Materials for lecture 13
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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

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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

  • Lecture 13 Scenario & Sensitivity.xls

  • Lecture 13 Sensitivity Elasticity.xls


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

  • The appropriate statistical test changes as we change the method for estimating the parameters


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 Tests

  • If the data are stationary and you want to simulate using a mean that is not equal tothe 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 Tests

  • If the data are non-stationaryand 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 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

  • 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 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

  • 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

  • Simetar simulation engine controls

    • Number of scenarios

    • Sensitivity analysis

    • Sensitivity elasticities


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 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

    • Use =SCENARIO() Simetar function to increment each of the scenario control variables


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

  • Create as big of table as needed

  • Add all control variables into the table


Results of the Scenario Analysis


Example Scenario Table of Controls


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 Analysis

  • Simetar uses the Simulation Engine to specify the change variable and the percentage changes to test

  • Specify as many KOVs as you want

  • Simulate the model and 7 scenarios are run


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 few KOVs

  • For demonstration purposes collect results for the variable doing the sensitivity test on

    • Could collect the results for several KOVs


Sensitivity Results

  • Test Sensitivity of the price received for the product being manufactured on Net Cash Income


Sensitivity Results


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

  • The more sensitive the KOV is to a variable, Vj, the larger the SEij

  • Display the SEij’s in a table and chart


Sensitivity Elasticities


Sensitivity Elasticities


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