Pension Fund Asset Risk Management

Transcript Pension Fund Asset Risk Management

Pension Fund Asset Risk Management

Monitoring market risk

7 november 2013 Tony de Graaf Principal Risk Manager

Disclaimer 2

All material contained herein is indicative and for discussion purposes only, is strictly confidential, may not be reproduced and is intended for your internal use only. This document has been solely prepared for discussion purposes and is not an offer, or a solicitation of an offer, to buy or sell any security or financial instrument, or any investment advice. This policy does not confer any rights to any third parties. PGGM Investments has taken all reasonable care to ensure that the information contained in this document is correct, but does not accept liability for any misprints. The information contained herein can be changed without notice.

Agenda 3 1. Trends in pension fund asset risk management 2. Pension fund balance sheet risk management 3. Asset risk measurement and attribution 4. Stress testing 5. AIFMD risk management measures

Trends in pension fund asset risk management 4 • • • • • • • • Pension fund boards want to be ‘in control’ Transparancy Increasing interest in good execution, robust operations and countervailing power, less in ‘alpha’ skills Understand what you invest in Higher compexity must pay-off Delegation may not lead to less control Detailed monitoring of investment process Detailed investment restrictions • • Between pension fund and asset manager Between asset manager and external managers Awareness of liquidity risk and counterparty risk

5 Balance sheet risk management

6 Investment process

Pension liabilities

100% nominal discounted

ALM

30% equities 5% commodities 65% fixed income 50% interest rate hedge

SBM

15% equities 5% Private Equity 5% Listed Real Estate 5% Private Real Estate 5% Commodities 45% Government Bonds 10% Credits 5% High Yield 5% Local Ccy Bonds 70% Currency hedge

Implementation

3.000 stocks 500 bonds 20 commodity futures Asset swaps Interest Rate Swaps Cross currency swaps Etc.

7 Balance sheet risk monitoring

Investment Process Balance sheet risk Pension Reserve vs. ALM Pension Reserve vs. SBM Pension Reserve vs. Implementation Allocation risk ALM vs. SBM ALM vs. Implementation Implementation risk Implementation risk (liquid assets) Risk Measurement SaR / CRaR 1 month

7.0 mln / 1.7% 9.9 mln / 2.1% 9.6 mln / 2.0%

RVaR / TE

6.9 mln / 1.2% 6.6 mln / 1.1%

CR risk 1 year

8.3% 11.7% 11.3%

Tracking error

4.2% 4.2%

Stress scenarios

Black Monday 1987 Credit crisis 2008 -3.3% -3.7% -3.6% -0.4% -0.3% -3.4% -8.5% -8.3% -5.1% -4.9% 0.5 mln / 0.1% 0.3% 0.1% 0.2%

8 Coverage Ratio at Risk (CRaR) 40% 30% 20% 10% 0% -10% -20% -30% -40% -50% 2011Q1 2011Q2 2011Q3 2011Q4 Delta Implementation-PR (LHS) Implementation vs PR (RHS) 2012Q1 2012Q2 Delta SBM-PR (LHS) SBM vs PR (RHS) 2012Q3 2012Q4 2013Q1 Delta ALM-VPV (LHS) ALM vs PR (RHS) 2013Q2 12,0% 10,0% 8,0% 6,0% 4,0% 2,0% 2013Q3 0,0%

Monitoring liquidity and controllability 9

Asset risk measurement and attribution 10

Popular asset risk measures • Tracking Error: • Value at Risk: • Relative Value at Risk: • Expected Shortfall: TE = Var 𝑅 𝑝 − 𝑅 𝑏𝑚 VaR 95% = min 𝑥 ∈ ℝ ∶ 𝑃 𝑅 𝑝 ≤ −𝑥 ≤ 5% RVaR 95% = min 𝑥 ∈ ℝ: 𝑃 𝑅 𝑝 − 𝑅 𝑏𝑚 ≤ −𝑥 ≤ 5% ES 95% = −𝐸 𝑅 𝑝 | 𝑅 𝑝 ≤ −Var 95% 11

Considerations • • • • • • • • • • Forward looking period (day, month, year) Backward looking period (months, year, multiple years) Ex-ante or ex-post Static vs dynamic portfolio (reinvestments?) Historical returns frequency (1D, 3D, 5D, 21D) Weighting scheme for historical returns (equal, decay factor, long memory) Overlapping vs. non-overlapping returns Returns distribution Dependence structure (standard multivariate distribution, copula) Parametric vs. Monte Carlo 12

