Global Life Actuarial INTERNAL USE ONLY ASSAL-IAIS Training Seminar: Market and Credit Risk in the Swiss Solvency Test 22nd November 2012 Alex Summers

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 2 Important note The views expressed in this presentation are the presenter’s own and do not necessarily represent the views of either Zurich Insurance Group (Zurich), or FINMA I am very grateful to colleagues within Zurich and at FINMA for their assistance in preparation Further information from FINMA on the Swiss Solvency Test can be found on FINMA’s website at

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 3 Agenda Recap: risk calculations in SST Market Risk in the SST Scenario based modelling of market risk Replicating Portfolios case study Credit Risk in the SST

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 4 Risk based framework for calculating SST Scenarios Standard Models or Internal Models Mix of predefined and company specific scenarios Target CapitalSST Report Market Consistent Data and Best Estimate Assumptions Market Risk Credit Risk Life P&C Market Value Assets Risk Models Valuation Models Best Estimate Liabilities Risk margin Output of analytical models (Distribution) Health Aggregation Method Source: FOPI, 2007

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 5 Risk measure is 99% expected shortfall Probability density of the change in available capital Average value of available capital in the 1% “bad” cases = Expected shortfall Probability < 1% Economic balance sheet at t=1 (stochastic) Year 1: uncertain Catastrophes Claims Revaluation of liabilities due to new information New business during one year Change in market value of assets Available capital changes due to random events Year 0: known Best estimate of liabilities Available Capital Market value of assets Economic balance sheet at t=0 (deterministic)

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 6 Market and credit risk in the SST Market risk Interest rates, spreads, foreign exchange, equity alternative investments, volatilities Credit risk Complete or partial default Migration: change in creditworthiness or rating For groups: changes in value of intra-group loans and other Capital and Risk Transfer Instruments

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 7 Agenda Recap: risk calculations in SST Market Risk in the SST Scenario based modelling of market risk Replicating Portfolios case study Credit Risk in the SST

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 8 Market risk is typically the dominant risk in SST, particularly for life insurers, but there is significant variation across companies Source: FINMA SST report 2012

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 9 SST Standard Model for Market Risk Incorporates large 82 risk drivers across 4 currencies Interest rates of different terms Credit spreads for different rating classes Swap – Government spread Exchange rates Implied volatilities Equities Real estate Hedge funds, private equity, direct participations Individual and pairwise combinations of stresses to available capital Consider impacts on both assets and liabilities in case there is any loss absorbency Simplifying assumptions of linear impact, underlying multivariate normal distribution FINMA supply standard deviation and correlation parameters based on historical analysis Covariance model for aggregation to overall analytic distribution for market risk

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 10 Worked example for market risk in SST standard model Consider risk driver of 10 year CHF risk-free rate Suppose a 100bp increase in the 10 year CHF risk-free rate reduces the market value of assets by CHF 1M, and reduces the best estimate liabilities by 1.2M The sensitivity of available capital per bp is (-1-(-1.2))/100 = CHF 2000 /bp FINMA supply an annual volatility parameter of 55bps, based on historical analysis If this were the only contribution to market risk, the standard deviation of the distribution of available capital over one year would be estimated as (2000x55) = CHF 110k Based on the assumption of a normal distribution, the 1 in 100 expected shortfall would then be 110k x 2.33 = CHF 256k

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 11 Internal models for market risk relax the simplifying assumptions, or else aim for a scenario based approach Can consider different: Probability distribution functions for risk factors Probability distribution parameters for risk factors Loss functions e.g. non-linear Cross-terms Aggregation e.g. copulas, particularly for increased tail dependencies Alternatively consider a stochastic approach using a real world economic scenario generator (ESG) Dealing with dynamic hedging / dynamic portfolio management can be a challenge

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 12 Source: FINMA SST report 2012 SST allows decomposition of market risk into different drivers. Comparison across companies shows significant variations

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 13 Market risk scenarios can make a significant contribution to overall SST target capital Source: FINMA SST report 2012 Scenarios can help with communication and understanding of risks, supporting focus on mitigation Total contribution of all scenarios to target capital is 10% for life, 19% for non-life

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 14 Agenda Recap: risk calculations in SST Market Risk in the SST Scenario based modelling of market risk Replicating Portfolios case study Credit Risk in the SST

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 15 SST requires use of Internal Models except where Standard Model is adequate The core of the SST framework are the underlying methodology and principles, not the standard models Methodology of the Solvency Test Internal ModelsStandard Models Implicit and explicit prudence, limits, etc. to take into account the approximations used for the standard model Company specific approach and simplifications Internal models are assessed with reference to the methodology of the SST framework Valuation, risk measure, time horizon,…

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 16 Generic structure for scenario based model for SST economic capital calculations Risk Factors Portfolio of Assets and Liabilities Capital and Risk Transfer Instruments Dependency Assumptions Scenarios Profit and Loss Valuation s 1, s 2,…………..……., s n e 1, e 2,………….……., e n SST economic capital models project the economic balance sheet 1 year into the future In a scenario based model, future states of the world at t=1 have to be simulated. These states encompass the evolution of all relevant risk factors over the whole duration of the assets and liabilities A key challenge is that revaluation of complex life insurance liabilities requires risk-neutral Monte Carlo valuation… within each of thousands of real- world scenarios

