- 60/40 equity/bond mix, 59
-
- Absolute momentum, 71
- Alternative risk premium (ARP), 68–72
- canonical forms, 68–70
- concave/convex ARP, payoffs, 69f
- distributions, 72
- moment contributions, 75f
- common types, 70f
- ubiquity, 70–71
- Approximation error
- Arbitrage pricing theory (APT), 81
- Asset allocation
- error bars, decrease, 97
- modern definition, 30–31
- sensitivity, 105–109
- Asset classes
- benchmarks, 73
- characteristics, 57
- defined 73–77
- KS test results, 89–90
- creation methodology, 73f
- paradigm, 66–77
- taxonomy, 74f
- Asset portfolio
- EU concept, extension,
- expected utility, –7
- Assets
- allocation, definition, 30–31
- higher moments, existence, 10
- comovement, 56, 63
- diversification, 48–49
- selection, 55–57
- skew/kurtosis, 11f
-
- Balance sheet model, 48f
- Basis risk, absence, 57
- Behavioral biases, moderation, 45–46
- accommodation, contrast, 46f
- embodied in utility function, 18–20
- Behavioral parameters, 18–20, 45
- Bernoulli, Daniel,
- Black-Litterman model (shrinkage estimator), 26, 30
- Bond prices
- interest rate sensitivity,
- Taylor expansion,
- Bootstrap
- definition, 83
- forecasting standard errors, 83–89
- asset allocation sensitivity, 106–109
- Break-even effect, 38
- Bretton Woods, cessation, 86
- Brownian motion assumptions, 68
-
- Capital Asset Pricing Model (CAPM), 10, 71, 81
- higher moment CAPM, empirical work, 12
- Capital gains taxes, 93
- forecasting adjustments, 94
- Capital market assumptions, 79
- Carry strategies, rate spread capture, 71
- Center for Research in Security Prices (CRSP), 60–61, 83, 99, 109
- Central Limit Theorem,
- Client
- benefit, 57
- irrational preference, 41
- portfolios, building, 13
- risk parameters, three-dimensional space, 99–100
- risk preferences, 30
- utility function
- shape,
- definition, 20
- uniqueness/complexity, 15
- Client risk profile, 33
- goals, incorporation, 43–54
- preferences, measurement, 34–43
- Cokurtosis, 29, 58
- Co-moments
- forecasting, 80
- standard errors, 83
- Comovements, 29, 56. See also Asset
- Concave/convex ARP, payoffs, 69f
- Concave/convex strategy, visual representation, 68–69
- Consumption assumptions, flexibility, 52
- Coskewness, 29, 58
- Covariance, 29, 58, 63
- Credit-dominated high-yield bonds, 66
- Cross-asset portfolio moment contributions, impact, 55
- Cross-sectional momentum, 72
-
- Decision variable, 22
- Decision weights, 19
- Discretionary wealth, 33, 47–51
- Dispersion, avoidance, 12
- Distinct assets, investment,
- Diversifying assets, 58–59
- Drawdowns, avoidance, 12
- Due diligence tools, 93
- Duration-dominated Treasuries, 66
-
- Earnings assumptions, flexibility, 52
- Emotional biases, 46
- Equity premium puzzle, explanation, 38
- Equity risk premium, 28
- Equity value strategies, 61
- Error bars, 86, 97
- forecasting
- confidence levels, 89
- improvement, 88
- post-winsorization, 88
- symmetry, 84–85
- Error sensitivity problem, addressing, 29–30
- Estimation error, , 23–30, 83–89
- effects, minimization, 30
- handling, 86–87
- impact, 14
- minimization, 24–28, 86–87
- sample size, contrast, 27f
- sensitivity, reduction, 28–30
- Estimators, distribution assumption, 25–26
- Excess kurtosis, 12
- Expected kurtosis. See Portfolio
- Expected returns, expected utility (contrast), 3f
- Expected utility (EU), ,
- concept, extension,
- next period wealth function,
- problem, distribution, 26
- returns-based EU maximization, 21–23
