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

1
Limits of quantitative risk management by
Jean Frijns(CIO ABP Investments)Presentation
for the seminar onQuantitative Financial Risk
Management

Lunteren January 14, 2000
2
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

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I 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

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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)

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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

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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

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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

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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
  BH-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

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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

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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

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Median Value of total portfolio

• 36 months horizon

300,00
250,00
200,00
Value
150,00
100,00
50,00
0,00
Buy Hold
Hakansson
Constant Mix
CPPI Constant Floor
Synthetic Put Constant Floor
Scenario 1
Scenario 2
Scenario 3
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5 Downside risk of total portfolio

• 36 months horizon

140,00
120,00
100,00
80,00
Value
60,00
40,00
20,00
0,00
Buy Hold
Hakansson
Constant Mix
CPPI Constant Floor
Synthetic Put Constant Floor
Scenario 1
Scenario 2
Scenario 3
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5 Upward potential of total portfolio

• 36 months horizon

800,00
700,00
600,00
500,00
Value
400,00
300,00
200,00
100,00
0,00
Buy Hold
Hakansson
Constant Mix
CPPI Constant Floor
Synthetic Put Constant Floor
Scenario 1
Scenario 2
Scenario 3
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Median value vs. 5 downside risk

• 36 months horizon

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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

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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
b
Allocation decisions within portfolios
Final actual portfolio
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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

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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

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Monthly Market Risk Report 1
Market Risk ABP
Actual
Benchmark position
position
Difference
Exposures
Equity
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
Risks
Absolute 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
12.07
12.07
0.00
Real Estate
TOTAL
6.32
6.16
1.15
Value at Risk
(mrd Euro)
10.66
11.08
0.45
Equity
5.77
5.90
2.55
Fixed Income
1.91
2.04
0.00
Real Estate
TOTAL
14.51
14.14
2.64
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Monthly Market Risk Report 2
Attribution of active risk ABP
Actual Risk in
6.16
Total Risk Portfolio
Total Risk Benchmark
6.32
Active Risk
1.15
Asset Allocation
0.14
Currency allocation
0.08
Regional Allocation
0.05

Selection
1.20
Equity
0.67
Fixed income
1.74
Real Estate
0.00
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Credit Risk definition
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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)

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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

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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

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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.)

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IV Pitfalls in risk measurement and
management (4)

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

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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