Ex Post Relative Valuation Process Honing

1. Sector Optimization for Fixed-Income Portfolios Constrained By Value-at-Risk and Traditional Risk Measures Ron D’Vari, Juan C. Sosa, Kishore Yalamanchili State Street Research and Management 8TH ANNUAL IAFE CONFERENCE New York City October 14-15, 1999

2. Risk-constrained Optimization Facilitates Integration of Various Sector Views In Portfolio Construction • Research • Macro • Quantitative • Credit • Ex Ante • Expectations • Markets • Spreads • Risks • Portfolio Synthesis • Maximize Return • Minimize Risk • Ex Post • Monitoring • Attribution • Ex Post • Relative Valuation • Process Honing State Street Research & Management

3. Risk-Constrained Fixed-Income Sector Optimization Incorporating VaR and Traditional Risk Measures • Objectives • Risk Models • Risk-Constrained Optimization • Results • Conclusions State Street Research & Management

4. Objectives • Validated, Comprehensive, and Flexible Risk Model • Tactical Sector Allocation and Optimization Model: • Integration of tactical views of all research teams • Incorporation of risk explicitly in the investment process • Comprehensive Tool to Synthesize Fixed-Income Portfolios: • Maximize return under a set of probability weighted scenarios • Constrain risk • Traditional measures such as relative duration, sector weights, duration contribution • Stress-scenarios incorporating outliers and extreme observations • Flexible historical Value-At-Risk (VaR) allowing for non-normal, time-variant distributions with fat tails State Street Research & Management

6. Value-At-Risk Models • Objectives: Calculate distribution of returns and downside risk • Comprehensive - include interest rate risk, curve and spreads, for all major fixed-income sectors • Flexible - allow specification of time window, decay factor, and confidence level • Accurate - account for non-normally distributed asset classes such as MBS, high yield, and emerging market debt State Street Research & Management

7. Methodology • Domestic High Grade • Weekly derived spread data from individual securities in the Government/Corporate/Mortgage universe • Variance/Covariance • High Yield • Weekly aggregate spread data for subsectors • GARCH with shocks • Emerging Markets • Weekly aggregate spread data for subsectors • GARCH with shocks • Portfolio VaR and Relative VaR estimated via Structured Monte Carlo simulation with rolling correlation matrix State Street Research & Management

8. Methodology Work-in-Progress • Asset Backed Securities • Nondollar • Alternative specification for domestic assets (e.g. AR(1) to address mean reversion) State Street Research & Management

9. Why Not Variance-Covariance? • Model choice has significant effect on the estimation of risk-return trade-offs, hence the optimal choice of portfolios • Variance-Covariance VaR underestimates risk of non-normal assets (e.g. High Yield and EMBI) State Street Research & Management

10. Certain Fixed Income Sectors Exhibit Strongly Non-Normal Behavior State Street Research & Management

11. 4-week 95% VaR for Government/Corporate/Mortgage Plus Alternative Sector, August 27, 1999 State Street Research & Management

12. Ratio of 4-week Simulated Expected Return to 4-week 95% VaR of Gov./Corp./Mtg. Plus Alternative Sector, August 27, 1999 State Street Research & Management

13. 4-week 95% VaR for Government/Corporate/Mortgage Plus Alternative Sector, August 27, 1999 State Street Research & Management

14. Ratio of 4-week Simulated Expected Return to 4-week 95% VaR of Gov/Corp/Mtg Plus Alternative Sector, August 27, 1999 State Street Research & Management

15. Constrained Optimization Test Case • Return optimized over 6 month horizon • Unchanged term structure and spreads returning to their mean • Choice of Constraints • Traditional: Duration • Value at Risk (4 Week, 95 Percentile) • Five Stress Scenarios: • Unchanged term structure and spreads (UNCH) • Unchanged term structure and max spreads (MAXSPD) • Unchanged term structure and min spreads (MINSPD) • Max treasury yields and corresponding spreads (MAXTSY) • Min treasury yields and corresponding spreads (MINTSY) • Time Period: July 5, 1996 to Aug 27, 1999 State Street Research & Management

16. State Street Research & Management

17. Optimization Test Case- Initial Data State Street Research & Management

18. Optimization Test Case - Scenario Set State Street Research & Management

19. Optimization Test Case - Scenario Set State Street Research & Management

20. Under No Constraints Emerging Market is Asset of Choice State Street Research & Management

21. Duration Constraint Alone Is Inadequate State Street Research & Management

22. VaR Constraint Leads to Reasonable Allocation State Street Research & Management

23. Addition of Duration Constraint Modifies Solution Modestly State Street Research & Management

24. Duration and Scenario Constraints AloneCould Lead to Extreme Solutions State Street Research & Management

25. VaR and Stress-Scenario Constraints Combined Lead to Reasonable Overall Allocation State Street Research & Management

26. VaR and Stress-Scenario Constraints Combined Lead to Reasonable Overall Allocation State Street Research & Management

27. VaR-Constrained Efficient Frontier State Street Research & Management

28. VaR-Constrained Efficient Frontier State Street Research & Management

29. Conclusions • VaR Model Choice Is Significant in Assessing Risk-Reward in Portfolios • Risk-Constrained Optimization Facilitates Integration of Various Sector Views In Portfolio Construction • Experience Is Required to Select Suitable Model Parameters and Choice of Constraints State Street Research & Management