Risk attribution • Static vs. dynamic • Allocation versus selection effect (similar to performance attribution) • Breakdown according to the fund management process • • • Countries Sectors Instrument types • 13 Risk type • Interest rate, spread, FX, … • • Maturity segments Equity factors Portfolio Return Benchmark Return Currency Effect Active Return Allocation Effect Selection Effect Specific Return Common Factor Style Industry

PGGM example 14

Classical risk attribution Euler: if 𝑓 𝑘𝑊 = 𝑘𝑓 𝑊 then 𝑓 𝑊 = 𝑖 𝑤 𝑖 𝜕 𝜕𝑤 𝑖 𝑓 𝑊 Therefore: VaR 95% = 𝑖 𝑤 𝑖 𝜕 𝜕𝑤 𝑖 VaR 95% 𝑊 With 𝑊 the portfolio weights vector We define Marginal VaR: MVaR 95% 𝑖 = 𝑤 𝑖 𝜕 𝜕𝑤 𝑖 VaR 95% In a normal parametric framework, we have: MVaR 95% 𝑖 = 𝑤 𝑖 𝜌 𝑖𝑃 𝜎 𝑖 We can now present a break down of VaR (or TE, or ES) that sums to portfolio VaR 15

Incorporating allocation and selection effect in TE Example: benchmark can be divided in sectors, fund manager over/underweights sectors and over/underweights on security level Portfolio weight to security 𝑖 : Portfolio weight to security Portfolio weight to sector 𝑗 : 𝑖 : Benchmark weight to sector 𝑗 : Benchmark return sector 𝑗 : 𝑤 𝑖 𝑝 𝑤 𝑖 𝑏 𝑊 𝑖 𝑝 𝑊 𝑖 𝑏 = 𝑖∈𝑆 𝑗 = 𝑖∈𝑆 𝑗 𝑤 𝑖 𝑝 𝑤 𝑖 𝑏 𝑅 𝑗 = 1 𝑊 𝑗 𝑏 𝑖∈𝑆 𝑗 𝑤 𝑖 𝑏 𝑟 𝑖 𝑏 Relative return: α = 𝑤 𝑖 𝑝 − 𝑤 𝑖 𝑏 𝑖 𝑟 𝑖 = 𝑗 𝑊 𝑗 𝑝 − 𝑊 𝑗 𝑏 𝑅 𝑗 + 𝑗 𝑖∈𝑆 𝑗 𝑤 𝑖 𝑝 − 𝑤 𝑖 𝑏 𝑟 𝑖 − 𝑅 𝑗 = 𝐴 𝑗 + 𝑆 𝑗 𝑗 16

Incorporating allocation and selection effect in TE (2) TE = TE 2 TE = Cov 𝛼, 𝛼 TE = Cov 𝛼, 𝐴 𝑗 𝑗 TE + Cov 𝛼, 𝑆 𝑗 TE 𝑗 The same results can be obtained for VaR using marginal VaRs: With: and VaR = 𝑗 𝑖 𝜑 𝑗 𝑖 MVaR 𝑖 + 𝑗 𝑖 𝜃 𝑗 𝑖 MVaR 𝑖 𝜑 𝑗 𝑖 = 𝑊 𝑗 𝑝 − 𝑊 𝑗 𝑏 𝑤 𝑖 𝑏 𝑊 𝑗 𝑏 − 𝑤 𝑖 𝑏 − 𝑊 𝑗 𝑝 − 𝑊 𝑗 𝑏 𝑤 𝑖 𝑏 , 𝑖 ∈ 𝑆 , 𝑖 ∉ 𝑆 𝑗 𝑗 𝜃 𝑗 𝑖 = 𝑊 𝑗 𝑝 − 𝑊 𝑗 𝑝 𝑊 𝑗 𝑏 𝑊 𝑗 𝑏 0, 𝑖 ∉ 𝑆 𝑗 , 𝑖 ∈ 𝑆 𝑗 See RiskMetrics working paper ‘Risk attribution for asset managers’ by Jorge Mina (2002) 17