-
- Fallacy of large numbers, 35
- Fama-French (F-F) factors
- definitions, 75
- long-only (LO) ARP, 74
- robustness factor (F-F RMW), 11
- value factor (F-F HML), 11, 76
- Fat tails, 10
- Financial goals, 14, 43–54, 97
- Financial markets, liquidity (improvement), 86
- Forecasting horizon, 80–81
- Forecasts
- adjustment, 91–96
- allocation sensitivity, 23f
- modification, 80
- French, Kenneth, 83, 93, 109
- Future assets, present value, 48
-
- Gain domain, 41–42
- Gambling phrasing, 35
- Generalized risk aversion, 14, 105, 107–108
- Geographic risk premium (GRP), 67–72, 89–90
- Glidepaths, SLR (comparison), 52–54
- Global cap-weighted benchmark, 26
- Globalization, 86
- Global market portfolio, reverse optimization, 81
- Goals, incorporation into asset allocation, 43–54
- Great Recession, 46–47
- principal/agent responses, 17
-
- Heuristic models, consideration (absence), 30
- Higher moment
- impact on asset allocation, 101
- motivation, –13
- preferences, 12–13
- High kurtosis distributions, fat tails, 10
- High minus low (HML) factor, 74
- High-yield bonds, 65
- Historical data, usage, 25, 27–28
- Historical return distributions, 79
- history-based forecast, usage, 92
- modification, 92f
- winsorization, 87f
- usage, forecast (example), 81–91
- Home bias, avoidance, 68
- House money effect, 38
- Human capital, inclusion/correlation, 53
-
- Incentive effects, 36
- Interest rates
- bond price sensitivity,
- regime shifts, 90f, 91–82
- Intermediate-term investment grade (IG) bonds, 65
- Intermediate-term Treasuries, 65
- Internal homogeneity, 63
- Investment, risk-free rate, 49
- Irrational risk preferences, 14–15
-
- Jarque-Bera test, 10
- Joint distribution forecasts, 87
- Joint return distribution, 22
- estimate, creation, 28–29
-
- Kinked utility, 58–59
- Kolmogorov-Smirnov (KS) test, 89–90
- Kurtosis
- contribution, 75–76
- decrease, 101
- distribution, 10
- effects, 9f
- excess, 12
- expected kurtosis,
- negative kurtosis, 21
- symmetrical effect, –10
-
- Large numbers, fallacy, 35
- Least squares, optimization, 64
- Liabilities, minimization, 49
- Linear comovements, 29
- Liquidity, improvement, 86
- Living risk, standard, 33
- Long-only (LO) ARP investment, 75
- Long-term (LT) Treasuries
- addition, 63
- impact, calculation, 59–62
- Long-term (LT) wealth optimization, 45
- Loss-averse portfolios, sub-optimal nature, 52
- Loss aversion, 39–41, 99
- absence, 34
- diagnosis, 38
- gambles, 43
- mapping, 41
- PT feature, 18, 20
- questionnaire, 40f
- score measurement, 39–40
- Loss domain, 41–42
- Loss, potential,
- Lottery-style questionnaires, usage, 33–34
- loss aversion, 39–41
- question sizing, 43
- reflection, 41–43
- risk aversion, 34–39
- Low-volatility bets, 71
-
- Management fees, deduction, 92–93
- Manager alpha, 93
- Market anomaly, template, 69–70
- Market portfolio, implied returns, 26
- Mean estimates, distribution, 84
- Mean return, secular shifts (effect), 91
- Mean-semivariance framework
- comparison, 102f
- mean-variance framework, comparison, 104f
- Mean-semivariance portfolio, deviation, 102
- Mean standard error, 88
- Mean-variance (M-V)
- asset allocation, 80
- dominance, 17
- efficient frontier, 14
- framework,
- comparison, 102f
- mean-semivariance framework, comparison, 104f
- Meucci, Attilio, 27
- Mimicking portfolio tracking error (MPTE), 76
- decision, 101–102
- definition/equation, 65
- example (fixed income), 65f
- geographies, 68, 73
