IFSWF Meeting, Beijing May 10-13

Aaron Drew, Macro Strategist, NZSF

William Kinlaw, Head of Portfolio and Risk Management Group, State Street Associates

Accounting for “fat tails” in portfolio risk management:

NZSF case study

Outline

• Motivation: why should we account for “fat tails” in portfolio risk management?

• Contrast two broad approaches for modeling fat tails:

(i) Structural

(ii) Statistical

• Applications of these approaches to the NZSF’s Reference Portfolio

Motivation

• The basic risk-profile choice that must be taken to suit the investment purpose of a fund relies on there being a “reasonable” ex-ante description of the distribution of asset returns.

• It is desirable stakeholder’s are prepared for the full range of outcomes that may occur, particularly downside losses.

• Internal management should similarly be prepared and know implications for fund liquidity, re-balancing, etc.

• Post GFC of course we are much more cogniscent of these issues. The challenge is to formally embed them into our portfolio decisions.

Motivation

• Challenges to the “traditional” mean-variance approach for describing downside risk:

I. Asset returns are clearly fat tailed: so-called “extreme” events are much more statistically likely than what would occur assuming returns are from a normal distribution.

II. Return correlations are shock specific: using historic average correlations may overstate portfolio diversification benefits in times of stress.

III. Historical risk and return patterns may not be a good guide for the future.

Accounting for fat tails

1. Structural approach: returns are modeled as a function of underlying macroeconomic (and possibly other) drivers. Fat tails in history or simulation are largely seen as the outcome of extreme events (scenarios) occurring.

This was the approach taken by the NZSF for its recent Reference Portfolio Review.

2. Statistical approach: as in traditional approach returns are modeled using historical data, but methods try to account for fat-tails and differences in co-movement in times of historical “stress”.

This is the approach taken by State Street Associates in application to the NZSF’s Reference Portfolio

• We see the two approaches as complementary…

Accounting for fat tailsStructural approaches Statistical approaches

Strengths Weaknesses Strengths Weaknesses

• Aids understanding of underlying economic drivers of risk and returns. Return outcomes are shock specific and conditional on modeled linkages.

• Relatively complicated to build and estimate models - especially at higher frequencies (monthly or greater)

• Relatively easy to estimate and ‘close’ to the historical data – less need for judgmental input and identification of what constitutes an “extreme event”.

• Does not unpick sources of historical extreme events and generally ‘lumps’ such events together (i.e. two state view of the world – normal or “extreme”.)

• Useful tool for “what if” scenario analysis and consideration of portfolio protection strategies to such scenarios

• Heavy requirement for judgmental and /or theoretical inputs given weak empirical linkages (identification problems).

• Can estimate at higher frequencies - enables examination of “within horizon” risk

• More difficult to embed views on how future may differ from past.

• Can embed views of how “shocks” and macro-financial linkages (shock propagation) may differ going forward from the past .

• Not all extreme market movements are result of well-defined shocks (e.g. 1987 “flash-crash”, accounting scandals)

• Relatively straight-forward extension of traditional asset allocation and VaR problems

• Can calibrate model to match important non-normal features of the data such as negative skew ,kurtosis and mean reversion

• Can incorporate important non-normal features of the data such as negative skew, kurtosis and mean reversion

Application: NZSF Reference PortfolioThe Idea

Slide 7

The reference portfolio is an equilibrium concept:

based on assumptions of what the long-term value of the various asset classes should be

disregards what is actually happening to those values in any given market conditions

responses to these valuation changes are part of the Fund’s value-adding activities

Expectedexcess return

Reference PortfolioReference Portfolio

Value Adding Activities

Value Adding Activities

11

22

Expected risk

Application: NZSF Reference PortfolioComposition

• Delivery of the Reference Portfolio• Low-cost, passive portfolio which can achieve Fund objective• Appropriate degree of risk for long-term investor (80:20)• Smaller over-weight allocation to NZ equities and global listed property• No allocation to commodities or to foreign currency

• Both blueprint and benchmark• Public assessment of whether we are adding value with active investment

Application: NZSF Reference PortfolioNZSF structural approach to modeling returns

• Simulation model developed for the NZSF’s 2010 Reference Portfolio Review that incorporated: macro-financial linkages, extreme shocks and mean reversion in risk-premia.

• Extreme shocks included: (i) a global negative supply shock ; (ii) a global financial crisis and (iii) a NZ specific shock.

Correlations under these shocks change markedly relative to average seen under normally distributed returns (increase between growth assets).

Shocks resulted in negative skew and kurtosis in returns close to observed historical data

• Simulation results presented to the Board of the NZSF as input into the risk profile decision for the Reference Portfolio.

.

Application: NZSF Reference PortfolioNZSF structural approach to modeling returns

• For differing growth-income allocations distributions (1st to 99th percentile outcomes) for various performance metrics over 1 to 30-year horizons were presented, such as:

o Nominal and real returnso Probability returns exceeded thresholds (NZ T-Bills and inflation)o Probability returns fell short of thresholdso NZ dollar value-added relative to NZ T-Bills (metric shown in this

presentation over page, see annex for simple graphical representation)

•Various sensitivities examined, including changing: equilbrium risk premia assumptions, degree of mean reversion, FX hedging, extreme shocks (fat tails), and capital contributions.

