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

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

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Is the Efficient Frontier Efficient? CAS 2001 Annual Meeting Marriott Marquis, Atlanta, GA, Nov 11-14, 2001. by William C. Scheel, William J. Blatcher, Gerald S. Kirschner, John J. Denman. An Apologue. My friend, Ralph “There’s more than one EF?” - PowerPoint PPT Presentation

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Page 1: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

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

Page 2: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

An Apologue

• My friend, Ralph

• “There’s more than one EF?”

• Will the real variance/covariance matrix please standup?

Page 3: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

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

Page 4: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

Questions We Might Like to Consider

1. What suggestions can you make to DFA modelers about the use of EFs?

2. Is the forecast performance of EF satisfactory?

3. Should all DFA applications use risk-return optimization?

4. Portfolios have to be constructed. What do you suggest be used, if not EFs?

Page 5: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

Efficient Surface and Sampling Error

0.00

00

0.00

45

0.00

89

0.01

34

0.01

79

0.02

24

0.02

68

0.03

13

0.03

58

0.0025

0.008

0.01

00.1

0.2

0.3

0.4

Probability

Risk Return

Efficient Surface(based on historical segments)

Page 6: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

Our Results in Risk-Return Space

Can’t Get Here

1. Dissimilar profiles

2. Mixed performance results

1. Similar profiles

2. Tight surface

3. Better forecast period performance

1. Off-frontier portfolios can perform well.

2. Mixed performance results.

Ret

urn

Risk

Page 7: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

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

Page 8: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

Data Used in the StudyClass Code Source Start

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 30 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

Page 9: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

Efficient Frontier

Efficient FrontierBased on 1988-1992 Historical Period Monthly Returns

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

1.6%

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0%

SD(Return)

E(R

etu

rn)

Historical

Page 10: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

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.

Page 11: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

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.

Review of Efficient Frontier

Page 12: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

Bootstrapped Efficient Frontiers

Resampled Efficient FrontiersBased on 1988-1992 Historical Period Monthly Returns

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

1.6%

0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0%

SD(Return)

E(R

etu

rn)

Historical Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6

Page 13: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

Efficient Portfolios Composition

EF Portfolio Composition

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.14% 0.14% 0.15% 0.19% 0.29% 0.94% 0.94% 1.04% 1.09% 1.19% 1.19% 1.23% 1.78% 2.31% 2.73% 3.48% 4.43%

SD(Return)

Wei

gh

t

EAFEU INTLUHD S&P5 USTB R_MID HIYLD CONV LBCORP LBGVT LBMBS

Page 14: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

Bootstrapped Portfolios Composition

Sample 5 EF Composition

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.13% 0.13% 0.14% 0.14% 0.14% 0.15% 0.19% 0.29% 0.94% 0.94% 1.04% 1.09% 1.19% 1.19% 1.23% 1.78% 2.31% 2.73% 3.48%

SD(Return)

Wei

gh

t

EAFEU INTLUHD S&P5 USTB R_MID HIYLD CONV LBCORP LBGVT LBMBS

Page 15: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

The Efficient Surface

0.00

00

0.00

47

0.00

94

0.01

41

0.01

88

0.02

35

0.02

82

0.03

29

0.03

76

0.0025

0.008

0.01

0

0.5

1

Probability

Risk Return

Efficient Surface(based on bootstrap samples)

Page 16: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

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.

Page 17: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

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

Page 18: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

Enumeration of Dominance

1

3

2

Strategic Option

Ret

urn

Dis

pers

ion

Page 19: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

Covariance Estimation

Rolling Five Year Monthly Standard Deviations

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301

EAFEU INTLUHD LBAGG S&P5 USTB R_MID HIYLD CONV LBCORP LBGVT LBMBS

10/87 Enters 10/87 Exits 8/98 Enters

Page 20: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

Computer Results

• Animations of historical and bootstrapped segments

• Implications of “avalanche” charts

Page 21: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

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.

Page 22: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

Comparison of On/Off Frontier Information Ratio Performance

Performance

-.238

-.038

.162

.362

.562

.762

1 21 41 61 81

Performance Information RatioHistorical Period: January, 1988 - December, 1992

Forecast: January, 1993 - December, 1999Expected annualized return=.0825

Multiplier 1

Multiplier 1.25

Multiplier 1.5

Multiplier 1.75

Multiplier 2

Page 23: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

Comparison of On/Off Frontier Geometric Return Performance

Performance

.049

.054

.059

.064

.069

.074

.079

1 21 41 61 81

Geometric returnHistorical Period: January, 1988 - December, 1992

Forecast: January, 1993 - December, 1999Expected annualized return=.0825

Multiplier 1

Multiplier 1.25

Multiplier 1.5

Multiplier 1.75

Multiplier 2

Page 24: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

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

Page 25: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

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”

Page 26: by William C. Scheel, William J. Blatcher,  Gerald S. Kirschner, John J. Denman

Questions for Audience Discussion

1. What suggestions can you make to DFA modelers about the use of EFs?

2. Is the forecast performance of EF satisfactory?

3. Should all DFA applications use risk-return optimization?

4. Portfolios have to be constructed. What do you suggest be used, if not EFs?