Dynamic risk attribution

Asset MW

1 2 3 4

Asset MW

1 2 3 4 30 40 30 10 30 45 30 15

Vol(%) Correlations

10% 1.0

0.5

15% 20% 15% 0.5

0.5

1.0

0.5

Vol(%) Correlations

15% 1.0

25% 20% 10% 0.6

0.5

0.4

0.6

1.0

0.5

0.7

0.5

1.0

0.5

1.0

0.5

As per the start (above) and end (below) of the analysis period 0.5

0.5

1.0

0.4

0.7

0.5

1.0

Dynamic risk attribution (2)

Asset

1 2 3 4

VaR (t=0)

4.94

9.87

2.47

21.93

MVaR (t=0)

3.61

8.33

1.67

21.93

VaR (t=1)

7.40

18.51

9.87

2.47

32.00

MVaR (t=1)

5.65

17.13

7.42

1.80

32.00

ΔMVaR

2.04

8.80

-0.91

0.13

10.07

• • Asset 3 has a larger impact on ΔMVaR then asset 4, although the parameters for asset 3 didn’t change Attribution cannot be broken down into single parameters 19

New method for dynamic risk attribution Some definitions: Var = 𝑓 𝑥 1 , 𝑥 2 , … , 𝑥 𝑛 ∆𝑓 𝑖 = 𝑓 𝑥 1 , 𝑥 2 , … , 𝑥 𝑖 + ∆𝑥 𝑖 , … , 𝑥 𝑛 ∆𝑓 𝑖𝑗 = 𝑓 𝑥 1 , 𝑥 2 , … , 𝑥 𝑖 + ∆𝑥 𝑖 , … , 𝑥 𝑗 𝑓 𝑥 1 , 𝑥 2 , … , 𝑥 𝑛 + ∆𝑥 𝑗 , … , 𝑥 𝑛 𝑓 𝑥 1 , 𝑥 2 , … , 𝑥 𝑛 etc.

On top of this, we define: ∆𝑓indices = 0 when two or more indices are equal, e.g. ∆𝑓1223 = 0 and when the indices aren’t in increasing order, e.g. ∆𝑓32 = 0 Then we define the contributions: 𝐶 𝑖 𝐶 𝑖𝑗 𝐶 = ∆𝑓 𝑖 𝑖𝑗𝑘 = ∆𝑓 𝑖𝑗 − 𝐶 𝑖 = ∆𝑓 𝑖𝑗𝑘 − 𝐶 − 𝐶 𝑖𝑗 𝑗 − 𝐶 𝑖𝑘 − 𝐶 𝑗𝑘 − 𝐶 𝑖 − 𝐶 𝑗 etc.

New method for dynamic risk attribution (2) We then have: ∆VaR = 𝑖 𝐶 𝑖 + 𝑖𝑗 𝐶 𝑖𝑗 + ⋯ + 𝐶 12…𝑛 Because And ∆𝑓 𝐶 12…𝑛 12…𝑛 = ∆𝑓 = ∆VaR 12…𝑛 − 𝑖 1 …𝑖 𝑛−1 𝐶 𝑖 1 …𝑖 𝑛−1 − … − 𝑖𝑗 𝐶 𝑖𝑗 − 𝑖 𝐶 𝑖 Now we assign all higher-order contributions to the lower-order contributions based on the absolute values of the lower order contibutions.

So, for the second order contributions we have: 𝐶 𝑖;2 And for the third order contributions: = 𝐶 𝑖 + 𝑗 𝐶 𝑖 𝐶 𝑖 + 𝐶 𝑗 𝐶 𝑖𝑗 𝐶 𝑖;3 = 𝐶 𝑖 + 𝑗 𝐶 𝑖 𝐶 𝑖 + 𝐶 𝑗 𝐶 𝑖𝑗 + 𝑗𝑘 𝐶 𝑖;2 𝐶 𝑖;2 + 𝐶 𝑗;2 + 𝐶 𝑘;2 𝐶 𝑖𝑗𝑘 etc.

