Table of Contents

1. Cover
2. Title Page
3. Foreword
4. Preface
5. SECTION One: Basics of Asset Allocation
   1. CHAPTER 1: What Is an Asset Class?
      1. STABLE AGGREGATION
      2. INVESTABLE
      3. INTERNALLY HOMOGENEOUS
      4. EXTERNALLY HETEROGENEOUS
      5. EXPECTED UTILITY
      6. SELECTION SKILL
      7. COST‐EFFECTIVE ACCESS
      8. POTENTIAL ASSET CLASSES
      9. REFERENCES
      10. NOTES
   2. CHAPTER 2: Fundamentals of Asset Allocation
      1. THE FOUNDATION: PORTFOLIO THEORY
      2. PRACTICAL IMPLEMENTATION
      3. REFERENCES
      4. NOTES
6. SECTION Two: Fallacies of Asset Allocation
   1. CHAPTER 3: The Importance of Asset Allocation
      1. FALLACY: ASSET ALLOCATION DETERMINES MORE THAN 90 PERCENT OF PERFORMANCE
      2. THE DETERMINANTS OF PORTFOLIO PERFORMANCE
      3. THE BEHAVIORAL BIAS OF POSITIVE ECONOMICS
      4. THE SAMUELSON DICTUM
      5. REFERENCES
      6. NOTES
   2. CHAPTER 4: Time Diversification
      1. FALLACY: TIME DIVERSIFIES RISK
      2. SAMUELSON'S BET
      3. TIME, VOLATILITY, AND PROBABILITY OF LOSS
      4. TIME AND EXPECTED UTILITY
      5. WITHIN‐HORIZON RISK
      6. A PREFERENCE‐FREE CONTRADICTION TO TIME DIVERSIFICATION
      7. THE BOTTOM LINE
      8. REFERENCES
      9. NOTES
   3. CHAPTER 5: Error Maximization
      1. FALLACY: OPTIMIZED PORTFOLIOS ARE HYPERSENSITIVE TO INPUT ERRORS
      2. THE INTUITIVE ARGUMENT
      3. THE EMPIRICAL ARGUMENT
      4. THE ANALYTICAL ARGUMENT
      5. THE BOTTOM LINE
      6. REFERENCES
      7. NOTES
   4. CHAPTER 6: Factors
      1. FALLACY: FACTORS OFFER SUPERIOR DIVERSIFICATION AND NOISE REDUCTION
      2. WHAT IS A FACTOR?
      3. EQUIVALENCE OF ASSET CLASS AND FACTOR DIVERSIFICATION
      4. NOISE REDUCTION
      5. WHERE DOES THIS LEAVE US?
      6. REFERENCES
      7. NOTES
   5. CHAPTER 7: 1/N
      1. FALLACY: EQUALLY WEIGHTED PORTFOLIOS ARE SUPERIOR TO OPTIMIZED PORTFOLIOS
      2. THE CASE FOR 1/N
      3. SETTING THE RECORD STRAIGHT
      4. EMPIRICAL EVIDENCE IN DEFENSE OF OPTIMIZATION
      5. PRACTICAL PROBLEMS WITH 1/N
      6. BROKEN CLOCK
      7. THE BOTTOM LINE
      8. REFERENCES
      9. NOTE
7. SECTION Three: Challenges to Asset Allocation
   1. CHAPTER 8: Necessary Conditions for Mean‐Variance Analysis
      1. THE CHALLENGE
      2. DEPARTURES FROM ELLIPTICAL DISTRIBUTIONS
      3. DEPARTURES FROM QUADRATIC UTILITY
      4. FULL‐SCALE OPTIMIZATION
      5. THE CURSE OF DIMENSIONALITY
      6. APPLYING FULL‐SCALE OPTIMIZATION
      7. SUMMARY
      8. REFERENCES
      9. NOTES
   2. CHAPTER 9: Constraints
      1. THE CHALLENGE
      2. WRONG AND ALONE
      3. MEAN‐VARIANCE‐TRACKING ERROR OPTIMIZATION
      4. REFERENCES
      5. NOTE
   3. CHAPTER 10: Currency Risk
      1. THE CHALLENGE
      2. WHY HEDGE?
      3. WHY NOT HEDGE EVERYTHING?
