{ From user Lonnie, Model Measures_of_risk_and at 20-May-2010 2:04:21 PM }
Softwareversion 4.2.3


{ System Variables with non-default values: }
Time := 0..100
Samplesize := 1000
Sampletype := 1
{!40000|Att_contlinestyle Run: 0}
Typechecking := 1
Checking := 1
Saveoptions := 2
Savevalues := 0
{!40000|Att_contlinestyle Graph_primary_valdim: 1}
{!40000|Att_contlinestyle Graph_pdf_valdim: 6}
{!40000|Att_contlinestyle Graph_cdf_valdim: 1}



Model Measures_of_risk_and
Title: Measures of Risk and Utility
Description: Model created during the fourth webinar in the "Gentle Introduction to Modeling Uncertainty" series.  Explore concepts and quantitative measures of Risk and Utility, various conceptions and types of risk, and explore topics relevant to model-building that include utility and loss functions, expected value, expected utility, risk neutrality, risk aversion, fractiles and Value-at-risk (VaR).
Author: Lonnie Chrisman~
Lumina Decision Systems
Date: Thu, May 20, 2010 9:54 AM
Saveauthor: Lonnie
Savedate: Thu, May 20, 2010 2:04 PM
Defaultsize: 48,24
Diagstate: 2,24,16,554,169,17
Fontstyle: Arial, 15
Fileinfo: 0,Model Measures_of_risk_and,2,2,0,0,W:\Training\User Group Webinars\Measures of Risk.ana

Module Deal_or_no_deal
Title: Deal or No Deal
Nodelocation: 80,40,1
Nodesize: 48,24

Variable Wealth
Title: wealth
Definition: Sequence(0,1M,10K)
Nodelocation: 96,56,1
Nodesize: 48,24

Chance Outcome_of_choose
Title: Outcome of choose
Definition: Bernoulli(0.5) * $1M
Nodelocation: 216,56,1
Nodesize: 48,24

Variable E_util_of_choose
Title: E Util of choose
Definition: Mean( ln(wealth + Outcome_of_choose ) )
Nodelocation: 336,56,1
Nodesize: 48,24
Valuestate: 2,399,3,416,300,0,MIDM

Variable E_util_of_stop
Title: E Util of Stop
Definition: Ln( Wealth + $400K)
Nodelocation: 216,112,1
Nodesize: 48,24
Valuestate: 2,375,20,416,300,0,MIDM

Variable Threshold
Title: Threshold
Definition: Exp(E_util_of_choose) - Wealth
Nodelocation: 336,112,1
Nodesize: 48,24
Valuestate: 2,280,20,590,450,1,MIDM

Close Deal_or_no_deal

Module Investment_property
Title: Investment Property
Defaultsize: 48,24
Nodelocation: 208,40,1
Nodesize: 48,24
Diagstate: 2,192,25,655,474,17

Variable Purchase_price
Title: Purchase Price
Definition: $250K
Nodelocation: 72,128,1
Nodesize: 48,24

Decision Investment_amt
Title: Investment Amt
Definition: $50K
Nodelocation: 312,32,1
Nodesize: 48,24

Chance Total_net_income
Title: Total net income
Units: $
Description: Net income while we own the property from rent receipts, less maint, loan pmts, mgt expenses, etc.
Definition: Normal(-25K,10K)
Nodelocation: 176,64,1
Nodesize: 48,24

Chance Appreciation
Title: Appreciation
Definition: Normal(12%,10%)
Nodelocation: 80,200,1
Nodesize: 52,24

Variable Mortgage_balance
Title: Mortgage balance
Definition: $185K
Nodelocation: 216,240,1
Nodesize: 48,24

Variable Sale_price
Title: Sale price
Definition: Purchase_price * (1+Appreciation)
Nodelocation: 184,160,1
Nodesize: 48,24
Valuestate: 2,441,178,416,303,1,CDFP

Objective Profit
Title: Profit
Definition: Sale_price - Investment_amt - Mortgage_balance + Total_net_income
Nodelocation: 368,136,1
Nodesize: 48,24
Valuestate: 2,204,36,632,432,1,CDFP

Objective Roi
Title: ROI
Definition: Profit / Investment_amt
Nodelocation: 480,136,1
Nodesize: 48,24
Valuestate: 2,93,-5,715,486,1,CDFP
Numberformat: 2,%,4,2,0,0,4,0,$,0,"ABBREV",0

Objective Prob_of_loss
Title: Prob of loss
Definition: Probability( Profit<0 )
Nodelocation: 384,232,1
Nodesize: 48,24

Objective A5__var
Title: 5% VaR
Definition: -GetFract( Profit, 5% )
Nodelocation: 384,288,1
Nodesize: 48,24

Objective Std_dev_profit
Title: Std dev profit
Definition: SDeviation(Profit)
Nodelocation: 488,232,1
Nodesize: 48,24

Constant Wealth1
Title: Wealth
Description: This would be your wealth before you made the investment.
Definition: $500K
Nodelocation: 592,232,1
Nodesize: 48,24

