IFSWF Meeting, Beijing May 10-13

1. Accounting for “fat tails” in portfolio risk management: NZSF case study IFSWF Meeting, Beijing May 10-13 Aaron Drew, Macro Strategist, NZSF William Kinlaw, Head of Portfolio and Risk Management Group, State Street Associates

2. Outline • Motivation: why should we account for “fat tails” in portfolio risk management? • Contrast two broad approaches for modeling fat tails: • Structural • Statistical • Applications of these approaches to the NZSF’s Reference Portfolio

3. 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.

4. Motivation • Challenges to the “traditional” mean-variance approach for describing downside risk: • 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. • Return correlations are shock specific: using historic average correlations may overstate portfolio diversification benefits in times of stress. • Historical risk and return patterns may not be a good guide for the future.

5. Accounting for fat tails • 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…

6. Accounting for fat tails

7. Application: NZSF Reference PortfolioThe Idea • 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 Expected excess return Value Adding Activities 2 Reference Portfolio 1 Expected risk

8. 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

9. 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. • .

10. 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: • Nominal and real returns • Probability returns exceeded thresholds (NZ T-Bills and inflation) • Probability returns fell short of thresholds • 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…

11. Application: NZSF Reference PortfolioNZSF structural approach to modeling returns

12. Application: NZSF Reference PortfolioNZSF structural approach to modeling returns

13. 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).

14. Application: NZSF Reference PortfolioState Street Associates statistical approach to modeling returns • Risk metrics are calculated given: • The conventional mean-variance approach • 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.

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

16. 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

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

18. Annex

19. NZSFs value-adding strategies anchored to beliefs Actual Portfolio Govern-ance Policies and procedures Value Adding Activities Reference Portfolio + = Portfolio Completion Capture Active Returns Strategic Tilting NZ Direct Private Equity Infra-structure Public mkts active Tilting Portfolio completion Timber Property Non market cap Other STRATEGIES 2. Asset allocation is key. 3. A long-term horizon investor can outperform. 1. Good governance adds value. 10. Managing fees and costs can prevent unnecessary cost. 4. Returns can mean revert. 8. Responsible asset owner has concern for ESG issues. 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. BELIEFS 9. Improving ESG can improve a company's financial performance.

20. NZSF performance against initial expectations Returns (post fees)

21. Moments of asset class returns Structural approach

22. Measuring returns Structural approach

23. Moments of asset class returns Statistical approach Source: State Street Global Markets

24. Correlations of asset class returns Statistical approach Pre-crisis correlations for full sample (left) and turbulent sample (right) Source: State Street Global Markets

25. 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