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 17 Real world scenarios one year into the future Risk factors need to be projected to possible future states in one year’s time The projections should lead to consistent states of the world Arbitrage-free Dependencies between the risk factors need to be taken into account, and might be higher in tails Real world projection, not risk-neutral,  based on observed historical data

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 18 Agenda Recap: risk calculations in SST Market Risk in the SST Scenario based modelling of market risk Replicating Portfolios case study Credit Risk in the SST

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 19 The stochastic-on-stochastic challenge for market risk in the SST t=0 For each future state of the world, a brute force approach would require a set of risk-neutral scenarios for full Monte Carlo simulation

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 20 A simplified central representation of liabilities makes SST assessment of market risks feasible and brings additional benefits Helps quantify and understand market risk: – Faster, simpler required capital calculations – Identification of unrewarded risks, non-hedgeable ALM risk – Improve quality of management information © 2010 The Actuarial Profession 

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 21 Replicating portfolios are just one of a number of similar alternatives for market risk measurement in SST internal models Different proxy methods describe liabilities and/or assets in different terms Least Squares Monte Carlo Curve fitting Replicating Portfolios All three approaches can be mathematically equivalent but practicalities and interpretations can differ Replicating portfolios give additional ease of communication, understanding and a helpful link to ALM

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 22 Replicating Portfolios are directly compatible with SST Principles Market-consistent valuation All assets and liabilities are valued market consistently, including options and guarantees Total balance sheet approach All material financial instruments must be taken into account. As a result, there are no off balance sheet items 8/23/2015

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 23 We can approximate valuation of a complex liability through a linear combination of financial instruments © 2010 The Actuarial Profession  GBP Time Market value development scenario 1 Market value development scenario 2 Guarantee Bonus scenario 1 Bond, replicating guarantee European call options, replicating bonus payments In practice we replicate the results of a liability cash flow model, not the true value of the liability

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 24 Replicating portfolios allow transfer and creation of information about liabilities Valuation, greeks and cash flow patterns can be obtained under any economic assumption quickly and easily © 2010 The Actuarial Profession 

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 25 Confidence in quality of replicating portfolios needed for ALM insight to add value Ideal replicating portfolio matches the cash flows from the liability it replicates in any economic scenario Not always possible in practice so defined acceptance criteria are needed A transparent process is critical in building confidence: no “black-boxes” Visualising goodness of fit tests is valuable in understanding model output © 2010 The Actuarial Profession 

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 26 Careful choice of scenarios for fitting and validation is important Using a wide range of scenarios gives confidence that replicating portfolios will suitably represent the market value of liabilities over the full distribution of one-year real world simulations © 2010 The Actuarial Profession 

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 27 Standardised communication helps share insights beyond replicating portfolio experts Standardised, automated reporting essential given high volume of data Training users important Careful analysis of constituents is useful Reveals nature of risks Demonstrates stability over time Avoiding “over-fitting” Thought required before use as a benchmark for investment management © 2010 The Actuarial Profession 

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 28 Analysis of Economic Capital for market risk using replicating portfolios gives deeper understanding of drivers © 2010 The Actuarial Profession  SST benefits extend beyond risk measurement into risk management

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 29 Using replicating portfolios to analyse non-hedgeable market risk The construction of replicating portfolios from candidate assets makes them ideal for identifying and understanding NH risks Can evaluate NH market risks by considering differences between tradable and non-tradable replicating portfolios A similar approach could be applied to apportioning required capital © 2010 The Actuarial Profession 

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 30 Replicating portfolios can make SST modelling of CRTIs feasible for large groups For SST, liability data are needed at both group and local level Diversification benefits need careful allocation to give correct capital requirement It can be very challenging to construct a dynamic model for interactions within an insurance group Replicating portfolios can be rapidly revalued and so provide an effective solution 30 © 2010 The Actuarial Profession 

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 31 Agenda Recap: risk calculations in SST Market Risk in the SST Scenario based modelling of market risk Replicating Portfolios case study Credit Risk in the SST

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 32 Credit risk in SST standard model SST credit risk model is based on standardised approach from Basel banking regulation Simplicative multiplicative factor model: 1. Assign a risk weighting factor according to counterparty and credit rating 2. Multiply market value of asset by risk weighting factor to give risk-weighted market value of assets 3. Multiply by 8% 4. Sum across all holdings to give required capital Risk weighting factors range from 0% for AAA government bonds, up to 1250% (=1/8%) for securitisations Factors already incorporate diversification effects Credit risk mitigation may be considered in calculation

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 33 SST Internal models for credit risk seek to address potential shortcomings of standard model The standard credit risk model relies on external credit rating agencies, and does not take specific portfolio inter-dependency and diversification into account Internal models May consider refinements to probability of default or loss given default Enable a more realistic modeling of the stochastic dependency between counterparties Take diversification effects into account Can enable a realistic modeling of the stochastic dependency between credit and market risk FINMA requires that companies model both default and migration risk Credit Spread Risks are allocated under Market risk

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 34 Overview of market and credit risk in SST SST allows a decomposition of required capital into different drivers Scenarios play a key role in correcting tails of the distribution and aiding communication and understanding of risks Market risks are often dominant but can be challenging to model SST Standard Model for market risk is based on shocks both to individual risk drivers, and pairwise combinations Replicating portfolios make modelling feasible Credit risk modelling in SST is based on the Basel framework Internal models may offer improved treatment of dependencies and diversification

© Zurich Insurance Company Ltd. INTERNAL USE ONLY 35 Thank you for your attention Any further questions?