied to both discrete and
  continuous distributions while the other two
  tests are restricted to continuous distributions
• To identify the probability distribution for a
  variable, select the probability with the lowest
  value of the goodness-of-fit test

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Interpreting Simulation Results

• The simulation outcomes are tabulated into
  probability distributions
• This distribution includes probabilities of all
  possible outcomes from the simulation, meaning
  that the area under the distribution is equal to
  one
• Two steps in interpreting these results are
  interesting and useful to the analyst
• Define a probability (certainty) level and obtain
  the cutoffs of the corresponding confidence
  interval
• Specify a cutoff value of interest and obtain the
  probability of observing outcomes above or below
  that cutoff

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Interpreting Simulation Results

• Another tool used to analyze simulation results
  is the examination of sensitivity charts
• Sensitivity charts identify the impact of the
  models various drivers on the outcome(s) when
  multiple interacting drivers are simulated
  together
• This tool enables the analyst to identify which
  drivers are the most significant for the outcomes
  produced by the simulation
• Simulation software, such as Crystal Ball, allows
  the analyst to easily produce these charts