Limits of quantitative risk management

Limits of quantitative risk Limits of quantitative risk managementmanagement

by Jean Frijnsby Jean Frijns

(CIO ABP Investments)(CIO ABP Investments)

Presentation for the seminar onPresentation for the seminar onQuantitative Financial Risk ManagementQuantitative Financial Risk Management

LunterenJanuary 14, 2000

Outline presentationOutline 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 modelI Pension fund model

• Market valuation

Assets 130 Liabilities 100 Pension put 30 Surplus

Total 130 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 I Pension fund model (2)(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 I Pension fund model (3)(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 I Pension fund model (4)(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 I Pension fund model (5) (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 pensionII Dynamic risk management for a pension fund 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 pensionII Dynamic risk management for a pension fund fund (2) (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 pensionII Dynamic risk management for a pension fund fund (3) (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 portfolioMedian Value of total portfolio36 months horizon

0,00

50,00

100,00

150,00

200,00

250,00

300,00

Buy & Hold Hakansson Constant Mix CPPI Constant Floor Synthetic Put Constant Floor

Val

ue

Scenario 1 Scenario 2 Scenario 3

5% Downside risk of total portfolio5% Downside risk of total portfolio

36 months horizon

Val

ue

Scenario 1 Scenario 2 Scenario 3

0,00

20,00

40,00

60,00

80,00

100,00

120,00

140,00

Buy & Hold Hakansson Constant Mix CPPI Constant Floor Synthetic Put Constant Floor

5% Upward potential of total portfolio5% Upward potential of total portfolio36 months horizon

Val

ue

Scenario 1 Scenario 2 Scenario 3

0,00

100,00

200,00

300,00

400,00

500,00

600,00

700,00

800,00

Buy & Hold Hakansson Constant Mix CPPI Constant Floor Synthetic Put Constant Floor

Median value vs. 5% downside riskMedian value vs. 5% downside risk36 months horizon

SP1

HK1PI1

BH1CM1

PI2PI3

HK2

HK3SP3

SP2

BH3BH2

CM3CM2

160,00

170,00

180,00

190,00

200,00

210,00

220,00

230,00

240,00

250,00

260,00

95,00 100,00 105,00 110,00 115,00 120,00 125,00

5% Downside Risk

Me

dia

n V

alu

e

III Risk measurement and risk management on III Risk measurement and risk management on portfolio level 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 onIII Risk measurement and risk management on portfolio level portfolio level (2)(2)

Top down investment process

b

a

Strategic Asset Mix

Monthly tactical allocation

Portfolio allocation within funds

Allocation decisions within portfolios

Neutral starting position

Operational Investment Plan

Final actual portfolio

III Risk measurement and risk management onIII Risk measurement and risk management on portfolio level portfolio level (3)(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 onIII Risk measurement and risk management on portfolio level portfolio level (4)(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 1Monthly Market Risk Report 1

ActualBenchmark position position Difference

ExposuresEquity 28.3% 28.9% 0.6%Fixed income 64.8% 63.7% -1.1%Real Estate 6.9% 7.4% 0.5%Cash 0.0% 0.0% 0.0%

TOTAL 100.0% 100.0% 0.0%

RisksAbsolute risk Absolute risk Active Risk

St.Dev. Benchmark Actual (tracking error)Equity 16.40% 16.68% 0.67%Fixed Income 3.88% 4.03% 1.74%

Real Estate

12.07% 12.07% 0.00%

TOTAL 6.32% 6.16% 1.15%

Value at Risk (mrd Euro)10.66 11.08 0.455.77 5.90 2.551.91 2.04 0.00

TOTAL 14.51 14.14 2.64

Market Risk ABP

EquityFixed Income

Real Estate

Monthly Market Risk Report 2Monthly Market Risk Report 2

Total Risk Portfolio 6.16

Total Risk Benchmark 6.32

Active Risk 1.15

Asset Allocation 0.14

Currency allocation 0.08

Regional Allocation 0.05

Selection 1.20Equity 0.67

Fixed income

1.74

Real Estate 0.00

Attribution of active risk ABP

Actual Risk in %

Credit Risk: definitionCredit Risk: definition

S pre ad r isk

C u rre n t P o te n tia l

P re -se tt lem en t r isk S e ttle m e n t R isk

D e fa u lt r isk

C o un te rp ar ty r isk

III Risk measurement and risk management onIII Risk measurement and risk management on portfolio level portfolio level (5)(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 andIV Pitfalls in risk measurement and management 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 andIV Pitfalls in risk measurement and management management (2)(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 andIV Pitfalls in risk measurement and management management (3)(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 andIV Pitfalls in risk measurement and management management (4)(4)

• Aggregation of risks– On strategic level : yes– For day to day management : no

V ConclusionsV 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