- low level, 98
- Modernized preference motivation, 13–15
- Modern portfolio theory (MPT)
- approximation, –7
- formulation, 103
- issues, 13–14
- solution, 17
- transition,
- usage, decision, 103–105
- Moment contributions, 57–63
- calculation, 59–62
- consideration, 73–74
- definition/equation, 60
- Moments
- deployment, 64
- estimates, standard error, 87f
- estimation, 88
- error bars, confidence levels, 89
- forecasting, 80
- standard errors, 87–88
- Momentum
- absolute momentum, 71
- cross-sectional momentum, 72
- time-series momentum, 71
- Monte Carlo simulations, deployment, 51–52
- Multi-dimensional questionnaires, value, 37
- Multi-period problem, 33
-
- National Institute of Standards and Technology (NIST) atomic clock, validity test, 37–38
- Negative outcome avoidance,
- Negative skew, effect, –9
- Non-normal assets, 101–102
- Non-normal distribution, estimate, 88
- Non-normality
- confidence, 88
- Jarque-Bera test, 10
- Non-parametric estimation, 25
- Normal distribution, skew/kurtosis effects, 9f
- Null estimate, 86
-
- Objective risk, 45, 50
- Opportunistic forecasting horizon, 80–81
- Optimization, 69. See also Portfolio
- framework, 22–23
- results, 98–103
- sensitivity, 56
- Optimizers
- asset allocation, 23–24
- input, 29
- optimizer-recommended portfolios, accuracy, 83
- running, 80
- Out-of-sample forecast accuracy, 86
-
- Payoffs
- Performance assets, 58–59
- Personality discovery process, 105
- Pompian, Michael, 45
- Portfolio
- building, hyper-fiduciary mission, 44–45
- cross-asset portfolio moment contributions, impact, 55
- diversification, 59
- expected kurtosis,
- expected monthly return, 62–63
- expected skew, –7
- expected utility, –7
- expected volatility,
- goals, 45
- loss-averse portfolios, sub-optimal nature, 52
- mimicking, 55, 63–66
- optimization, 97
- portfolio-level higher moments, 10
- return distributions,
- variations, 100
- volatility, 58–59
- Positive convexity, 72
- Positively skewed distributions, shaping, 10–11
- Positive payoff outcome, –4
- Positive premia, 72
- Positive skew, 21, 72
- Post-dividend tax shifts, 94
- Post-tax adjustments, 93–96
- Power utility, 58–59
- function, curvature (determination), 34–35
- plotting, 16
- Preference moderation, SLR (usage), 43–48, 50f
- Present value (PV), 48
- Pre-tax adjustments, 91–93
- Pre-tax shifts, 94
- Prospect theory (PT), 18, 47
-
- Qualitative questionnaires, value, 37
- Questionnaire
- reliability, 42
- validity, 37–38, 42
-
- Rate spread capture, 71
- Real estate, example, –4
- Reflection (PT feature), 18, 41–43
- Regression, coefficients, 64
- Relative momentum, 71
- Reliability, questionnaire, 42
- Retirement, income level reduction, 49
- Return distribution, 29
- characterization,
- forecast, 92
- non-parametric estimation, viewpoint, 27
- scaling process, 94
- shifting/scaling, calculation steps, 95, 95f
- Returns-based asset allocation framework, 79
- Returns-based EU maximization, 21–23
- Returns-based framework, , 88–89
- Returns-based optimization, 22
- requirement for full utility function, 31
- Reverse optimization, global market portfolio, 81
- Risk
- capacity, 45
- factor model, 62
- parity, error bars, 107–108
- sharing, 94
- tolerance, self-assessment, 37
- Risk aversion, 14, 16, 20, 99
- deployment, avoidance, 104
- generalized, 14, 105, 107–108
- mapping, 36f, 40
- non-linear representation, 35–36
- parameter, 48
- preferences, measurement, 34–39
