risk drivers revealed steve craighead 1. introduction regression var conditional var example...

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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