      4. LINEAR HEDGING STRATEGIES
      5. NONLINEAR HEDGING STRATEGIES
      6. ECONOMIC INTUITION
      7. REFERENCES
      8. NOTES
   4. CHAPTER 11: Illiquidity
      1. THE CHALLENGE
      2. SHADOW ASSETS AND LIABILITIES
      3. EXPECTED RETURN AND RISK OF SHADOW ALLOCATIONS
      4. OTHER CONSIDERATIONS
      5. CASE STUDY
      6. THE BOTTOM LINE
      7. APPENDIX
      8. REFERENCES
      9. NOTES
   5. CHAPTER 12: Risk in the Real World
      1. THE CHALLENGE
      2. END‐OF‐HORIZON EXPOSURE TO LOSS
      3. WITHIN‐HORIZON EXPOSURE TO LOSS
      4. REGIMES
      5. THE BOTTOM LINE
      6. REFERENCES
      7. NOTES
   6. CHAPTER 13: Estimation Error
      1. THE CHALLENGE
      2. TRADITIONAL APPROACHES TO ESTIMATION ERROR
      3. STABILITY‐ADJUSTED OPTIMIZATION
      4. BUILDING A STABILITY‐ADJUSTED RETURN DISTRIBUTION
      5. DETERMINING THE OPTIMAL ALLOCATION
      6. EMPIRICAL ANALYSIS
      7. THE BOTTOM LINE
      8. REFERENCES
      9. NOTES
   7. CHAPTER 14: Leverage versus Concentration
      1. THE CHALLENGE
      2. LEVERAGE IN THEORY
      3. LEVERAGE IN PRACTICE
      4. THE BOTTOM LINE
      5. REFERENCES
      6. NOTES
   8. CHAPTER 15: Rebalancing
      1. THE CHALLENGE
      2. THE DYNAMIC PROGRAMMING SOLUTION
      3. THE MARKOWITZ–VAN DIJK HEURISTIC
      4. THE BOTTOM LINE
      5. REFERENCES
      6. NOTES
   9. CHAPTER 16: Regime Shifts
      1. THE CHALLENGE
      2. PREDICTABILITY OF RETURN AND RISK
      3. REGIME‐SENSITIVE ALLOCATION
      4. TACTICAL ASSET ALLOCATION
      5. THE BOTTOM LINE
      6. APPENDIX: BAUM‐WELCH ALGORITHM
      7. REFERENCES
      8. NOTES
8. SECTION Four: Addendum
   1. CHAPTER 17: Key Takeaways
   2. CHAPTER 18: Statistical and Theoretical Concepts
      1. DISCRETE AND CONTINUOUS RETURNS
      2. ARITHMETIC AND GEOMETRIC AVERAGE RETURNS
      3. STANDARD DEVIATION
      4. CORRELATION
      5. COVARIANCE
      6. COVARIANCE INVERTIBILITY
      7. MAXIMUM LIKELIHOOD ESTIMATION
      8. MAPPING HIGH‐FREQUENCY STATISTICS ONTO LOW‐FREQUENCY STATISTICS
      9. PORTFOLIOS
      10. PROBABILITY DISTRIBUTIONS
      11. THE CENTRAL LIMIT THEOREM
      12. THE NORMAL DISTRIBUTION
      13. HIGHER MOMENTS
      14. THE LOGNORMAL DISTRIBUTION
      15. ELLIPTICAL DISTRIBUTIONS
      16. PROBABILITY OF LOSS
      17. VALUE AT RISK
      18. UTILITY THEORY
      19. SAMPLE UTILITY FUNCTIONS
      20. ALTERNATIVE UTILITY FUNCTIONS
      21. EXPECTED UTILITY
      22. CERTAINTY EQUIVALENTS
      23. MEAN‐VARIANCE ANALYSIS FOR MORE THAN TWO ASSETS
      24. EQUIVALENCE OF MEAN‐VARIANCE ANALYSIS AND EXPECTED UTILITY MAXIMIZATION
      25. MONTE CARLO SIMULATION
      26. BOOTSTRAP SIMULATION
      27. REFERENCES
      28. NOTE
   3. CHAPTER 19: Glossary of Terms
9. Index
10. End User License Agreement