• Key trade-off elicited: tolerance for short-term losses vs. longer run gains as growth allocation increased. Incorporation of extreme shocks (fat-tails) makes the choice tougher…

Application: NZSF Reference PortfolioNZSF structural approach to modeling returns

Application: NZSF Reference PortfolioNZSF structural approach to modeling returns

Application: NZSF Reference PortfolioState Street Associates statistical approach to modeling returns

• Monthly historical returns for assets comprising the Reference Portfolio decomposed into two regimes: normal and “turbulent” periods. Historic data does not include the GFC period forward.

• A multivariate return outliers technique is used to estimate turbulent periods. In these periods the cross-section of returns is unusual from a correlation or returns perspective (see Annex for graphical representation).

• Over the turbulent months correlations between growth assets and standard deviations of returns are generally higher than non-turbulent periods (see Annex).

Application: NZSF Reference PortfolioState Street Associates statistical approach to modeling returns

• Risk metrics are calculated given: (i) The conventional mean-variance approach(ii) The variance-covariance matrix of the turbulent months (20% and

30% thresholds are examined).

• Key finding is that the conventional approach underestimates the “true” downside loss exposure, as proxied by the GFC period.

•Tail outcomes using the turbulent months are more consistent with losses the Reference Portfolio would have experienced in the GFC.

Application: NZSF Reference PortfolioState Street Associates statistical approach to modeling returns

Risk metric What does it measure? Inputs & methodology

Conventional value at risk(5-year, 95%)

The most that an investor can expect to lose at the end of a 5-year period with 95% confidence. Losses should exceed this threshold one out of twenty 5-year periods (5% of the time).

•Long-term average standard deviations•Long-term average correlations•Ignores interim losses

Within-horizon, turbulent value at risk(5-year, 95%)

The most that an investor can expect to lose at any time throughout a 5-year turbulent period with 95% confidence. Losses should exceed this threshold one out of twenty 5-year periods.

•Standard deviations during the 20% most turbulent months•Correlations during the 20% most turbulent months•Models interim losses

Conditional within-horizon, turbulent value at risk(5-year, 95%)

The amount than an investor should expect to lose when value at risk is breached at any time throughout a 5-year turbulent period.

•Same as above, and…•Measures expected loss once VaR is breached

Application: NZSF Reference PortfolioState Street Associates statistical approach to modeling returns

Staasdasdasd

Value-at-risk estimates and hypothetical Reference Portfolio loss during the crisis (5-year 95% confidence interval)

Source: State Street Associates

Managing tail risk at the NZSF

• NZSF Board and stakeholders recognise that large losses are possible with risk profile choice – no pressure to change this post-GFC

• We have changed the way we measure and manage Fund liquidity to better prepare for extreme events.

• Active part of current research is examining the portfolio’s exposure to well-defined extreme downside risks and approaches to mitigate these e.g.:

o via portfolio ‘tilts’ to assets less prone to risks o and/or via implementing tail-risk option protection strategies

Annex

NZSFs value-adding strategies anchored to beliefs

Capture Active ReturnsStrategic

TiltingPortfolio

Completion

Reference Portfolio

Govern-ance

Policies and

procedures

Value Adding ActivitiesActual

Portfolio=+

Public mkts active

TiltingPrivate Equity

PropertyTimber

Infra-structure

NZ Direct Portfolio completion

Non market

cap

2. Asset allocation

is key.

3. A long-term horizon investor can outperform.

5. True manager skill is rare.

6. Some strategies are conducive to the generation of excess returns.

7. Identifying the life-cycle of an investment is important.

8. Responsible asset owner has concern for ESG

issues.

4. Returns can mean revert.

1. Good governance adds

value.

9. Improving ESG can improve a company's financial performance.

10. Managing fees and costs

can prevent unnecessary

cost.

BELIEFS

STRATEGIESOther

NZSF performance against initial expectations

Returns (post fees)

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1.3

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Cumulative Fund Return

NZSF Actual (Net of Fees) NZSF Initial Expectation NZ T-Bills NZ T-Bills +2.5% Reference Portfolio

Initial Lower Expectation (95% Confidence Interval)

Initial Upper Expectation (95%

Confidence Interval)

09/10 SOI Median Exp.

09/10 SOI Upper Exp.

To 28 February 2011

09/10 SOI Lower Exp.

Moments of asset class returns Structural approach

Global Equities

New Zealand Equities Property

FixedInterest

Normal shocks

Mean (long-run) 9.5% 8.5% 8.6% 6.6%

Std deviation (single year) 15% 16% 15% 4.0%

Skew (single year) 0.0 0.0 0.0 0.0

Kurtosis (single year) 3.0 3.0 3.0 3.0

Normal plus extreme shocks (base case model for Reference Portfolio Review)

Mean 9.1% 8.4% 8.6% 6.7%

Std deviation (single year) 16% 18% 16% 5.0%

Skew (single year) -0.5 -0.3 -0.2 -0.5

Kurtosis (single year) 4.3 3.6 3.4 5.9

Measuring returns Structural approach

Moments of asset class returns Statistical approach

Source: State Street Global Markets

Correlations of asset class returns Statistical approach

Source: State Street Global Markets

Pre-crisis correlations for full sample (left) and turbulent sample (right)

Standard deviation of asset class returnsStatistical approach to modeling returns

Staasdasdasd

Standard deviation of returns estimated on pre-crisis data (Jan 91 to Aug 08?)

Source: State Street Global Markets