More Accurate Measurement for Enhanced Control: VaR vs ES?

A Regulatory Driven Systemic Risk

Paris, February 19th, 2016

Authors:Dominique GuéganBertrand Hassani

Disclaimer: The opinions, ideas and approaches expressed or presented are those of the author and do not necessarily reflect Santander’s position. As a result, Santander cannot be held responsible for them. The values presented are just illustrations and do not represent Santander losses.

Copyright: ALL RIGHTS RESERVED. This presentation contains material protected under International Copyright Laws and Treaties. Any unauthorized reprint or use of this material is prohibited. No part of this presentation may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system without express written permission from the author.

2Risk Measurements and Control

KEY REGULATORS AND SUPERVISORS

Fed

OCC

European level

Bundesbank

Global level

Narodowy Bank Polski

BCB

BISIASB

FDICCNBV

SEC

FSB

EBA ESMA EIOPA ECBEC

PRA

CNMV

BdE

FCA

Regulatory environment considered

3Risk Measurements and Control

Regulatory Statements

• Risk Measures in the Regulation:

• Market Risk: VaR 95% historical or Guassian (traditionally). Moving toward Expected Shortfall

• Credit Risk: Percentile at 99% used. LGD is an expected shortfall (spectrum). Usually a logistic regression for theProbability of Default.

• Counterparty: Expected Positive Exposure (EPE). Gaussian assumption.

• Operational Risk: VaR at 99.9% for the regulatory capital and 99.95-8 for the economic capital. Any distribution could beused.

• Stress Testing: Stress VaR, etc. A lot more latitude though?

• False Statements?

• Stability of the risk measures when data are not stationary?

• Data sets selected? 5y, 10y?

• VaR non sub-additive – ES sub-additive?

• VaR not capturing tail information?

• Empirical distribution not conservative enough?

4Risk Measurements and Control

1. For a single kind of risk (univariate): the choice of the level of confidence is not determining, while thedistribution is….?

2. For multiple kind of risks (multivariate): for which combination of distributions is the sub-additivity propertyfulfilled ?

• Are the model reliable to evaluate these risk measures?

3. Given that each risk may be modelled considering different distributions and using different confidencelevel for the risk measure, what is the impact of the non sub-additivity?

4. Is that more efficient in terms of risk management to measure the risk and then build a capital buffer or toadjust the risk taken considering the capital we have? (Inverse problem)

5. The previous points are all based on uni-modal parametric distributions, what is the impact of usingmultimodal distributions in terms of risk measurement and management?

• How can we combine the various risk to obtain a holistic metric?• Can we combine various risk measure evaluated at different confidence level?

Problematic

Does the concept of risk measure as we know it really exist?

5Risk Measurements and Control

Experimentation

• Distributions

• Empirical, lognormal, Weibull, GPD, GH, Alpha-stable, GEV

• Parameterization: MLE, Hill, Block Maxima

• Goodness-of-fit: KS, AD

• Risk Measures

• ES

• VaR

• Spectral

• Distortion

• Data

• Market data (Dow Jones)

• Operational Risk data (EDPM)

6Risk Measurements and Control

Parameters Table 109-14

Table 209-11

Table 312-14

7Risk Measurements and Control

VaR vs ES?

Table 109-14

Table 209-11

Table 312-14

Univariate Risk Measures - This table exhibits the VaRs and ESs for the height types of distributions considered - empirical,lognormal, Weibull, GPD, GH, -stable, GEV and GEV fitted on a series of maxima - for five confidence level (90%, 95%, 97.5%, 99% and 99.9%) evaluated on the period 2009-2014.

8Risk Measurements and Control

Spectral Conundrum……… VaR(X + Y) vs VaR(X) + VaR(Y)

Gaussian BenchmarkGPD Weibull

Alpha-Stable GEV lognormal Weibull

VaR(X+Y)

VaR(X) + VaR(Y)

9Risk Measurements and Control

With value…..

10Risk Measurements and Control

0 100 200 300 400 500 600

0.00

0.05

0.10

0.15

LogNormal PDF Distortion Illustration

x

Fn(x

)

Distortion Risk Measures

0 200 400 600 800 1000

0e+0

01e

-06

2e-0

63e

-06

EPDF Distortion Spectrum

x

Fn(x

)

Impact on a parametric distribution

Impact on non-parametric distribution

11Risk Measurements and Control

Interesting Behaviour

12Risk Measurements and Control

Conclusions

• The problem should be discussed in its entirety:

• Risk Measure, Distribution, Estimation, Numerical error, level of confidence should be treated as a singlepolymorphic organism

• Complete mis-alignement between Risk Management and Capital Calculations

• Capital calculation: buffer to face materialisation of risk- therefore we assume it happened, the risk measure is alimit

• Risk Management: try to prevent and mitigate, therefore the risk measure represents an exposure

• The wrong regulation leads to a dreadful systemic risk:

• All the bank adopting the same methodology leads in case of failure to a domino effect

• The current regulation prevents the construction of a hollistic approach

This project has received funding from the European Union’s

Seventh Framework Programme for research, technological

development and demonstration under grant agreement n° 320270

www.syrtoproject.eu

This document reflects only the author’s views.

The European Union is not liable for any use that may be made of the information contained therein.