New method for dynamic risk attribution (3)

Parameter Value (t=0)

MW 1 MW 2 MW 3 MW 4 Vol 1 Vol 2 Vol 3 Vol 4 Cor 1x2 Cor 1x3 Cor 1x4 Cor 2x3 Cor 2x4 Cor 3x4 30.00

40.00

30.00

10.00

0.10

0.15

0.20

0.15

0.50

MVaR (t=0)

30.00

45.00

30.00

15.00

0.15

0.25

0.20

0.10

0.60

0.50

0.40

0.50

0.70

0.50

1st order contribution 2nd order contribution 3rd order contribution ≥4th order contribution ΔMVaR

0.00

1.05

0.00

0.85

1.86

5.78

0.00

-0.55

0.22

0.00

-0.06

0.00

0.22

0.00

9.38

0.00

0.15

0.00

-0.14

0.00

0.77

0.00

-0.15

0.01

0.00

0.64

0.00

0.01

0.04

0.00

0.05

0.00

-0.01

0.00

-0.01

0.00

1.20

0.00

0.70

1.88

6.58

0.00

-0.69

0.23

0.00

-0.06

0.00

0.22

0.00

10.07

New method for dynamic risk attribution (4) 23

Asset

1 2 3 4

VaR (t=0)

4.94

9.87

2.47

VaR (t=1)

7.40

18.51

9.87

2.47

Average VaR Attribution

6.17

14.19

9.87

2.47

1.91

8.13

0.00

0.03

10.07

Compare with attribution based on MVaR!

Drawback: computationally intensive See article in “De Actuaris” by Tony de Graaf (2012)

Returns based risk measurement • Ex-post TE or VaR attribution • Returns based style analysis 𝑅 𝑡 𝑖 = 𝛼 + 𝑖 𝛽 𝑖 = 1 𝛽 𝑖 𝐹 𝑖𝑡 + 𝜀 𝑡 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 24 Quality Growth Value

Stress testing 25

Stress testing for asset managers • Applicable at instrument level • Methodology must be sensitive to all instrument characteristics • Only key risk drivers need to be specified • Secondary risk drivers must follow in a consistent manner • Results should reflect current market sensitivities and dependencies 26

The predictive stress test then:            1 2   , 

1 | 

2 

  ,         11 21  12  22   with:     E[ 

2 | 

1 Cov [ 

1 | 

]  

]  1     12   1 22 11  

  2  12   1  22 21  This gives: 

 

V V

 

1 ,  E[

2  

1 | 

2 ],

2  

2  See article ‘Stress Testing in a Value at Risk Framework’ by Paul Kupiec (1998) In a normal framework, this amounts to multivariate linear regression.

The predictive stress test • • • Each instrument is valued as a function of its risk factors:





1 ,

2 ,...

 Determine sensitivites of the risk drivers to the specified scenario factors: 

  1  

1   2  

2  ...

The sensitivities depend on market volatilities and correlations, simple linear regression gives the approximation: • 

   

, 

R i

   

R i

Varying the estimation period, one can get anything from a structural relation to a short-term trend 28

Predictive stress test example • Scenario: Credit Crisis 2008 H2 • Specified in scenario S&P 500 and USD • In this example, S&P 500 loses 29% and USD gains 13% (against EUR) • Betas estimated over an 8-year period, using weekly returns 29

Predictive stress test example (2) 30

Risk factor

S&P 400 EPRA/NAREIT US GSCI SPOT GBP in EUR S&P 500 USD in EUR

Volatilities

Volatility

20.5% 28.4% 26.6% 7.6% 17.7% 10.4%

S&P 400 NAREIT GSCI GBP S&P 500 USD S&P 400

NAREIT

0.78

GSCI

0.31

0.25

GBP

0.08

0.03

0.07

S&P 500

0.95

0.75

0.26

0.07

USD

-0.24

-0.25

-0.36

0.36

-0.22

Correlations

Predictive stress test example (3) 31

Factor

S&P 500 USD in EUR

Scenario

Stress

-29% +13%    12   1 22



   

, 

R i

  

R i

Factor

S&P 400 EPRA/NAREIT US -38% GSCI Spot -19% GBP in EUR

Stress

-33% +2%

Predicted results

Factor

S&P 400

Stress

-39% EPRA/NAREIT US -45% GSCI Spot GBP in EUR -24% +3% Compare with:

Factor

S&P 400 EPRA/NAREIT US -37% GSCI Spot -60% GBP in EUR

Stress

-34% -18%

2008 H2 realisation

AIFMD • Mandatory for non-UCITS investment funds • Gross & commitment leverage • Fund liquidity • Regular measurement • Stress test 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 1D 3D 1W 1M 6M 1Y 32