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Materials for Lecture 13. Purpose summarize the selection of distributions and their appropriate validation tests Explain the use of Scenarios and Sensitivity Analysis in a simulation model Chapter 10 pages 1-3 Chapter 16 Sections 7, 8 and 9 Lecture 13 Scenario.xls

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materials for lecture 13
Materials for Lecture 13
  • Purpose summarize the selection of distributions and their appropriate validation tests
  • Explain the use of Scenarios and Sensitivity Analysis in a simulation model
  • Chapter 10 pages 1-3
  • Chapter 16 Sections 7, 8 and 9
  • Lecture 13 Scenario.xls
  • Lecture 13 Scenario & Sensitivity.xls
  • Lecture 13 Sensitivity Elasticity.xls
summarize validation tests
Summarize Validation Tests
  • Validation of simulated distributions is critical to building good simulation models
  • Selection of the appropriate statistical tests to validate the simulated random variables is essential
  • Appropriate statistical tests changes as we change the method for estimating the parameters
summarize univariate validation tests
Summarize Univariate Validation Tests
  • If the data are stationary and you want to simulate using the historical mean
  • Distribution
    • Use Normal as =NORM(Ῡ, σY) or
    • Empirical as =EMP(Historical Ys)
  • Validation Tests for Univariate distribution
    • Compare Two Series tab in Simetar
      • Student-t test of means as H0: ῩHist = ῩSim
      • F test of variances as H0: σ2Hist = σ2Sim
      • You want both tests to Fail to Reject the null H0
summarize univariate validation tests1
Summarize Univariate Validation Tests
  • If the data are stationary and you want to simulate using a mean that is not equal to the historical mean
  • Distribution
    • Use Empirical as a fraction of the mean so the Si = Sorted((Yi - Ῡ)/Ῡ) and simulate using the formula

Ỹ = Ῡ(new mean) * ( 1 + EMP(Si, F(Si), [CUSDi] ))

  • Validation Tests for Univariate distribution
    • Test Parameters
      • Student-t test of means as H0: ῩNew Mean = ῩSim
      • Chi-Square test of Std Dev as H0: σHist = σSim
      • You want both tests to Fail to Reject the null H0
summarize univariate validation tests2
Summarize Univariate Validation Tests
  • If the data are non-stationary and you use OLS, Trend, or time series to project Ŷ
  • Distribution
    • Use =NORM(Ŷ , Standard Deviation of Residuals)
    • Use Empirical and the residuals as fractions of Ŷ calculated for Si = Sorted((Yi - Ŷj)/Ŷ) and simulate each variable using

Ỹi = Ŷi * (1+ EMP(Si, F(Si) ))

  • Validation Tests for Univariate distribution
    • Test Parameters
      • Student-t test of means as H0: ŶNew Mean = ῩSim
      • Chi-Square test of Std Dev as H0: σê = σSim
      • You want both tests to Fail to Reject the null H0
summarize univariate validation tests3
Summarize Univariate Validation Tests
  • If the data have a cycle, seasonal, or structural pattern and you use OLS or any econometric forecasting method to project Ŷ
  • Distribution
    • Use =NORM(Ŷ, σê standard deviation of residuals)
    • Use Empirical and the residuals as fractions of Ŷ calculated for Si = Sorted((Yi - Ŷ)/Ŷ) and simulate using the formula

Ỹ = Ŷ * (1 + EMP(Si, F(Si) ))

