by William C. Scheel, William J. Blatcher, Gerald S. Kirschner, John J. Denman

1. Using the Efficient Frontier in DFA2000 CAS Dynamic Financial Analysis SeminarNew 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. Class Code Source Start Date EAFEU 1/1970 INTLHDG 1/1970 S&P5 1/1970 International Equities USTB 1/1970 RMID 1/1982 MSCI EAFE Index HIYLD 1/1986 International Fixed Income CONV 1/1982 LBCORP 1/1973 JP Morgan Non-US Traded Index LBGOVT 1/1973 LBMBS 1/1986 Large Cap Domestic Equities S&P 500 Index Cash 90 Day US Treasury Bill Mid Cap Domestic Equities S&P Mid Cap 400 Index High Yield CSFB High Yield Bond Index Convertible Securities CSFB Convertible Index Corporate Bonds Lehman Brothers Corporate Bond Index Government Bonds Lehman Brothers Government Bond Index Mortgage Backed Securities Lehman Brothers Mortgage Backed Securities Index Data Used in the Study

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 • Generate an exogenous economic scenario • Generate a (paired) endogenous company scenario • Repeat (1) and (2) to get many pairs • Let Optimizer suggest an asset portfolio at t0. Use it for each pair. Calculate optimizer goal metric at tn. Give optimizer distributional features of metric.

12. Covariance.DFA • Covar stationary over time. Optimal portfolio determined at t0 based on history. • Generate multivariate returns for t. • DFA rebalancing strategy applied at t based on t0 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