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

1. Is the Efficient Frontier Efficient?CAS 2001 Annual MeetingMarriott Marquis, Atlanta, GA, Nov 11-14, 2001 by William C. Scheel, William J. Blatcher, Gerald S. Kirschner, John J. Denman

2. An Apologue • My friend, Ralph • “There’s more than one EF?” • Will the real variance/covariance matrix please standup?

3. What We’ll Do • Discuss sampling error in EF and efficient surfaces. Overview of results • Describe data used • Review efficient frontiers • Look at use of optimization in DFA • Look at how EF is used in practice • Examine performance of efficient and inefficient portfolios • Open discussion

4. Questions We Might Like to Consider • What suggestions can you make to DFA modelers about the use of EFs? • Is the forecast performance of EF satisfactory? • Should all DFA applications use risk-return optimization? • Portfolios have to be constructed. What do you suggest be used, if not EFs?

5. Efficient Surface and Sampling Error

6. Our Results in Risk-Return Space • Dissimilar profiles • Mixed performance results Can’t Get Here Return • Off-frontier portfolios can perform well. • Mixed performance results. • Similar profiles • Tight surface • Better forecast period performance Risk

7. 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

8. 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 30 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

9. Efficient Frontier

10. Review of Efficient Frontier • EF is a curve in risk-return space. • A point on the curve, (risk, return), is one where the portfolio has minimum risk for a given level of return, or conversely, maximum return for a given level of risk. • There are constraints on the portfolio such as (1) budget constraint and (2) no short sales for any component.

11. Review of Efficient Frontier Various methods of tracing the EF: • Markowitz Critical Line Method • Quadratic Programming Methods (methods of Wolfe and Beale) • Non-Linear Methods • All optimizations done using FrontLine Premium Solver Plus V3.5 (frontsys.com) and Microsoft Excel. In excess of 100,000 optimizations done for study.

12. Bootstrapped Efficient Frontiers

13. Efficient Portfolios Composition

14. Bootstrapped Portfolios Composition

15. The Efficient Surface

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

17. Optimal Strategies in DFA • Comparison of metrics for alternative strategies (stochastic dominance identified through enumeration and often represented as floating bar charts) • Allocation of assets as a constrained optimization

18. Enumeration of Dominance 3 2 1 Return Dispersion Strategic Option

19. Covariance Estimation

20. Computer Results • Animations of historical and bootstrapped segments • Implications of “avalanche” charts

21. Performance Failure within CAPM • Capital asset pricing model predicts risk-free rates that do not measure up in practice. • Beta is unstable and its value changes over time. • Estimated betas are unreliable. • Betas differ according to the market proxy they are measured against. • Average monthly return for low and high betas differs from predictions over a wide historical span.

22. Comparison of On/Off Frontier Information Ratio Performance

23. Comparison of On/Off Frontier Geometric Return Performance

24. 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

25. Related Reference • Richard O. Michaud, Efficient Asset Management, 1998, Harvard Business School Press. “…optimized portfolios are ‘error maximized’ and often have little, if any, reliable investment value. Indeed, an equally weighted portfolio may often be substantially closer to true MV optimality than an optimized portfolio”

26. Questions for Audience Discussion • What suggestions can you make to DFA modelers about the use of EFs? • Is the forecast performance of EF satisfactory? • Should all DFA applications use risk-return optimization? • Portfolios have to be constructed. What do you suggest be used, if not EFs?