Presented by: D Sykes Wilford SPS HOLDINGS Designed for AXA Belgium

1. Asset/Liability; The Evolution Goes On Presented by: D Sykes Wilford SPS HOLDINGS Designed for AXA Belgium SPS Holdings wsykes@laudisi.com

2. Asset/Liability; The Evolution Goes On MODERN PORTFOLIO THEORY The Risk of a portfolio can be lower than the risk of any of its components CONDITION: A sufficient number of weakly correlated assets in the portfolio SPS Holdings wsykes@laudisi.com

3. Asset/Liability; The Evolution Goes On Portfolio Risk 2 assets/equal weights case: Var (1/2A+1/2B)=1/4Var(A)+1/4Var(B)+2.1/4.Cov(A,B) where Cov(A,B)=Corr(A,B)ÖVar(A) ÖVar(B) or if Corr(A,B)<1, and Var(A)=Var(B) Var(1/2A+1/2B)<Var(A) and Var(1/2A+1/2B)<Var(B) Investing in both assets is less risky than investing in either one of them separately! SPS Holdings wsykes@laudisi.com

4. Asset/Liability; The Evolution Goes On The Theoretical Efficient Frontier Return ? Risk SPS Holdings wsykes@laudisi.com

5. Risk ý Locally Diversifiable ý Globally Diversifiable Non Diversifiable Risk Number of Assets Asset/Liability; The Evolution Goes On Modern Portfolio Theory SPS Holdings wsykes@laudisi.com

6. Asset/Liability; The Evolution Goes On SPS Holdings wsykes@laudisi.com

7. Asset/Liability; The Evolution Goes On SPS Holdings wsykes@laudisi.com

8. Asset/Liability; The Evolution Goes On SPS Holdings wsykes@laudisi.com

9. Asset/Liability; The Evolution Goes On Bankers Trust Company SPS Holdings wsykes@laudisi.com

10. Asset/Liability; The Evolution Goes On But What Does This Practically Mean? or A Step By Step Approach to Theoretical Correctness SPS Holdings wsykes@laudisi.com

11. Diversify Asset/Liability; The Evolution Goes On Back to Basics Bankers Trust Company SPS Holdings wsykes@laudisi.com

12. Diversify Diversify Diversify Asset/Liability; The Evolution Goes On Back to Basics SPS Holdings wsykes@laudisi.com

13. Diversify Diversify Diversify Asset/Liability; The Evolution Goes On Back to Basics Nobel Prize Nobel Prize Nobel Prize SPS Holdings wsykes@laudisi.com

14. Asset/Liability; The Evolution Goes On Back to Basics Portfolio Theory is about Diversification • Everywhere • All the time • In a friction free world SPS Holdings wsykes@laudisi.com

15. Asset/Liability; The Evolution Goes On Portfolio Theory Exists Because No One Is Prescient ! SPS Holdings wsykes@laudisi.com

16. Asset/Liability; The Evolution Goes On Remember No One Is Prescient • If so then you do not need a Portfolio • Since you are going to be wrong; how wrong? Big Wrong Little Wrong SPS Holdings wsykes@laudisi.com

17. Asset/Liability; The Evolution Goes On We need a guess about the future: A Forecast of Expected Returns E[R] SPS Holdings wsykes@laudisi.com

18. Asset/Liability; The Evolution Goes On Back to Basics s = Standard Deviation of E[R] r= Correlation of the errors in those expected returns SPS Holdings wsykes@laudisi.com

19. Asset/Liability; The Evolution Goes On Back to Basics sis NOT Actual Variance ris NOT Actual Correlation SPS Holdings wsykes@laudisi.com

20. Asset/Liability; The Evolution Goes On Back to Basics The r needed for portfolio allocation need not reflect what actually happens ---- Indeed it should not if our forecaster of E[R] is not perfect SPS Holdings wsykes@laudisi.com

21. Asset/Liability; The Evolution Goes On Being Theoretically Correct ! "No PC Allowed" Science is more important than what "sounds" right! SPS Holdings wsykes@laudisi.com

22. Asset/Liability; The Evolution Goes On Back to Basics - Rule 1 What Expected Return? Not Total Return but Excess Return E[R] = Total Return - Risk Free Rate SPS Holdings wsykes@laudisi.com

23. Asset/Liability; The Evolution Goes On Back to Basics - Rule 2 Thuss and rare relative to the expected Excess Return But s Total Return @s Excess Return SPS Holdings wsykes@laudisi.com

24. Asset/Liability; The Evolution Goes On Back to Basics - Examples Classic Example Total Return Risk Total Return Ratios Excess Returns Example Excess Return Risk Excess Return Ratios Equities 12 12 1 Equities 6 12 .5 Bonds 8 8 1 Bonds 2 8 .25 Cash 6 0 N/A Cash 0 0 N/A SPS Holdings wsykes@laudisi.com

25. Asset/Liability; The Evolution Goes On Back to Basics - Rule 2: An Example Currency of Denomination • Total Return Portfolio • Excess Return Portfolio SPS Holdings wsykes@laudisi.com

26. Asset/Liability; The Evolution Goes On Back to Basics - Rule 3 Optimization in Excess Return space • Excess Returns • E[R] • s of E[R's] • r of Errors in those E[R's] No Constraints SPS Holdings wsykes@laudisi.com

27. Cumulative Excess Return DSUR 0.60 0.50 0.40 0.30 DOLS 0.20 0.10 0.00 CASH -0.10 8612 8706 8712 8806 8812 8906 8912 9006 9012 9106 9112 9206 9212 9306 Asset/Liability; The Evolution Goes On DSUR and DOLS Portfolio Performance SPS Holdings wsykes@laudisi.com

28. Asset/Liability; The Evolution Goes On Back to Basics Consistency is the Key • E[R] • Variance of E[R] • Correlation of E[R] SPS Holdings wsykes@laudisi.com

29. Asset/Liability; The Evolution Goes On RULES: • Excess Return Space • s and r relate to the E[R's] • No Constraints SPS Holdings wsykes@laudisi.com