List of Tables

1. Chapter 02
   1. TABLE 2.1 Expected Returns
   2. TABLE 2.2 Standard Deviations and Correlations
   3. TABLE 2.3 Optimal Allocation to Stocks and Bonds
   4. TABLE 2.4 Conservative, Moderate, and Aggressive Efficient Portfolios
   5. TABLE 2.5 Exposure to Loss
   6. TABLE 2.6 Distribution of Wealth 15 Years Forward (as a multiple of initial investment)
2. Chapter 03
   1. TABLE 3.1 Imaginary Performance
   2. TABLE 3.2 Standard Deviation, Correlation, and Relative Volatility
3. Chapter 04
   1. TABLE 4.1 Time, Volatility, and Probability of Loss
   2. TABLE 4.2 Expected Wealth and Expected Utility
   3. TABLE 4.3 Probability of a Within‐Horizon 10 Percent Loss
4. Chapter 05
   1. TABLE 5.1 Country Expected Returns, Standard Deviations, and Correlations
   2. TABLE 5.2 Misestimated Country Expected Returns
   3. TABLE 5.3 Distortion in Optimal Country Weights
   4. TABLE 5.4 Exposure to Loss for Correct and Incorrect Country Weights
   5. TABLE 5.5 Asset Class Expected Returns, Standard Deviations, and Correlations
   6. TABLE 5.6 Misestimated Asset Class Expected Returns
   7. TABLE 5.7 Distortion in Optimal Asset Class Weights
   8. TABLE 5.8 Exposure to Loss for Correct and Incorrect Asset Class Weights
   9. TABLE 5.9 Sensitivity of Weights to Changes in Expected Return
   10. TABLE 5.10 Sensitivity of Portfolio Standard Deviation to Changes in Expected Return
5. Chapter 06
   1. TABLE 6.1 Principal Components
   2. TABLE 6.2 Instability of Industry, Size, Value, and Momentum Portfolios
6. Chapter 08
   1. TABLE 8.1 Skewness over Increasing Return Intervals
   2. TABLE 8.2 Excess Kurtosis over Increasing Return Intervals
   3. TABLE 8.3 Expected Utility for 75 Percent Stock Portfolio
   4. TABLE 8.4 Expected Utility for 45/55 Percent Stock/Bond Portfolio
   5. TABLE 8.5 The Curse of Dimensionality
   6. TABLE 8.6 Full‐Scale and Mean‐Variance Allocations and Characteristics
7. Chapter 09
   1. TABLE 9.1 Potential Absolute and Relative Performance Outcomes
8. Chapter 10
   1. TABLE 10.1 Linear Hedging Strategies and Their Constraints
   2. TABLE 10.2 Expected Returns, Standard Deviations, and Correlations for Assets and Currencies
   3. TABLE 10.3 Risk‐Minimizing Hedge Ratios (%)
   4. TABLE 10.4 Hedging Performance with Individual Quarterly Put Options (%)
   5. TABLE 10.5 Full‐Scale Optimal Hedging Results with Forwards and Options (%)
9. Chapter 11
   1. TABLE 11.1 Expected Returns, Standard Deviations, and Correlations (unadjusted)
   2. TABLE 11.2 Optimal Allocations Including and Excluding Real Estate (unadjusted)
   3. TABLE 11.3 Expected Returns, Standard Deviations, and Correlations (adjusted for performance fees and valuation smoothing)
   4. TABLE 11.4 Expected Return and Standard Deviation of Shadow Asset and Liability
   5. TABLE 11.5 Expected Returns, Standard Deviations, and Correlations (adjusted for performance fees and valuation smoothing) and Including Shadow Asset and Liability
   6. TABLE 11.6 Optimal Allocations Accounting for Performance Fees, Valuation Smoothing, and Liquidity (%)
10. Chapter 12
    1. TABLE 12.1 Conditional Annualized Returns to Risky Assets January 1976–December 2015
    2. TABLE 12.2 Value at Risk (1%)
    3. TABLE 12.3 Probability of 35.9% or Greater Loss
11. Chapter 13
    1. TABLE 13.1 Risk Instability across Asset Classes (in standardized units)
    2. TABLE 13.2 Full‐Scale Optimization
    3. TABLE 13.3 Mean‐Variance Approach to Stability Optimization
12. Chapter 14
    1. TABLE 14.1 Leverage versus Concentration in Theory
    2. TABLE 14.2 Leverage versus Concentration with Nonelliptical Returns and Kinked Utility
    3. TABLE 14.3 Asset Class Semi–Standard Deviations
    4. TABLE 14.4 Leverage versus Concentration with Estimation Error
    5. TABLE 14.5 Leverage versus Concentration with Borrowing Costs
    6. TABLE 14.6 Leverage versus Concentration with Kinked Utility, Nonellipticality, Estimation Error, and Higher Borrowing Costs
13. Chapter 15
    1. TABLE 15.1 Return Distribution and Expected Log‐Wealth Utility for a 60/40 Portfolio
    2. TABLE 15.2 Asset Class Transaction Costs
    3. TABLE 15.3 Performance of Rebalancing Strategies
14. Chapter 16
    1. TABLE 16.1 Risk Characteristics in Turbulent and Nonturbulent Regimes
    2. TABLE 16.2 Full‐Sample and Regime‐Conditioned Optimal Portfolios
    3. TABLE 16.3 Hidden Markov Model Fit and Conditional Asset Class Performance
    4. TABLE 16.4 Backtest Performance

