Internationalization 3.0 Beth Kirschner University of Michigan.
by William C. Scheel, William J. Blatcher, Gerald S. Kirschner, John J. Denman
description
Transcript of 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
An Apologue
• My friend, Ralph• “There’s more than one EF?”• Will the real variance/covariance matrix
please standup?
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
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?
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)
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
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
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
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(Re
turn
)
Historical
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.
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
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(Re
turn
)
Historical Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6
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
ght
EAFEU INTLUHD S&P5 USTB R_MID HIYLD CONV LBCORP LBGVT LBMBS
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
ght
EAFEU INTLUHD S&P5 USTB R_MID HIYLD CONV LBCORP LBGVT LBMBS
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)
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.
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
Enumeration of Dominance
1
3
2
Strategic Option
Ret
urn
Dis
pers
ion
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
Computer Results
• Animations of historical and bootstrapped segments
• Implications of “avalanche” charts
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.
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 1Multiplier 1.25Multiplier 1.5Multiplier 1.75Multiplier 2
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 1Multiplier 1.25Multiplier 1.5Multiplier 1.75Multiplier 2
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
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”
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?