1. Using the Efficient Frontier in DFA 2000 CAS Dynamic Financial Analysis Seminar New York Marriott Marquis, New York, NY, July 17-18, 2000 by William C. Scheel, William J. Blatcher, Gerald S. Kirschner, John J. Denman

2. What We’ll Do Review Efficient Frontiers Describe Data Used Look at Use of Optimization in DFA Discuss Sampling Error in EF and Efficient Surfaces Examine Performance of Efficient and Inefficient Portfolios Look at How EF is Used in Practice Open Discussion

3. Conclusions and Operational Implications The EF surface gets slipperier where you need it most…higher levels of risk/return. EFs for different historical segments are divergent and have inconsistent performance. Bootstrap samples show high degrees of potential sampling error Rational decision-making with Efs is problematic

4. Review of Efficient Frontier EF is a curve in risk-return space. It is traced with repeated use of quadratic or non-linear programming. A point on the curve, {risk,return} is one where the portfolio has minimum risk at the return. There are constraints on the portfolio such as no short sales for any component.

5. Efficient Frontier

6. EF Frontier Profile

7. Data Used in the Study ClassCodeSourceStart Date International Equities EAFEU MSCI EAFE Index 1/1970 International Fixed Income INTLHDG JP Morgan Non-US Traded Index 1/1970 Large Cap Domestic Equities S&P5 S&P 500 Index 1/1970 Cash USTB 90 Day US Treasury Bill 1/1970 Mid Cap Domestic Equities RMID S&P Mid Cap 400 Index 1/1982 High Yield HIYLD CSFB High Yield Bond Index 1/1986 Convertible Securities CONV CSFB Convertible Index 1/1982 Corporate Bonds LBCORP Lehman Brothers Corporate Bond Index 1/1973 Government Bonds LBGOVT Lehman Brothers Government Bond Index 1/1973 Mortgage Backed Securities LBMBS Lehman Brothers Mortgage Backed Securities Index 1/1986

8. The EF Surface

9. Does EF Have Sampling Error? Sampling in hybrid DFA models. Business scenario model fitted to history through calibration. Sampling in multivariate normal, covariance models. Covariance matrix estimated from history. One instance of history.

10. Optimization in DFA Comparison of metrics for alternative strategies (stochastic dominance identified through enumeration) Allocation of assets as a constrained optimization

11. Hybrid Optimization.DFA 1.Generate an exogenous economic scenario 2.Generate a (paired) endogenous company scenario 3.Repeat (1) and (2) to get many pairs 4.Let Optimizer suggest an asset portfolio at t 0. Use it for each pair. Calculate optimizer goal metric at t n. Give optimizer distributional features of metric.

12. Covariance.DFA Covar stationary over time. Optimal portfolio determined at t 0 based on history. Generate multivariate returns for t. DFA rebalancing strategy applied at t based on t 0 optimal allocation and other conditions prevailing at t, t -1, t -2,….

13. Is EF a Good Predictor of Performance? Revisit Animations Performance Measurement Off-frontier Performance

14. Usage of EF at Two Insurance Companies Liberty Mutual Aegis Insurance Services

15. Conclusions and Operational Implications The EF surface gets slipperier where you need it most…higher levels of risk/return. EFs for different historical segments are divergent and have inconsistent performance. Bootstrap samples show high degrees of potential sampling error Rational decision-making with Efs is problematic