List of Illustrations

1. Chapter 02
   1. FIGURE 2.1 Efficient Frontier
2. Chapter 03
   1. FIGURE 3.1 Regression of Portfolio Performance on Asset Class Performance
3. Chapter 04
   1. FIGURE 4.1 Log‐Wealth Utility Function
4. Chapter 06
   1. FIGURE 6.1 Asset Class and Principal Component Efficient Frontiers
5. Chapter 08
   1. FIGURE 8.1 Annual Skewness, Excess Kurtosis, and Statistical Significance Bands
   2. FIGURE 8.2 U.S. and Foreign Equity Returns (12‐Month Horizon)
   3. FIGURE 8.3 Kinked Utility Function
   4. FIGURE 8.4 S‐shaped Utility Function
   5. FIGURE 8.5 Expected Utility for Different Allocations to Stocks (5 percent increments)
6. Chapter 09
   1. FIGURE 9.1 Efficient Surface
   2. FIGURE 9.2 Iso‐Expected Return Curve
7. Chapter 10
   1. FIGURE 10.1 Minimum‐Variance Hedge Ratio
   2. FIGURE 10.2 Currency Exposure as a Percentage of Portfolio Value
   3. FIGURE 10.3 Impact of Hedging Strategies on Distribution of Portfolio Currency Returns (Quarterly)
8. Chapter 11
   1. FIGURE 11.1 Optimal Allocation to Real Estate with and without Adjustments
9. Chapter 12
   1. FIGURE 12.1 Scatter Plot of U.S. and Foreign Equities
10. Chapter 13
    1. FIGURE 13.1 Components of Estimation Error
    2. FIGURE 13.2 Monthly Returns of U.S. and Emerging Market Equities
    3. FIGURE 13.3 Five‐Year Returns of U.S. and Emerging Market Equities
    4. FIGURE 13.4 Constructing the Stability‐Adjusted Return Distribution
    5. FIGURE 13.5 Mixture of Two Normal Distributions
    6. FIGURE 13.6 Multivariate Mixture of Asset Classes with Unstable Correlation
    7. FIGURE 13.7 Stability Adjustment Improvement to Optimization That Ignores Errors (10% Worst Outcomes)
11. Chapter 14
    1. FIGURE 14.1 Efficient Frontier with Borrowing and Lending
    2. FIGURE 14.2 Outperformance of Leverage versus Concentration
12. Chapter 15
    1. FIGURE 15.1 Trading and Suboptimality Costs over Two Periods
    2. FIGURE 15.2 Performance of Rebalancing Strategies
    3. FIGURE 15.3 Performance of Rebalancing Strategies
13. Chapter 16
    1. FIGURE 16.1 Monthly Correlation of U.S. Equities and Treasury Bonds (Five‐Year Rolling Subsamples)
    2. FIGURE 16.2 Financial Turbulence
    3. FIGURE 16.3 Hidden Markov Model Regime Probabilities
    4. FIGURE 16.4 Hidden Markov Model Regime Probability Forecasts (Out of Sample)
    5. FIGURE 16.5 Cumulative Returns
14. Chapter 18
    1. FIGURE 18.1 Kinked Utility Function
    2. FIGURE 18.2 S‐Shaped Utility Function

Guide

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