Objective Bernoulli_s_utility
Title: Bernoulli's utility
Definition: mean(ln(wealth1+profit) - ln(wealth1))
Nodelocation: 488,288,1
Nodesize: 48,24
Valuestate: 2,91,183,416,303,0,MIDM

Text Te1
Description: Various risk metrics
Nodelocation: 428,288,-1
Nodesize: 124,104
Nodeinfo: 1,0,0,1,1,1,0,,0,

Objective A5__expected_shortfa
Title: 5% expected shortfall
Definition: mean( -profit, w:-profit>=A5__var)
Nodelocation: 384,345,1
Nodesize: 48,31
Valuestate: 2,68,161,416,303,0,MIDM
Numberformat: 2,F,4,2,1,1,4,0,$,0,"ABBREV",0

Close Investment_property

Module Transition_system
Title: Transition system
Description: This example is in the power point slides, but I didn't get to it during the webinar.  See the slices for details.  It involves a 3-state Markov process, with the change in value each day determined by the state.~
~
It is used to demonstrate how VaR can miss highly important risks that can have a major impact, and thus motivate Expected Shortfall, or CVaR
Author: Lonnie Chrisman
Defaultsize: 48,24
Nodelocation: 328,40,1
Nodesize: 48,24
Diagstate: 2,108,91,662,390,17

Index State
Title: State
Definition: ['Bull','Bear','Crash']
Nodelocation: 96,56,1
Nodesize: 48,24
{!40000|Att_previndexvalue: ['Bull','Bear','Crash']}

Index Next_state
Title: Next state
Definition: copyindex(state)
Nodelocation: 216,56,1
Nodesize: 48,24
{!40000|Att_previndexvalue: ['Bull','Bear','Crash']}

Variable Transition_probs
Title: Transition Probs
Definition: Table(State,Next_state)(~
0.9,0.1,0,~
0.1,0.899,1m,~
0.1,0,0.9~
)
Nodelocation: 96,128,1
Nodesize: 48,24
Reformdef: [Next_state,State]
Numberformat: 2,F,4,3,0,0,4,0,$,0,"ABBREV",0

Variable Initial_state
Title: Initial state
Definition: 'Bear'
Nodelocation: 96,192,1
Nodesize: 48,24

Variable Next_trans_prob
Title: Next Trans Prob
Definition: Transition_probs[State=Cur_state]
Nodelocation: 216,192,1
Nodesize: 48,24
Reformval: [Time,Next_state]

Variable Cur_state
Title: Cur State
Definition: Dynamic(Initial_state, Next_state1[Time-1])
Nodelocation: 216,128,1
Nodesize: 48,24
Domain: State
{!40000|Att_previndexvalue: ['Bull','Bear','Crash']}

Chance Next_state1
Title: Next state
Definition: ChanceDist(Next_trans_prob,Next_state)
Nodelocation: 336,192,1
Nodesize: 48,24

Variable Daily_change
Title: Daily change
Definition: Determtable(Cur_state)(~
3m,-2m,-0.1)
Nodelocation: 336,128,1
Nodesize: 48,24
Numberformat: 2,%,4,2,0,0,4,0,$,0,"ABBREV",0

Variable Rel_value
Title: Rel value
Definition: cumproduct( 1+Daily_change, Time )
Nodelocation: 448,128,1
Nodesize: 48,24
Valuestate: 2,65,58,645,476,1,SAMP
Graphsetup: {!40000|Att_contlinestyle Run:5}
Reformval: [Time,Undefined,2,Undefined,Undefined,0]
{!40000|Att_resultslicestate: [Run,15,Time,1]}

Objective A5__var1
Title: 5% VaR
Definition: GetFract(loss,95%)
Nodelocation: 448,272,1
Nodesize: 48,24
Valuestate: 2,125,254,416,303,0,MIDM

Variable Loss
Title: Loss
Definition: 1-Rel_value[Time=100]
Nodelocation: 448,192,1
Nodesize: 48,24
Valuestate: 2,132,139,416,303,1,SAMP

Objective Worst_case_in_all_ru
Title: Worst case in all runs
Definition: max( sample(Loss), run )
Nodelocation: 560,272,1
Nodesize: 48,24
Valuestate: 2,49,256,416,312,0,MIDM

Text Te2
Description: Notice how the VaR is dramatically different from the worst loss out of the 1000 runs.
Nodelocation: 252,278,-1
Nodesize: 132,30

Variable View_worst_case_run
Title: View worst case run
Definition: Sample(rel_value[ Run = ArgMin(Rel_value[Time=100]) ] )
Nodelocation: 560,192,1
Nodesize: 48,24
Valuestate: 2,25,90,416,303,1,MIDM

Objective A5__expected_shortva
Title: 5% Expected Shortvall
Description: Expected shortfall, also known as expected tail loss or Conditional Value at risk (CVaR) is better at taking extreme, but extremely rare, scenarios into account in the risk measure.
Definition: mean(loss, w:loss>=A5__VaR1)
Nodelocation: 560,344,1
Nodesize: 48,31

Close Transition_system

Close Measures_of_risk_and