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# Materials for Lecture 13 - PowerPoint PPT Presentation

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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• 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

• 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

• 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

• 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

• 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

• 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

• 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)

• 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

• 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

• Simetar simulation engine controls

• Number of scenarios

• Sensitivity analysis

• Sensitivity elasticities

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

• 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

• 5 Scenarios for the risk and VC

• Purpose is to look at the impacts of different management scenarios on net returns

• Create as big of scenario table as needed

• Add all control variables into the table

• 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

• 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

• 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

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

• 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

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

• Display the SEij’s in a table and chart