Paris, March 2015 Alexander Denev

 As of today stress testing scenarios used by institutions are  Often lacking a coherent story behind  Run through backward-looking models calibrated on historical data  Insight free as based purely on macroeconomic aggregates  Excessively complex to run  Yielding results difficult to interpret and to understand

 A silo approach to Stress Testing is still predominant in institutions  The models used for Stress Testing are based on hundreds of variables built on different datasets Y W Z X99 X X3 X2 X1 Oil prices GDP Volatility

 The outputs of these models are sometimes aggregated at a firm-wide level, generally without accounting for diversification/amplification between them Stress Test Result = Output Model 1 Output Model 2 Output Model 3 + +

1. Gives rise to transparent structures where all the components interact in a visible manner and can be understood by the Board/ Senior Management

2. Can aggregate different sources of information e.g. historical datasets, market prices, expert opinions etc

1. Gives rise to transparent structures where all the components interact in a visible manner and can be understood by the Board/ Senior Management 2. Can aggregate different sources of information e.g. historical datasets, market prices, expert opinions etc 3. Can be easily updated in the light of new information

1. Gives rise to transparent structures where all the components interact in a visible manner and can be understood by the Board/ Senior Management 2. Can aggregate different sources of information e.g. historical datasets, market prices, expert opinions etc 3. Can be easily updated in the light of new information 4. Has a rigorous mathematical framework behind it

1. Gives rise to transparent structures where all the components interact in a visible manner and can be understood by the Board/ Senior Management 2. Can aggregate different sources of information e.g. historical datasets, market prices, expert opinions etc 3. Can be easily updated in the light of new information 4. Has a rigorous mathematical framework behind it 5. Allows to model holistically different risk types e.g. credit, market and liquidity risks

Probabilistic Graphical Models (PGM) Variables Probabilistic Relationship

 Probabilistic Graphical Models (PGM) allow:  To represent visually systems of regression equations  Understand how the different equations interact through simple topological rules and hence unveil inconsistencies

 A simple topological rule allows to read independencies between error terms i.e. how the different equations interact GDPUnemployment PD Mortgages PD Real Estate Companies The error terms between these two variables are independent but is it realistic? PGM as carriers of regression relationships

 Probabilistic Graphical Models (PGM) allow to incorporate for some of the variables forward- looking information not purely based on historical regressions and thus be used for scenario analyses e.g.  Market implied distributions  Statistical surveys  Expert opinions

Default of a Bank Restriction of Credit to the Economy Major readjustment of risk premia House prices fall Event or Factor Causal Relationship Conditional Event or Variable PGM as carriers of non-regression based causal relationships

 We think that if the vote is for independence Scotland will take 50% oil reserves, 25% of the debt (though could be less) and will have to establish its own currency. It will have to establish new regulators and because the Scottish government will be weaker we expect a lot of deposits to leave Scotland for England. We think that the cost of funding in Scotland will be driven largely by the Oil price, the share of reserves they take, and the debt they assume. We think that the taxes the government charge will also be affected by the oil prices, oil reserves they have, debt assumed and whether their new currency is pegged. Whether their new current is pegged will depend on the debt they have to service and the oil share they take.  The equity of the Scottish banks will depend on the approach of the new regulators and the degree of deposit flight they experience – and also the cost of funds for Scotland has a whole.  Scottish unemployment will be affected by the taxes the new government levy and the cost of funds in Scotland.  Scottish GDP will depend on the cost of Funds for Scotland and the taxes that the new government can raise. PGM as a tool to distil complex economic narratives

 We think that if the vote is for independence Scotland will take 50% oil reserves, 25% of the debt (though could be less) and will have to establish its own currency. It will have to establish new regulators and because the Scottish government will be weaker we expect a lot of deposits to leave Scotland for England. We think that the cost of funding in Scotland will be driven largely by the Oil price, the share of reserves they take, and the debt they assume. We think that the taxes the government charge will also be affected by the oil prices, oil reserves they have, debt assumed and whether their new currency is pegged. Whether their new current is pegged will depend on the debt they have to service and the oil share they take.  The equity of the Scottish banks will depend on the approach of the new regulators and the degree of deposit flight they experience – and also the cost of funds for Scotland has a whole.  Scottish unemployment will be affected by the taxes the new government levy and the cost of funds in Scotland.  Scottish GDP will depend on the cost of Funds for Scotland and the taxes that the new government can raise.

Liquidity Risk Credit Risk Market Risk

ST What if scenarios … conditioning on events that we suppose might happen - but now able to place a probability on them! PDF Produce a PDF for key factors based on aggregating hard and soft data. Reverse ST Condition on a bad event happening and see what the world would need to look like to make it so. Cognitive Ease / Coherent Check the board recognises the way we think this risk happens.

Portfolio Management under Stress A Bayesian Net Approach to Coherent Asset Allocation Riccardo Rebonato, Alexander Denev Probabilistic Graphical Models in Finance Alexander Denev – May 2015

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