risk drivers revealed steve craighead 1. introduction regression var conditional var example...
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Risk Drivers Revealed
Steve Craighead
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IntroductionRegressionVaRConditional VaRExampleDashboards
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IntroductionRegressionVaRConditional VaRExampleDashboards
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Economic Capital (EC)
• Economic Scenarios Simulation– Expensive– Only used to determine EC
• Extract additional information– Which economic conditions have an impact on the
extreme (VaR) target percentage– Offsetting risks– Dash Boards from the stochastic results
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IntroductionRegressionVaRConditional VaRExampleDashboards
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Regression
• Formula:Y = a0 + a1X1 +a2X2 + … + anXn + e
• Least Squares – The conditional mean of Y is modeled
• Quantile Regression – A conditional percentage of Y is modeled
• Two Dimensional Example
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IntroductionRegressionVaRConditional VaRExampleDashboards
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Value at Risk (VaR)
• Traditional– Normal distribution
• Empirical– Simulate using scenarios– Sort the results– Find the VaR target percentage
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IntroductionRegressionVaRConditional VaRExampleDashboards
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Conditional VaR
• In addition to determining Empirical VaR– Use Quantile Regression to model how the
conditional percentile relates to the economic scenarios.
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IntroductionRegressionVaRConditional VaRExampleDashboards
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0.5% Conditional VaR model
Standard Significant Influence
Time Coefficient Error t value Pr($>|t|$) Coefficient Percent Ranking
(Intercept) 1.28 0.475 2.696 0.007 NA NA NA
1 92.396 32.402 2.852 0.004 92.396 9.5 F
2 -98.147 35.508 -2.764 0.006 -98.147 10.1 E
3 -247.593 36.637 -6.758 0 -247.593 25.5 A
4 -160.356 30.791 -5.208 0 -160.356 16.5 C
5 -180.837 29.105 -6.213 0 -180.837 18.6 B
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0.5% Conditional VaR model
Time Coefficient
(Intercept) 1.28
1 92.396
2 -98.147
3 -247.593
4 -160.356
5 -180.83714
0.5% Conditional VaR model
Standard
Coefficient Error
1.28 0.475
92.396 32.402
-98.147 35.508
-247.593 36.637
-160.356 30.791
-180.837 29.10515
0.5% Conditional VaR model
Standard
Error t value
0.475 2.696
32.402 2.852
35.508 -2.764
36.637 -6.758
30.791 -5.208
29.105 -6.21316
0.5% Conditional VaR model
t value Pr($>|t|$)
2.696 0.007
2.852 0.004
-2.764 0.006
-6.758 0
-5.208 0
-6.213 017
0.5% Conditional VaR model
Significant
Pr($>|t|$) Coefficient
0.007 NA
0.004 92.396
0.006 -98.147
0 -247.593
0 -160.356
0 -180.83718
0.5% Conditional VaR model
Significant Influence
Coefficient Percent
NA NA
92.396 9.5
-98.147 10.1
-247.593 25.5
-160.356 16.5
-180.837 18.619
0.5% Conditional VaR model
Influence
Percent Ranking
NA NA
9.5 F
10.1 E
25.5 A
16.5 C
18.6 B20
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IntroductionRegressionVaRConditional VaRExampleDashboards
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Dashboards – QR models
• To create a dashboard using the QR model, take the current yield curve and develop the 10-year rates specific periods forward. For instance, create the find the rates 2, 3, 4, 5 and 6 years forward. Take the difference between the 3rd year forward and the 2nd year forward and use it as input for the formula.
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Dashboards• To model spreads, create the forward rates for
the short rate and long rate and calculate the spread at each time in the future.
• If the risk driver is an equity return – The current return is held constant into the future
due to a no arbitrage assumption, and all of the predictors in the QR model will be replaced with that single value.
– Use a simple economic generator to produce multiple equity scenarios and quickly process these future returns through the QR model and average the results.
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Questions
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