# Limits of quantitative risk management by Jean Frijns

- Slides: 27

Limits of quantitative risk management by Jean Frijns (CIO ABP Investments) Presentation for the seminar on Quantitative Financial Risk Management Lunteren January 14, 2000

Outline presentation I Appropriate setting: a pension fund model II Dynamic risk management III Risk measurement and risk management on portfolio level IV Pitfalls in risk measurement V Conclusions

I Pension fund model • Market valuation Assets 130 Liabilities 100 Pension put 30 Surplus Total 130 – Market value liabilities based on risk free rates (either nominal or real) – Pension put is market value guarantee that all pension obligations will be honored

I Pension fund model (2) – Value pension put depends on » » riskyness asset mix riskyness liabilities matching assets and liabilities funded ratio – Solvency contrants » A L+P » other short term constraints (supervisory bodies)

I Pension fund model (3) • Value creation through – Asset mix: higher expected returns lead to lower contribution rates – Risk management: reduces value pension put – Increase funded ratio: reduces value pension put • Put adjusted value added: PAVA – NPV lower contribution rates* – Change value pension put minus PAVA * Lower NPV contribution rates allows for higher initial rates followed by very low contribution rates later

I Pension fund model (4) • Theory versus practice – Economic approach: A L + P » » maximize PAVA consistent with economic theory valuation put option complicated see Ph-D thesis Tom Steenkamp – Practitioners: A L + VAR » minimize PV contribution rates subject to » A L + VAR » ad hoc approach › which shortfall probability › which horizon » easy to compute

I Pension fund model (5) • Solvency constraints hold at all times – Implies dynamic approach to optimal asset mix: dynamic risk management – can lead to additional funding requirements and/or change in pension obligations (conditional indexation) – ad hoc solvency constraints can frustrate process of economic value creation

II Dynamic risk management for a pension fund • Solvency constraints and possible solutions – Adjust riskyness asset mix: sort of portfolio insurance strategy » quarterly adjustment or threshold trigger – Buy short term put options: alternative for portfolio insurance – Increase funded ratio in combination with B&H-strategy: pay off in form higher expected returns and (much) lower future contribution rates – Stochastic dynamic programming approach is too complicated*; in practice common sense strategies tested in stochastic simulation environment * See Ph-D theses F. Brouwer, C. Dert

II Dynamic risk management for a pension fund (2) • Evaluation of strategies: an example – Assets only – End value – Different scenarios with respect to dynamics financial markets – Strategies » mix of bonds and equities » growth optimal allocation strategy (Hakansson) maximize one period geometric mean » rebalance portfolio to constant mix » buy & hold » portfolio insurance: CPPI with constant floor » portfolio insurance: synthetic put with constant floor

II Dynamic risk management for a pension fund (3) • Scenarios – Base case: VAR-model – Scenario II : - persistence and trending - strong and persistent stock price reactions to changes in economic variables – Scenario III: - bubbles and crashes - stochastic trigger • Objective function/output variables – – End value over 36 months 5% downside risk value 5% upward potential value Output over 4000 runs per scenario

Median Value of total portfolio 36 months horizon 300, 00 250, 00 Value 200, 00 150, 00 100, 00 50, 00 Buy & Hold Hakansson Scenario 1 Constant Mix Scenario 2 CPPI Constant Floor Scenario 3 Synthetic Put Constant Floor

5% Downside risk of total portfolio 36 months horizon 140, 00 120, 00 Value 100, 00 80, 00 60, 00 40, 00 20, 00 Buy & Hold Hakansson Scenario 1 Constant Mix Scenario 2 CPPI Constant Floor Scenario 3 Synthetic Put Constant Floor

5% Upward potential of total portfolio 36 months horizon 800, 00 700, 00 600, 00 Value 500, 00 400, 00 300, 00 200, 00 100, 00 Buy & Hold Hakansson Scenario 1 Constant Mix Scenario 2 CPPI Constant Floor Scenario 3 Synthetic Put Constant Floor

Median value vs. 5% downside risk 36 months horizon 260, 00 250, 00 SP 3 HK 3 SP 2 HK 2 PI 3 PI 2 240, 00 Median Value 230, 00 220, 00 SP 1 210, 00 HK 1 PI 1 200, 00 190, 00 BH 3 BH 2 CM 3 CM 2 180, 00 170, 00 160, 00 95, 00 BH 1 CM 1 100, 00 105, 00 110, 00 5% Downside Risk 115, 00 120, 00 125, 00