  • Validation Tests for Univariate distribution
    • Test Parameters tab
      • Student-t test of means as H0: ŶNew Mean = ῩSim
      • Chi-Square test of Std Dev as H0: σê = σSim
      • You want both tests to Fail to Reject the null H0
summarize multivariate validation tests
Summarize Multivariate Validation Tests
  • If the data are stationary and you want to simulate using the historical means and variance
  • Distribution
    • Use Normal =MVNORM(Ῡ vector, ∑ matrix) or
    • Empirical =MVEMP(Historical Ys,,,, Ῡ vector, 0)
  • Validation Tests for Multivariate distributions
    • Compare Two Series for 10 or fewer variables
      • Hotelling T2 test of mean vectors as H0: ῩHist = ῩSim
      • Box’s M Test of Covariances as H0: ∑Hist = ∑Sim
      • Complete Homogeneity Test of mean vectors and covariance simultaneously
      • You want all three tests to Fail to Reject the null H0
    • Check Correlation
      • Performs a Student-t test on each correlation coefficient in the correlation matrix: H0: ρHist = ρSim
      • You want all calculated t statistics to be less than the Critical Value t statistic so you fail to reject each t test (Not Bold)
summarize multivariate validation tests1
Summarize Multivariate Validation Tests
  • If you want to simulate using projected means such that Ŷt ≠ Ῡhistory
  • Distribution
    • Use Normal as = MVNORM(Ŷ Vector, ∑matrix) or
    • Empirical as = MVEMP(Historical Ys ,,,, Ŷ vector, 2)
  • Validation Tests for Multivariate distribution
    • Check Correlation
      • Performs a Student-t test on each correlation coefficient in the matrix: H0: ρHist = ρSim
      • You want all calculated t statistics to be less than the Critical Value t statistic so you fail to reject each t test
    • Test Parameters, for each j variable
      • Student-t test of means as H0: ŶProjected j = ῩSim j
      • Chi-Square test of Std Dev as H0: σê j = σSim j
using a simulation model
Using a Simulation Model
  • Now lets change gears
  • Assume we have a working simulation model
  • The Model has the following parts
    • Input section where the user enters all input values that are management control variables and exogenous policy or time series data
    • Stochastic variables that have been validated
    • Equations to calculate all dependent variables
    • Equations to calculate the KOVs
    • A KOV table to send to the simulation engine
scenario and sensitivity analysis
Scenario and Sensitivity Analysis
  • Simetar simulation engine controls
    • Number of scenarios
    • Sensitivity analysis
    • Sensitivity elasticities
scenario analysis

Scenario loop

IS = 1, M

Change management variables (X) from one scenario to the next

Iteration loop

IT = 1, N

Next scenario

Scenario Analysis
  • Base scenario – complete simulation of the model for 500 or more iterations with all variables set at their initial or base values
  • Alternative scenario – complete simulation of the model for 500 or more iterations with one or more of the control variables changed from the Base
  • All scenarios must use the same random values

Use the same random values for all random variables, so identical risk for each scenario

scenario analysis1
Scenario Analysis
  • All values in the model are held constant and you systematically change one or more variables
    • Number of scenarios determined by analyst
    • Random number seed is held constant and this forces Simetar to use the same random values for the stochastic variables for every scenario (Pseudo Random Numbers)
    • Use =SCENARIO() Simetar function to increment each of the scenario (manager) control variables
example of a scenario table
Example of a Scenario Table
  • 5 Scenarios for the risk and VC
  • Purpose is to look at the impacts of different management scenarios on net returns
scenario table of the controls
Scenario Table of the Controls
  • Create as big of scenario table as needed
  • Add all control variables into the table
sensitivity analysis
Sensitivity Analysis
  • Sensitivity analysis seeks to determine how sensitive the KOVs are to small changes in one particular variable
    • Does net return change a little or a lot when you change variable cost per unit?
    • Does NPV change greatly if the assumed fixed cost changes?
  • Simulate the model numerous times changing the “change” variable for each simulation
    • Must ensure that the same random values are used for each simulation
  • Simetar has a sensitivity option that insures the same random values used for each run
sensitivity analysis1
Sensitivity Analysis
  • Simetar uses the Simulation Engine to specify the change variable and the percentage changes to test
  • Specify as many KOVs as you want
  • Specify ONE sensitivity variable
  • Simulate the model and 7 scenarios are run
demonstrate sensitivity simulation
Demonstrate Sensitivity Simulation
  • Change the Price per unit as follows
    • + or – 5%
    • + or – 10%
    • + or – 15%
  • Simulates the model 7 times
    • The initial value you typed in
    • Two runs for + and – 5% for the control variable
    • Two runs for + and – 10% for the control variable
    • Two runs for + and – 15% for the control variable
  • Collect the statistics for only a few KOVs
  • For demonstration purposes collect results for the variable doing the sensitivity test on
    • Could collect the results for several KOVs
sensitivity results
Sensitivity Results
  • Test Sensitivity of the price received for the product being manufactured on Net Cash Income
sensitivity elasticities se
Sensitivity Elasticities (SE)
  • Sensitivity of a KOV with respect to (wrt) multiple variables in the model can be estimated and displayed in terms of elasticities, calculated as:

SEij = % Change KOVi

% Change Variablej

  • Calculate SE’s for a KOVi wrt change variablesj at each iteration and then calculate the average and standard deviation of the SE
  • SEij’s can be calculated for small changes in Control Variablesj, say, 1% to 5%
    • Necessary to simulate base with all values set initially
    • Simulate model for an x% change in Vj
    • Simulate model for an x% change in Vj+1
sensitivity elasticities
Sensitivity Elasticities
  • The more sensitive the KOV is to a variable, Vj, the larger the SEij
  • Display the SEij’s in a table and chart
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