- questionnaire, 35f
- questions, dollar amount, 39
- SLR-based objective risk aversion, 50
- time-varying risk aversion, usage, 38
- Risk preferences
- mathematicaly defined, 15–21
- measured, 34–43
- Risk premia, 57
- alternative risk premium (ARP), 68–69
- definition, 66–67
- geographic risk premium (GRP), 67–68
- justification, 71–72
- review, 11–12, 67–72
- traditional risk premium (TRP), 67–72
- Robust minus weak (RMW), 74, 76
-
- Sample size, 83–89
- estimation error, contrast, 27f
- function, 108f
- Samuelson, Paul, 35
- Savings, increase, 49
- Second derivative, measure, 14
- Second order approximation,
- Self-control bias, assumption, 47
- Sharpe ratio, 68, 70
- Shrinkage, 81
- Single-period expected utility problem, focus, 44
- Single-period lifecycle framework, selection, 54
- Single-period problem, 33
- Skew
- contributions, 62
- effects, 9f
- increase, 101
- Skewness risk premium, proxy, 74
- S-shaped function, curvature (setting), 41–42
- S-shaped utility, construction, 19–20
- Stable, term (usage), 82
- Standard error, concept, 80
- Standard of living risk (SLR)
- basis, 105
- definition, purpose, 51
- equation, 49
- glidepaths, comparison, 52–54
- level, selection, 51
- measurement, 47–48
- portfolio goal, 45
- SLR-based objective risk aversion, 50
- SLR-mapped loss aversion, 51
- usage, 43–48, 50
- Standard & Poor's 500 (S&P 500) return, 25
- Stationarity, 89–91
- Stationary returns (estimates deployment), out-of-sample accuracy (goal), 86
- Stochastic processes, 82
- St. Petersburg paradox,
- Structured models, avoidance, 81
- Subjective risk, 36, 45
- Survey of Consumer Finance (SCF) risk assessment, 37
-
- Tactical forecasting horizon, 80–81
- Test-retest reliability procedure, 42–43
- Three-dimensional risk preference utility function, 20–21
- deployed, 98–103
- importance, 97
- moderation, 103–05
- moment sensitivity, increase, 102
- second order approximation, equation, 103
- Timeframe, question, 80–81
- Time-series momentum, 71
- Time-varying risk aversion, usage, 38
- Tracking error, 65–66
- Traditional risk premium (TRP), 67–72
- asset class, inclusion, 77
- Treasuries
- constant maturity indices, 11
- grouping, 63
- Trend-following momentum, 72
- Trend-following strategy, 69–70
- True distribution, 24
- non-parametric estimation, 25
-
- Uncertainty, choice under, 3f
- Unconstrained regression model, replication (shift), 64
- US equities
- average monthly return, bootstrap estimates, 84f
- mean estimate, error, 86
- moment estimates, standard error, 85f, 87f
- monthly returns, 83–84
- US large cap equities, 23–24
- US small cap equities, 23–24
- Utility
- benefit, 56–57
- contribution, 62–63
- higher order expansion, equation, –6
- maximization,
- optimization, 69
- outcomes, probabilities, –5
- preferences, moderation, 50
- utility-maximized portfolio, 107–108
- Utility function, 15–21
- graphical representation, 16f
- maximization,
- returns-based optimization, requirement, 31
- ordinality,
- parameters, 33
- preference,
- results, 97
- series approximation, expected value solution,
-
- Validity, questionnaire, 37–38, 42
- Volatility, 86
- aversion, 14
- error bars, 107–108
- estimate, accuracy, 88
- shorting, 71
-
- Willingness-to-accept (WTA) test, 47
- Willingness-to-purchase (WTP) test, 47
- Winsorized changes, 90–91
- Winsorized commodities data, usage, 91
- Winsorizing, 87–88
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