III Risk measurement and risk management on portfolio level • Risk management follows top-down investment process – Risk management follows the investment process – The investment process is structured top down – Investment process = risk allocation process » determine the maximum/prudent pension fund risk level: how much (active) risk a pension plan can tolerate? » Optimal allocation of the prudent budget of risk units to the various investment decisions, maximizing the return on the risk units

III Risk measurement and risk management on portfolio level (2) Top down investment process Neutral starting position Strategic Asset Mix Operational Investment Plan a Monthly tactical allocation Portfolio allocation within funds Allocation decisions within portfolios b Final actual portfolio

III Risk measurement and risk management on portfolio level (3) • Top down investment process – Asset Liability Management » liability structure, time horizon, capital position – Strategic allocation » asset and regional allocation, currency hedge allocation, duration allocation – Tactical allocation » asset and regional allocation, currency hedge allocation, duration allocation – Portfolio management » yield curve management » style allocation, sector allocation, stock picking » transaction execution, settlement and custody – Control (monitoring & reporting) » risk measurement and analysis: statistical tools » performance measurement and attribution » management & financial accounting

III Risk measurement and risk management on portfolio level (4) • Control instruments – Limits on: » exposures (assets, regions & countries, sectors) » statistical risk measures: st-deviation, VAR » duration and interest rate gaps – List of approved instruments (incl. derivatives) – Stress testing (to be developed) – Performance and statistical risk analysis

Monthly Market Risk Report 1 Market Risk ABP Benchmark position Actual position Exposures Equity Fixed income Real Estate Cash 28. 3% 64. 8% 6. 9% 0. 0% 28. 9% 63. 7% 7. 4% 0. 0% 0. 6% -1. 1% 0. 5% 0. 0% TOTAL 100. 0% Absolute risk Benchmark 16. 40% 3. 88% 12. 07% Absolute risk Actual 16. 68% 4. 03% 12. 07% Active Risk (tracking error) 0. 67% 1. 74% 0. 00% 6. 32% 6. 16% 1. 15% Equity Fixed Income Real Estate 10. 66 5. 77 1. 91 11. 08 5. 90 2. 04 0. 45 2. 55 0. 00 TOTAL 14. 51 14. 14 2. 64 Difference Risks St. Dev. Equity Fixed Income Real Estate TOTAL Value at Risk (mrd Euro)

Monthly Market Risk Report 2 Attribution of active risk ABP Actual Risk in % Total Risk Portfolio Total Risk Benchmark 6. 16 6. 32 1. 15 Active Risk Asset Allocation 0. 14 Currency allocation 0. 08 Regional Allocation 0. 05 Selection 1. 20 Equity Fixed income Real Estate 0. 67 1. 74 0. 00

Credit Risk: definition

III Risk measurement and risk management on portfolio level (5) • Control instruments for credit risk – limits on individual counterparts, regions and sectors – total level of default risk on portfolio level in terms of VAR (measured by credit metrics system)

IV Pitfalls in risk measurement and management • Extreme events: empirical observations – Frequency extreme events much higher than predicted by standard probability distributions: fat tails – Short term impact much higher than predicted due to » diversification effect ceases to hold › between individual stocks and bonds › between countries › between market and credit risk » liquidity dries up under extreme market conditions › hedging downward risk impossible or extremely expensive – Remarkable long term resilience financial markets » sharp recovery SE-Asian markets » idem default spreads due to Russian debt crisis

IV Pitfalls in risk measurement and management (2) – Appropriate policy reaction wrt. extreme events » banks » pension funds and insurers » central banks • Measurement errors and error maximizing optimization – Estimated covariance matrix subject to estimation error – Optimizing rules for portfolio construction minimize tracking error for given expected outperformance – Out of sample tracking errors much higher than optimized tracked errors – See eg. Michaud

IV Pitfalls in risk measurement and management (3) • Credit risk modeling – Too much focus on individual titles » Z-score Altman » option approach Merton – Credit risk modeling on portfolio level still in its infancy » credit metrics » serious lack of data » high correlation with common factors (“credit cycle”) limit room for risk diversification – Correlation credit and market risk under extreme market conditions (systematic risk, etc. )

IV Pitfalls in risk measurement and management (4) • Aggregation of risks – On strategic level – For day to day management : : yes no

V Conclusions • Risk management on strategic level ill defined due to diffuse objectives • Risk management on portfolio level well defined and ideal platform for statistical risk analysis • Statistical risk analysis may give false impression of precision and control